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8.1 Heap
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
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<span class="md-ellipsis">
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5.1 Stack
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
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<span class="md-ellipsis">
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5.2 Queue
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<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
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<span class="md-ellipsis">
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5.3 Double-ended queue
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<span class="md-ellipsis">
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5.4 Summary
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</a>
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_hashing/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
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<span class="md-ellipsis">
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Chapter 6. Hash table
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</span>
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</a>
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<label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_8">
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<span class="md-nav__icon md-icon"></span>
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Chapter 6. Hash table
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
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<span class="md-ellipsis">
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6.1 Hash table
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</span>
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</a>
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<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
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<span class="md-ellipsis">
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6.2 Hash collision
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
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<span class="md-ellipsis">
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6.3 Hash algorithm
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<li class="md-nav__item">
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<a href="../../chapter_hashing/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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6.4 Summary
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</a>
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<a href="../../chapter_tree/" class="md-nav__link ">
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<span class="md-ellipsis">
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Chapter 7. Tree
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</span>
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</a>
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<label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_9">
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<span class="md-nav__icon md-icon"></span>
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Chapter 7. Tree
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.1 Binary tree
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</span>
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</a>
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<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
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<span class="md-ellipsis">
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7.2 Binary tree Traversal
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</span>
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</a>
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<a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.3 Array Representation of tree
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.4 Binary Search tree
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
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<span class="md-ellipsis">
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7.5 AVL tree *
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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7.6 Summary
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</span>
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</a>
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</li>
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</nav>
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<li class="md-nav__item md-nav__item--active md-nav__item--nested">
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<div class="md-nav__link md-nav__container">
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<a href="../" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
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<span class="md-ellipsis">
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Chapter 8. Heap
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</span>
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</a>
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<label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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</div>
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Chapter 8. Heap
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8.1.1 Common operations on heaps
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8.1.3 Common applications of heaps
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8.2 Building a heap
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<!-- Page content -->
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<h1 id="81-heap">8.1 Heap<a class="headerlink" href="#81-heap" title="Permanent link">¶</a></h1>
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<p>A "heap" is a complete binary tree that satisfies specific conditions and can be mainly divided into two types, as shown in the Figure 8-1 .</p>
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<ul>
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<li>"Min heap": The value of any node <span class="arithmatex">\(\leq\)</span> the values of its child nodes.</li>
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<li>"Max heap": The value of any node <span class="arithmatex">\(\geq\)</span> the values of its child nodes.</li>
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</ul>
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<p><a class="glightbox" href="../heap.assets/min_heap_and_max_heap.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Min heap and max heap" class="animation-figure" src="../heap.assets/min_heap_and_max_heap.png" /></a></p>
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<p align="center"> Figure 8-1 Min heap and max heap </p>
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<p>As a special case of a complete binary tree, heaps have the following characteristics:</p>
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<ul>
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<li>The bottom layer nodes are filled from left to right, and nodes in other layers are fully filled.</li>
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<li>The root node of the binary tree is called the "heap top," and the bottom-rightmost node is called the "heap bottom."</li>
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<li>For max heaps (min heaps), the value of the heap top element (root node) is the largest (smallest).</li>
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</ul>
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<h2 id="811-common-operations-on-heaps">8.1.1 Common operations on heaps<a class="headerlink" href="#811-common-operations-on-heaps" title="Permanent link">¶</a></h2>
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<p>It should be noted that many programming languages provide a "priority queue," which is an abstract data structure defined as a queue with priority sorting.</p>
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<p>In fact, <strong>heaps are often used to implement priority queues, with max heaps equivalent to priority queues where elements are dequeued in descending order</strong>. From a usage perspective, we can consider "priority queue" and "heap" as equivalent data structures. Therefore, this book does not make a special distinction between the two, uniformly referring to them as "heap."</p>
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<p>Common operations on heaps are shown in the Table 8-1 , and the method names depend on the programming language.</p>
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<p align="center"> Table 8-1 Efficiency of Heap Operations </p>
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<div class="center-table">
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<table>
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<thead>
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<tr>
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<th>Method name</th>
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<th>Description</th>
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<th>Time complexity</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td><code>push()</code></td>
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<td>Add an element to the heap</td>
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<td><span class="arithmatex">\(O(\log n)\)</span></td>
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</tr>
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<tr>
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<td><code>pop()</code></td>
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<td>Remove the top element from the heap</td>
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<td><span class="arithmatex">\(O(\log n)\)</span></td>
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</tr>
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<tr>
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<td><code>peek()</code></td>
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<td>Access the top element (for max/min heap, the max/min value)</td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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</tr>
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<tr>
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<td><code>size()</code></td>
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<td>Get the number of elements in the heap</td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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</tr>
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<tr>
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<td><code>isEmpty()</code></td>
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<td>Check if the heap is empty</td>
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<td><span class="arithmatex">\(O(1)\)</span></td>
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</tr>
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</tbody>
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</table>
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</div>
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<p>In practice, we can directly use the heap class (or priority queue class) provided by programming languages.</p>
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<p>Similar to sorting algorithms where we have "ascending order" and "descending order," we can switch between "min heap" and "max heap" by setting a <code>flag</code> or modifying the <code>Comparator</code>. The code is as follows:</p>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 初始化小顶堆</span>
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">min_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="mi">1</span>
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 初始化大顶堆</span>
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<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="o">-</span><span class="mi">1</span>
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<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
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<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="c1"># Python 的 heapq 模块默认实现小顶堆</span>
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<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># 考虑将“元素取负”后再入堆，这样就可以将大小关系颠倒，从而实现大顶堆</span>
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<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="c1"># 在本示例中，flag = 1 时对应小顶堆，flag = -1 时对应大顶堆</span>
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<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>
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<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="c1"># 元素入堆</span>
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<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">3</span><span class="p">)</span>
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<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span>
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<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">5</span><span class="p">)</span>
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<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">4</span><span class="p">)</span>
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<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>
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<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># 获取堆顶元素</span>
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<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">peek</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># 5</span>
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<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
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<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="c1"># 堆顶元素出堆</span>
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<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># 出堆元素会形成一个从大到小的序列</span>
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<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 5</span>
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<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 4</span>
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<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 3</span>
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<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 2</span>
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<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 1</span>
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<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>
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<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a><span class="c1"># 获取堆大小</span>
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<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span>
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<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
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<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="c1"># 判断堆是否为空</span>
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<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">max_heap</span>
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<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>
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<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="c1"># 输入列表并建堆</span>
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<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="n">min_heap</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
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<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heapify</span><span class="p">(</span><span class="n">min_heap</span><span class="p">)</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 初始化堆 */</span>
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<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 初始化小顶堆</span>
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<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">priority_queue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">minHeap</span><span class="p">;</span>
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<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="c1">// 初始化大顶堆</span>
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<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">priority_queue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">less</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">;</span>
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<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
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<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
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<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
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<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
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<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
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<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
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<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* 获取堆顶元素 */</span>
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<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">top</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
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<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
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<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
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<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
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<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
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<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
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<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
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<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
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<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
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<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
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<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* 获取堆大小 */</span>
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<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
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<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
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<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* 判断堆是否为空 */</span>
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<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
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<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a>
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<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="cm">/* 输入列表并建堆 */</span>
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<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">input</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">};</span>
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<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="n">priority_queue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o"><</span><span class="kt">int</span><span class="o">>></span><span class="w"> </span><span class="n">minHeap</span><span class="p">(</span><span class="n">input</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">input</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 初始化堆 */</span>
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<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 初始化小顶堆</span>
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<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">Queue</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o"><></span><span class="p">();</span>
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<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1">// 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）</span>
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<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">Queue</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o"><></span><span class="p">((</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">-></span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
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<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>
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<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
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<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
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<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
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<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
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<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
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<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* 获取堆顶元素 */</span>
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<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">peek</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
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<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
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<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
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<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
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<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
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<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
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<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
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<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
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<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
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<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a>
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<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="cm">/* 获取堆大小 */</span>
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<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
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<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a>
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<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="cm">/* 判断堆是否为空 */</span>
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<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
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<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
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<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="cm">/* 输入列表并建堆 */</span>
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<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o"><></span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">));</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 初始化堆 */</span>
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<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 初始化小顶堆</span>
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<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">PriorityQueue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
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<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）</span>
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<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">PriorityQueue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">Comparer</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="p">.</span><span class="n">Create</span><span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=></span><span class="w"> </span><span class="n">y</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">x</span><span class="p">));</span>
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<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
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<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
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<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">);</span>
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<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">);</span>
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<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">);</span>
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<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">);</span>
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<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
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<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* 获取堆顶元素 */</span>
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<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Peek</span><span class="p">();</span><span class="c1">//5</span>
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<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a>
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<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
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<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
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<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
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<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
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<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
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<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
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<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
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<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a>
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<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="cm">/* 获取堆大小 */</span>
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<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
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<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a>
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<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="cm">/* 判断堆是否为空 */</span>
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<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
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<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a>
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<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="cm">/* 输入列表并建堆 */</span>
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<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o"><</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">></span><span class="p">([(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">1</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">)]);</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// Go 语言中可以通过实现 heap.Interface 来构建整数大顶堆</span>
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<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// 实现 heap.Interface 需要同时实现 sort.Interface</span>
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<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">type</span><span class="w"> </span><span class="nx">intHeap</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
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<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
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<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// Push heap.Interface 的方法，实现推入元素到堆</span>
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<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Push</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// Push 和 Pop 使用 pointer receiver 作为参数</span>
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<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="c1">// 因为它们不仅会对切片的内容进行调整，还会修改切片的长度。</span>
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<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="o">*</span><span class="nx">h</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">,</span><span class="w"> </span><span class="nx">x</span><span class="p">.(</span><span class="kt">int</span><span class="p">))</span>
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<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
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<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
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<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="c1">// Pop heap.Interface 的方法，实现弹出堆顶元素</span>
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<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="c1">// 待出堆元素存放在最后</span>
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<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="nx">last</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
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<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="o">*</span><span class="nx">h</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
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<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">last</span>
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<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="p">}</span>
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<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a>
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<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="c1">// Len sort.Interface 的方法</span>
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<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span>
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<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
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<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a>
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<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="c1">// Less sort.Interface 的方法</span>
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<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Less</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w"> </span><span class="c1">// 如果实现小顶堆，则需要调整为小于号</span>
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<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span>
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<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
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<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a>
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<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="c1">// Swap sort.Interface 的方法</span>
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<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
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<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="p">}</span>
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<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a>
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<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="c1">// Top 获取堆顶元素</span>
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<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Top</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
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<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="p">}</span>
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<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a>
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<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="cm">/* Driver Code */</span>
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<a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="kd">func</span><span class="w"> </span><span class="nx">TestHeap</span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">testing</span><span class="p">.</span><span class="nx">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w"> </span><span class="cm">/* 初始化堆 */</span>
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<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w"> </span><span class="c1">// 初始化大顶堆</span>
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<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w"> </span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&</span><span class="nx">intHeap</span><span class="p">{}</span>
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<a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Init</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span>
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<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="w"> </span><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a><span class="w"> </span><span class="c1">// 调用 heap.Interface 的方法，来添加元素</span>
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<a id="__codelineno-4-49" name="__codelineno-4-49" href="#__codelineno-4-49"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-4-50" name="__codelineno-4-50" href="#__codelineno-4-50"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
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<a id="__codelineno-4-51" name="__codelineno-4-51" href="#__codelineno-4-51"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
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<a id="__codelineno-4-52" name="__codelineno-4-52" href="#__codelineno-4-52"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
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<a id="__codelineno-4-53" name="__codelineno-4-53" href="#__codelineno-4-53"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
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<a id="__codelineno-4-54" name="__codelineno-4-54" href="#__codelineno-4-54"></a>
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<a id="__codelineno-4-55" name="__codelineno-4-55" href="#__codelineno-4-55"></a><span class="w"> </span><span class="cm">/* 获取堆顶元素 */</span>
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<a id="__codelineno-4-56" name="__codelineno-4-56" href="#__codelineno-4-56"></a><span class="w"> </span><span class="nx">top</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">Top</span><span class="p">()</span>
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<a id="__codelineno-4-57" name="__codelineno-4-57" href="#__codelineno-4-57"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">"堆顶元素为 %d\n"</span><span class="p">,</span><span class="w"> </span><span class="nx">top</span><span class="p">)</span>
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<a id="__codelineno-4-58" name="__codelineno-4-58" href="#__codelineno-4-58"></a>
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<a id="__codelineno-4-59" name="__codelineno-4-59" href="#__codelineno-4-59"></a><span class="w"> </span><span class="cm">/* 堆顶元素出堆 */</span>
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<a id="__codelineno-4-60" name="__codelineno-4-60" href="#__codelineno-4-60"></a><span class="w"> </span><span class="c1">// 调用 heap.Interface 的方法，来移除元素</span>
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<a id="__codelineno-4-61" name="__codelineno-4-61" href="#__codelineno-4-61"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5</span>
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<a id="__codelineno-4-62" name="__codelineno-4-62" href="#__codelineno-4-62"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 4</span>
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<a id="__codelineno-4-63" name="__codelineno-4-63" href="#__codelineno-4-63"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 3</span>
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<a id="__codelineno-4-64" name="__codelineno-4-64" href="#__codelineno-4-64"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 2</span>
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<a id="__codelineno-4-65" name="__codelineno-4-65" href="#__codelineno-4-65"></a><span class="w"> </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 1</span>
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<a id="__codelineno-4-66" name="__codelineno-4-66" href="#__codelineno-4-66"></a>
|
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<a id="__codelineno-4-67" name="__codelineno-4-67" href="#__codelineno-4-67"></a><span class="w"> </span><span class="cm">/* 获取堆大小 */</span>
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<a id="__codelineno-4-68" name="__codelineno-4-68" href="#__codelineno-4-68"></a><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span>
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<a id="__codelineno-4-69" name="__codelineno-4-69" href="#__codelineno-4-69"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">"堆元素数量为 %d\n"</span><span class="p">,</span><span class="w"> </span><span class="nx">size</span><span class="p">)</span>
|
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<a id="__codelineno-4-70" name="__codelineno-4-70" href="#__codelineno-4-70"></a>
|
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|
<a id="__codelineno-4-71" name="__codelineno-4-71" href="#__codelineno-4-71"></a><span class="w"> </span><span class="cm">/* 判断堆是否为空 */</span>
|
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<a id="__codelineno-4-72" name="__codelineno-4-72" href="#__codelineno-4-72"></a><span class="w"> </span><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
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<a id="__codelineno-4-73" name="__codelineno-4-73" href="#__codelineno-4-73"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">"堆是否为空 %t\n"</span><span class="p">,</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">)</span>
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<a id="__codelineno-4-74" name="__codelineno-4-74" href="#__codelineno-4-74"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 初始化堆 */</span>
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<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swift 的 Heap 类型同时支持最大堆和最小堆，且需要引入 swift-collections</span>
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<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span> <span class="nv">heap</span> <span class="p">=</span> <span class="n">Heap</span><span class="p"><</span><span class="nb">Int</span><span class="p">>()</span>
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<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
|
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<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
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<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
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<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
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<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
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<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
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<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 获取堆顶元素 */</span>
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<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">var</span> <span class="nv">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="bp">max</span><span class="p">()</span><span class="o">!</span>
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<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>
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<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* 堆顶元素出堆 */</span>
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<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 5</span>
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<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 4</span>
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<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 3</span>
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<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 2</span>
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<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="n">peek</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span> <span class="c1">// 1</span>
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<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a>
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<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="cm">/* 获取堆大小 */</span>
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<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="kd">let</span> <span class="nv">size</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="bp">count</span>
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<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a>
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<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="cm">/* 判断堆是否为空 */</span>
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<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="kd">let</span> <span class="nv">isEmpty</span> <span class="p">=</span> <span class="n">heap</span><span class="p">.</span><span class="bp">isEmpty</span>
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<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a>
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<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="cm">/* 输入列表并建堆 */</span>
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<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="kd">let</span> <span class="nv">heap2</span> <span class="p">=</span> <span class="n">Heap</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">])</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// JavaScript 未提供内置 Heap 类</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// TypeScript 未提供内置 Heap 类</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// Dart 未提供内置 Heap 类</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">collections</span>::<span class="n">BinaryHeap</span><span class="p">;</span>
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<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span>::<span class="n">cmp</span>::<span class="n">Reverse</span><span class="p">;</span>
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<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
|
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<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* 初始化堆 */</span>
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<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// 初始化小顶堆</span>
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<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span>::<span class="o"><</span><span class="n">Reverse</span><span class="o"><</span><span class="kt">i32</span><span class="o">>></span>::<span class="n">new</span><span class="p">();</span>
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<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// 初始化大顶堆</span>
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<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span>::<span class="n">new</span><span class="p">();</span>
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<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a>
|
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<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
|
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<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
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<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
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<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
|
|
|
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
|
|
|
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* 获取堆顶元素 */</span>
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|
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">peek</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
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|
|
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a>
|
|
|
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="cm">/* 堆顶元素出堆 */</span>
|
|
|
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
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<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
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|
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
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<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
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|
<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
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|
<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
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|
<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a>
|
|
|
<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="cm">/* 获取堆大小 */</span>
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<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
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<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a>
|
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|
<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="cm">/* 判断堆是否为空 */</span>
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<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
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<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a>
|
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|
<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="cm">/* 输入列表并建堆 */</span>
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<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="kd">let</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span>::<span class="n">from</span><span class="p">(</span><span class="fm">vec!</span><span class="p">[</span><span class="n">Reverse</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">5</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">4</span><span class="p">)]);</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// C 未提供内置 Heap 类</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 初始化堆 */</span>
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<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 初始化小顶堆</span>
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<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o"><</span><span class="kt">Int</span><span class="o">></span><span class="p">()</span>
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<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="c1">// 初始化大顶堆（使用 lambda 表达式修改 Comparator 即可）</span>
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<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="kd">val</span><span class="w"> </span><span class="nv">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">a</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">-></span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
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<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">1</span><span class="p">)</span>
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<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">3</span><span class="p">)</span>
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<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">2</span><span class="p">)</span>
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<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
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<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">4</span><span class="p">)</span>
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<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a>
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<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="cm">/* 获取堆顶元素 */</span>
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<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="kd">var</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">peek</span><span class="p">()</span><span class="w"> </span><span class="c1">// 5</span>
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<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a>
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<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="cm">/* 堆顶元素出堆 */</span>
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<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="c1">// 出堆元素会形成一个从大到小的序列</span>
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<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 5</span>
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<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 4</span>
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<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 3</span>
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<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 2</span>
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<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 1</span>
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<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a>
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<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="cm">/* 获取堆大小 */</span>
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<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">size</span>
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<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a>
|
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<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="cm">/* 判断堆是否为空 */</span>
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<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="kd">val</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span>
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<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a>
|
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<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="cm">/* 输入列表并建堆 */</span>
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<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="p">(</span><span class="n">mutableListOf</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">))</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">heap.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>
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</code></pre></div>
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</div>
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</div>
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</div>
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<details class="pythontutor">
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<summary>可视化运行</summary>
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<p>https://pythontutor.com/render.html#code=import%20heapq%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20min_heap,%20flag%20%3D%20%5B%5D,%201%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20max_heap,%20flag%20%3D%20%5B%5D,%20-1%0A%20%20%20%20%0A%20%20%20%20%23%20Python%20%E7%9A%84%20heapq%20%E6%A8%A1%E5%9D%97%E9%BB%98%E8%AE%A4%E5%AE%9E%E7%8E%B0%E5%B0%8F%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%80%83%E8%99%91%E5%B0%86%E2%80%9C%E5%85%83%E7%B4%A0%E5%8F%96%E8%B4%9F%E2%80%9D%E5%90%8E%E5%86%8D%E5%85%A5%E5%A0%86%EF%BC%8C%E8%BF%99%E6%A0%B7%E5%B0%B1%E5%8F%AF%E4%BB%A5%E5%B0%86%E5%A4%A7%E5%B0%8F%E5%85%B3%E7%B3%BB%E9%A2%A0%E5%80%92%EF%BC%8C%E4%BB%8E%E8%80%8C%E5%AE%9E%E7%8E%B0%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E5%9C%A8%E6%9C%AC%E7%A4%BA%E4%BE%8B%E4%B8%AD%EF%BC%8Cflag%20%3D%201%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%B0%8F%E9%A1%B6%E5%A0%86%EF%BC%8Cflag%20%3D%20-1%20%E6%97%B6%E5%AF%B9%E5%BA%94%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%201%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%203%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%202%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%205%29%0A%20%20%20%20heapq.heappush%28max_heap,%20flag%20*%204%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20flag%20*%20max_heap%5B0%5D%20%23%205%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%0A%20%20%20%20%23%20%E5%87%BA%E5%A0%86%E5%85%83%E7%B4%A0%E4%BC%9A%E5%BD%A2%E6%88%90%E4%B8%80%E4%B8%AA%E4%BB%8E%E5%A4%A7%E5%88%B0%E5%B0%8F%E7%9A%84%E5%BA%8F%E5%88%97%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%205%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%204%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%203%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%202%0A%20%20%20%20val%20%3D%20flag%20*%20heapq.heappop%28max_heap%29%20%23%201%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%0A%20%20%20%20size%20%3D%20len%28max_heap%29%0A%20%20%20%20%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20not%20max_heap%0A%20%20%20%20%0A%20%20%20%20%23%20%E8%BE%93%E5%85%A5%E5%88%97%E8%A1%A8%E5%B9%B6%E5%BB%BA%E5%A0%86%0A%20%20%20%20min_heap%20%3D%20%5B1,%203,%202,%205,%204%5D%0A%20%20%20%20heapq.heapify%28min_heap%29&cumulative=false&curInstr=3&heapPrimitives=nevernest&mode=display&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false</p>
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</details>
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<h2 id="812-implementation-of-heaps">8.1.2 Implementation of heaps<a class="headerlink" href="#812-implementation-of-heaps" title="Permanent link">¶</a></h2>
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<p>The following implementation is of a max heap. To convert it into a min heap, simply invert all size logic comparisons (for example, replace <span class="arithmatex">\(\geq\)</span> with <span class="arithmatex">\(\leq\)</span>). Interested readers are encouraged to implement it on their own.</p>
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<h3 id="1-storage-and-representation-of-heaps">1. Storage and representation of heaps<a class="headerlink" href="#1-storage-and-representation-of-heaps" title="Permanent link">¶</a></h3>
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<p>As mentioned in the "Binary Trees" section, complete binary trees are well-suited for array representation. Since heaps are a type of complete binary tree, <strong>we will use arrays to store heaps</strong>.</p>
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<p>When using an array to represent a binary tree, elements represent node values, and indexes represent node positions in the binary tree. <strong>Node pointers are implemented through an index mapping formula</strong>.</p>
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<p>As shown in the Figure 8-2 , given an index <span class="arithmatex">\(i\)</span>, the index of its left child is <span class="arithmatex">\(2i + 1\)</span>, the index of its right child is <span class="arithmatex">\(2i + 2\)</span>, and the index of its parent is <span class="arithmatex">\((i - 1) / 2\)</span> (floor division). When the index is out of bounds, it signifies a null node or the node does not exist.</p>
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<p><a class="glightbox" href="../heap.assets/representation_of_heap.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Representation and storage of heaps" class="animation-figure" src="../heap.assets/representation_of_heap.png" /></a></p>
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<p align="center"> Figure 8-2 Representation and storage of heaps </p>
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<p>We can encapsulate the index mapping formula into functions for convenient later use:</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span> <span class="nf">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w"> </span><span class="sd">"""获取左子节点的索引"""</span>
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<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
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<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>
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<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="k">def</span> <span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w"> </span><span class="sd">"""获取右子节点的索引"""</span>
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<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a> <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
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<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>
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<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="k">def</span> <span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w"> </span><span class="sd">"""获取父节点的索引"""</span>
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<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a> <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="c1"># 向下整除</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
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<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
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<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
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<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
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<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
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<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
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<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
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<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
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<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="cm">/* 获取父节点的索引 */</span>
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<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
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<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
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<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
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<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="p">}</span>
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<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a>
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<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
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<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
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<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
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<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
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<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* 获取父节点的索引 */</span>
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<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
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<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
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<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
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<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">}</span>
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|
<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a>
|
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|
<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
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<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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|
<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
|
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|
<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
|
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|
<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a>
|
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|
<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="cm">/* 获取父节点的索引 */</span>
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<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
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<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
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<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
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<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="p">}</span>
|
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|
<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
|
|
|
<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
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<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="o">*</span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
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<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="p">}</span>
|
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|
<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a>
|
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|
<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="cm">/* 获取父节点的索引 */</span>
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<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
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|
<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="w"> </span><span class="c1">// 向下整除</span>
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<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span>
|
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<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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|
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
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<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">func</span> <span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
|
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<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="p">}</span>
|
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|
<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a>
|
|
|
<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
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<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="kd">func</span> <span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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|
<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
|
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<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="p">}</span>
|
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<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a>
|
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|
<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="cm">/* 获取父节点的索引 */</span>
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<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="kd">func</span> <span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="mi">2</span> <span class="c1">// 向下整除</span>
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<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
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<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="err">#</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
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<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="p">}</span>
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<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a>
|
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<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
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<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="err">#</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
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<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="p">}</span>
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<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a>
|
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<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="cm">/* 获取父节点的索引 */</span>
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<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="err">#</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 向下整除</span>
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<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
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<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
|
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|
<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a>
|
|
|
<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
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<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span>
|
|
|
<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="p">}</span>
|
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|
<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a>
|
|
|
<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
|
|
<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
|
|
<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
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</div>
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|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
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<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">_left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
|
|
|
<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a>
|
|
|
<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
|
|
<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="kt">int</span><span class="w"> </span><span class="n">_right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span><span class="p">;</span>
|
|
|
<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a>
|
|
|
<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
|
|
<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">_parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">~/</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
|
|
<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
|
|
<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="k">fn</span> <span class="nf">left</span><span class="p">(</span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">usize</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span>
|
|
|
<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a>
|
|
|
<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
|
|
<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="k">fn</span> <span class="nf">right</span><span class="p">(</span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">usize</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span>
|
|
|
<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a>
|
|
|
<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
|
|
<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="k">fn</span> <span class="nf">parent</span><span class="p">(</span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">usize</span> <span class="p">{</span>
|
|
|
<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 向下整除</span>
|
|
|
<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
|
|
<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
|
|
|
<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a>
|
|
|
<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
|
|
|
<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
|
|
<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="p">}</span>
|
|
|
<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a>
|
|
|
<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="cm">/* 获取父节点的索引 */</span>
|
|
|
<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
|
|
|
<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="p">}</span>
|
|
|
</code></pre></div>
|
|
|
</div>
|
|
|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="cm">/* 获取左子节点的索引 */</span>
|
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<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span>
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<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="p">}</span>
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<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a>
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<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="cm">/* 获取右子节点的索引 */</span>
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<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">2</span>
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<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="p">}</span>
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<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a>
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<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="cm">/* 获取父节点的索引 */</span>
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<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">):</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="c1">// 向下整除</span>
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<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left</span><span class="p">}</span>
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<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
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<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right</span><span class="p">}</span>
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<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
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<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">parent</span><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="c1">// 获取左子节点的索引</span>
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<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
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<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="p">}</span>
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<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a>
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<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="c1">// 获取右子节点的索引</span>
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<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="k">fn</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
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<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="p">}</span>
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<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>
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<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="c1">// 获取父节点的索引</span>
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<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="k">fn</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w"> </span><span class="c1">// return (i - 1) / 2; // 向下整除</span>
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<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nb">@divFloor</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
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<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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</div>
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</div>
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<h3 id="2-accessing-the-top-element-of-the-heap">2. Accessing the top element of the heap<a class="headerlink" href="#2-accessing-the-top-element-of-the-heap" title="Permanent link">¶</a></h3>
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<p>The top element of the heap is the root node of the binary tree, which is also the first element of the list:</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span> <span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w"> </span><span class="sd">"""访问堆顶元素"""</span>
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<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
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<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
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<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
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<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="kd">func</span> <span class="nf">peek</span><span class="p">()</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a> <span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
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<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="nx">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
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<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="nx">peek</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
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<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="m">0</span><span class="p">];</span>
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<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="k">fn</span> <span class="nf">peek</span><span class="p">(</span><span class="o">&</span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-> <span class="nb">Option</span><span class="o"><</span><span class="kt">i32</span><span class="o">></span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">first</span><span class="p">().</span><span class="n">copied</span><span class="p">()</span>
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<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
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<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="cm">/* 访问堆顶元素 */</span>
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<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">peek</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="m">0</span><span class="o">]</span>
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<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">peek</span><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="c1">// 访问堆顶元素</span>
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<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">peek</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">)</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
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<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="p">}</span><span class="w"> </span>
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</code></pre></div>
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</div>
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</div>
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</div>
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<details class="pythontutor">
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<summary>Code Visualization</summary>
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<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%AE%BF%E9%97%AE%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.max_heap%5B0%5D%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%20%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20max_heap.peek%28%29%0A%20%20%20%20print%28f%22%5Cn%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E4%B8%BA%20%7Bpeek%7D%22%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
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<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20peek%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%AE%BF%E9%97%AE%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.max_heap%5B0%5D%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%20%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20peek%20%3D%20max_heap.peek%28%29%0A%20%20%20%20print%28f%22%5Cn%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%E4%B8%BA%20%7Bpeek%7D%22%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=7&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Full Screen ></a></div></p>
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</details>
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<h3 id="3-inserting-an-element-into-the-heap">3. Inserting an element into the heap<a class="headerlink" href="#3-inserting-an-element-into-the-heap" title="Permanent link">¶</a></h3>
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<p>Given an element <code>val</code>, we first add it to the bottom of the heap. After addition, since <code>val</code> may be larger than other elements in the heap, the heap's integrity might be compromised, <strong>thus it's necessary to repair the path from the inserted node to the root node</strong>. This operation is called "heapifying".</p>
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<p>Considering starting from the node inserted, <strong>perform heapify from bottom to top</strong>. As shown in the Figure 8-3 , we compare the value of the inserted node with its parent node, and if the inserted node is larger, we swap them. Then continue this operation, repairing each node in the heap from bottom to top until passing the root node or encountering a node that does not need to be swapped.</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="4:9"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1"><1></label><label for="__tabbed_4_2"><2></label><label for="__tabbed_4_3"><3></label><label for="__tabbed_4_4"><4></label><label for="__tabbed_4_5"><5></label><label for="__tabbed_4_6"><6></label><label for="__tabbed_4_7"><7></label><label for="__tabbed_4_8"><8></label><label for="__tabbed_4_9"><9></label></div>
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<p><a class="glightbox" href="../heap.assets/heap_push_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Steps of element insertion into the heap" class="animation-figure" src="../heap.assets/heap_push_step1.png" /></a></p>
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<p><a class="glightbox" href="../heap.assets/heap_push_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step2" class="animation-figure" src="../heap.assets/heap_push_step2.png" /></a></p>
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<p><a class="glightbox" href="../heap.assets/heap_push_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step3" class="animation-figure" src="../heap.assets/heap_push_step3.png" /></a></p>
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<p><a class="glightbox" href="../heap.assets/heap_push_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step4" class="animation-figure" src="../heap.assets/heap_push_step4.png" /></a></p>
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<p><a class="glightbox" href="../heap.assets/heap_push_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step5" class="animation-figure" src="../heap.assets/heap_push_step5.png" /></a></p>
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<p><a class="glightbox" href="../heap.assets/heap_push_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step6" class="animation-figure" src="../heap.assets/heap_push_step6.png" /></a></p>
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<p><a class="glightbox" href="../heap.assets/heap_push_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step7" class="animation-figure" src="../heap.assets/heap_push_step7.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_push_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step8" class="animation-figure" src="../heap.assets/heap_push_step8.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_push_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step9" class="animation-figure" src="../heap.assets/heap_push_step9.png" /></a></p>
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</div>
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</div>
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</div>
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<p align="center"> Figure 8-3 Steps of element insertion into the heap </p>
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<p>Given a total of <span class="arithmatex">\(n\)</span> nodes, the height of the tree is <span class="arithmatex">\(O(\log n)\)</span>. Hence, the loop iterations for the heapify operation are at most <span class="arithmatex">\(O(\log n)\)</span>, <strong>making the time complexity of the element insertion operation <span class="arithmatex">\(O(\log n)\)</span></strong>. The code is as shown:</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span> <span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
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<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w"> </span><span class="sd">"""元素入堆"""</span>
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<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a> <span class="c1"># 添加节点</span>
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<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
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<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a> <span class="c1"># 从底至顶堆化</span>
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<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>
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<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="k">def</span> <span class="nf">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
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<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w"> </span><span class="sd">"""从节点 i 开始，从底至顶堆化"""</span>
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<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
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<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a> <span class="c1"># 获取节点 i 的父节点</span>
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<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a> <span class="n">p</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
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<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a> <span class="c1"># 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a> <span class="k">if</span> <span class="n">p</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]:</span>
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<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a> <span class="k">break</span>
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<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a> <span class="c1"># 交换两节点</span>
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<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
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<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a> <span class="c1"># 循环向上堆化</span>
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<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a> <span class="n">i</span> <span class="o">=</span> <span class="n">p</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
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<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="p">}</span>
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<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a>
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<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
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<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">]);</span>
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<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
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<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-43-22" name="__codelineno-43-22" href="#__codelineno-43-22"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
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<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="p">}</span>
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<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a>
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<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">p</span><span class="p">))</span>
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<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
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<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
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<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
|
|
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<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
|
|
|
<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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|
<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w"> </span><span class="n">SiftUp</span><span class="p">(</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
|
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|
<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="p">}</span>
|
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<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a>
|
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|
<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
|
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<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="k">void</span><span class="w"> </span><span class="nf">SiftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w"> </span><span class="c1">// 若“越过根节点”或“节点无须修复”，则结束堆化</span>
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<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
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<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w"> </span><span class="n">Swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
|
|
<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
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<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-45-22" name="__codelineno-45-22" href="#__codelineno-45-22"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">,</span><span class="w"> </span><span class="nx">val</span><span class="p">)</span>
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<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="p">}</span>
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<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a>
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<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
|
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<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span>
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<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
|
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<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">p</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
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<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w"> </span><span class="k">break</span>
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<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
|
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|
<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">)</span>
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<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
|
|
|
<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">p</span>
|
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<a id="__codelineno-46-22" name="__codelineno-46-22" href="#__codelineno-46-22"></a><span class="w"> </span><span class="p">}</span>
|
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<a id="__codelineno-46-23" name="__codelineno-46-23" href="#__codelineno-46-23"></a><span class="p">}</span>
|
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</code></pre></div>
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</div>
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<div class="tabbed-block">
|
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|
<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* 元素入堆 */</span>
|
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<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kd">func</span> <span class="nf">push</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
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|
|
<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a> <span class="c1">// 添加节点</span>
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<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a> <span class="n">maxHeap</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
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<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a> <span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a> <span class="n">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
|
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<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="p">}</span>
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<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a>
|
|
|
<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="kd">func</span> <span class="nf">siftUp</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">i</span>
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<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a> <span class="k">while</span> <span class="kc">true</span> <span class="p">{</span>
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|
<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a> <span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a> <span class="kd">let</span> <span class="nv">p</span> <span class="p">=</span> <span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
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<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a> <span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a> <span class="k">if</span> <span class="n">p</span> <span class="o"><</span> <span class="mi">0</span> <span class="o">||</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">]</span> <span class="p">{</span>
|
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|
<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a> <span class="k">break</span>
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<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a> <span class="p">}</span>
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|
<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a> <span class="c1">// 交换两节点</span>
|
|
|
<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">p</span><span class="p">)</span>
|
|
|
<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a> <span class="c1">// 循环向上堆化</span>
|
|
|
<a id="__codelineno-47-22" name="__codelineno-47-22" href="#__codelineno-47-22"></a> <span class="n">i</span> <span class="p">=</span> <span class="n">p</span>
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|
<a id="__codelineno-47-23" name="__codelineno-47-23" href="#__codelineno-47-23"></a> <span class="p">}</span>
|
|
|
<a id="__codelineno-47-24" name="__codelineno-47-24" href="#__codelineno-47-24"></a><span class="p">}</span>
|
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|
</code></pre></div>
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</div>
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|
<div class="tabbed-block">
|
|
|
<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* 元素入堆 */</span>
|
|
|
<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
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|
<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
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<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="p">}</span>
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|
<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a>
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<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="err">#</span><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
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<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
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<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">p</span><span class="p">;</span>
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<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
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<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">siftUp</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
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<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="p">}</span>
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<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a>
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<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="nx">siftUp</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">parent</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
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<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">p</span><span class="p">);</span>
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<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">p</span><span class="p">;</span>
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<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w"> </span><span class="n">_maxHeap</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
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<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
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<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="p">}</span>
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<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a>
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<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="kt">void</span><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
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<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
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<a id="__codelineno-50-22" name="__codelineno-50-22" href="#__codelineno-50-22"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-50-23" name="__codelineno-50-23" href="#__codelineno-50-23"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">fn</span> <span class="nf">push</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span>: <span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
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<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="p">}</span>
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<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a>
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<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="k">fn</span> <span class="nf">sift_up</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w"> </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w"> </span><span class="c1">// 节点 i 已经是堆顶节点了，结束堆化</span>
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<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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|
<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w"> </span><span class="c1">// 当“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
|
|
|
<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-51-22" name="__codelineno-51-22" href="#__codelineno-51-22"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-51-23" name="__codelineno-51-23" href="#__codelineno-51-23"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
|
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<a id="__codelineno-51-24" name="__codelineno-51-24" href="#__codelineno-51-24"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-51-25" name="__codelineno-51-25" href="#__codelineno-51-25"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
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<a id="__codelineno-51-26" name="__codelineno-51-26" href="#__codelineno-51-26"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-51-27" name="__codelineno-51-27" href="#__codelineno-51-27"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="w"> </span><span class="c1">// 默认情况下，不应该添加这么多节点</span>
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<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">MAX_SIZE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"heap is full!"</span><span class="p">);</span>
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<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
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<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
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<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
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<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a>
|
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<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a><span class="p">}</span>
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<a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a>
|
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|
<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-52-22" name="__codelineno-52-22" href="#__codelineno-52-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-52-23" name="__codelineno-52-23" href="#__codelineno-52-23"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-52-24" name="__codelineno-52-24" href="#__codelineno-52-24"></a><span class="w"> </span><span class="p">}</span>
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|
<a id="__codelineno-52-25" name="__codelineno-52-25" href="#__codelineno-52-25"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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|
<a id="__codelineno-52-26" name="__codelineno-52-26" href="#__codelineno-52-26"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
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<a id="__codelineno-52-27" name="__codelineno-52-27" href="#__codelineno-52-27"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-52-28" name="__codelineno-52-28" href="#__codelineno-52-28"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
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<a id="__codelineno-52-29" name="__codelineno-52-29" href="#__codelineno-52-29"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-52-30" name="__codelineno-52-30" href="#__codelineno-52-30"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 元素入堆 */</span>
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<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">_val</span><span class="p">)</span>
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<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
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<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="p">}</span>
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<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a>
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<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="cm">/* 从节点 i 开始，从底至顶堆化 */</span>
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<a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="nb">it</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w"> </span><span class="c1">// Kotlin的函数参数不可变，因此创建临时变量</span>
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<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">it</span>
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<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
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<a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="m">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">p</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="k">break</span>
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<a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">)</span>
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<a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span>
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<a id="__codelineno-53-22" name="__codelineno-53-22" href="#__codelineno-53-22"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-53-23" name="__codelineno-53-23" href="#__codelineno-53-23"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">push</span><span class="p">}</span>
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<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a>
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<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">sift_up</span><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="c1">// 元素入堆</span>
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<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w"> </span><span class="c1">// 添加节点</span>
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<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
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<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w"> </span><span class="c1">// 从底至顶堆化</span>
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|
<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">siftUp</span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="p">}</span><span class="w"> </span>
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<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a>
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<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="c1">// 从节点 i 开始，从底至顶堆化</span>
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<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="k">fn</span><span class="w"> </span><span class="n">siftUp</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">i_</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i_</span><span class="p">;</span>
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<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="w"> </span><span class="c1">// 获取节点 i 的父节点</span>
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<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a><span class="w"> </span><span class="c1">// 当“越过根节点”或“节点无须修复”时，结束堆化</span>
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<a id="__codelineno-55-16" name="__codelineno-55-16" href="#__codelineno-55-16"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="k">or</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">p</span><span class="p">])</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-55-17" name="__codelineno-55-17" href="#__codelineno-55-17"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-55-18" name="__codelineno-55-18" href="#__codelineno-55-18"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
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<a id="__codelineno-55-19" name="__codelineno-55-19" href="#__codelineno-55-19"></a><span class="w"> </span><span class="c1">// 循环向上堆化</span>
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<a id="__codelineno-55-20" name="__codelineno-55-20" href="#__codelineno-55-20"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
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<a id="__codelineno-55-21" name="__codelineno-55-21" href="#__codelineno-55-21"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-55-22" name="__codelineno-55-22" href="#__codelineno-55-22"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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</div>
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</div>
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<details class="pythontutor">
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<summary>Code Visualization</summary>
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<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20swap%28self,%20i%3A%20int,%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BA%A4%E6%8D%A2%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D,%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D,%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20push%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20self.max_heap.append%28val%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BB%8E%E5%BA%95%E8%87%B3%E9%A1%B6%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20self.sift_up%28self.size%28%29%20-%201%29%0A%0A%20%20%20%20def%20sift_up%28self,%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BB%8E%E8%8A%82%E7%82%B9%20i%20%E5%BC%80%E5%A7%8B%EF%BC%8C%E4%BB%8E%E5%BA%95%E8%87%B3%E9%A1%B6%E5%A0%86%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E8%8A%82%E7%82%B9%20i%20%E7%9A%84%E7%88%B6%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20p%20%3D%20self.parent%28i%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BD%93%E2%80%9C%E8%B6%8A%E8%BF%87%E6%A0%B9%E8%8A%82%E7%82%B9%E2%80%9D%E6%88%96%E2%80%9C%E8%8A%82%E7%82%B9%E6%97%A0%E9%A1%BB%E4%BF%AE%E5%A4%8D%E2%80%9D%E6%97%B6%EF%BC%8C%E7%BB%93%E6%9D%9F%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20p%20%3C%200%20or%20self.max_heap%5Bi%5D%20%3C%3D%20self.max_heap%5Bp%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E4%B8%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i,%20p%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E5%90%91%E4%B8%8A%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20p%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20val%20%3D%207%0A%20%20%20%20max_heap.push%28val%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
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<div style="margin-top: 5px;"><a href="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20swap%28self,%20i%3A%20int,%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BA%A4%E6%8D%A2%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D,%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D,%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20push%28self,%20val%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20self.max_heap.append%28val%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BB%8E%E5%BA%95%E8%87%B3%E9%A1%B6%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20self.sift_up%28self.size%28%29%20-%201%29%0A%0A%20%20%20%20def%20sift_up%28self,%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BB%8E%E8%8A%82%E7%82%B9%20i%20%E5%BC%80%E5%A7%8B%EF%BC%8C%E4%BB%8E%E5%BA%95%E8%87%B3%E9%A1%B6%E5%A0%86%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E8%8A%82%E7%82%B9%20i%20%E7%9A%84%E7%88%B6%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20p%20%3D%20self.parent%28i%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BD%93%E2%80%9C%E8%B6%8A%E8%BF%87%E6%A0%B9%E8%8A%82%E7%82%B9%E2%80%9D%E6%88%96%E2%80%9C%E8%8A%82%E7%82%B9%E6%97%A0%E9%A1%BB%E4%BF%AE%E5%A4%8D%E2%80%9D%E6%97%B6%EF%BC%8C%E7%BB%93%E6%9D%9F%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20p%20%3C%200%20or%20self.max_heap%5Bi%5D%20%3C%3D%20self.max_heap%5Bp%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E4%B8%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i,%20p%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E5%90%91%E4%B8%8A%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20p%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%88%E6%B3%95%E7%9A%84%E5%A0%86%0A%20%20%20%20max_heap%20%3D%20MaxHeap%28%5B9,%208,%206,%206,%207,%205,%202,%201,%204,%203,%206,%202%5D%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E5%A0%86%0A%20%20%20%20val%20%3D%207%0A%20%20%20%20max_heap.push%28val%29&codeDivHeight=800&codeDivWidth=600&cumulative=false&curInstr=8&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false" target="_blank" rel="noopener noreferrer">Full Screen ></a></div></p>
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</details>
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<h3 id="4-removing-the-top-element-from-the-heap">4. Removing the top element from the heap<a class="headerlink" href="#4-removing-the-top-element-from-the-heap" title="Permanent link">¶</a></h3>
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<p>The top element of the heap is the root node of the binary tree, that is, the first element of the list. If we directly remove the first element from the list, all node indexes in the binary tree would change, making it difficult to use heapify for repairs subsequently. To minimize changes in element indexes, we use the following steps.</p>
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<ol>
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<li>Swap the top element with the bottom element of the heap (swap the root node with the rightmost leaf node).</li>
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<li>After swapping, remove the bottom of the heap from the list (note, since it has been swapped, what is actually being removed is the original top element).</li>
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<li>Starting from the root node, <strong>perform heapify from top to bottom</strong>.</li>
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</ol>
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<p>As shown in the Figure 8-4 , <strong>the direction of "heapify from top to bottom" is opposite to "heapify from bottom to top"</strong>. We compare the value of the root node with its two children and swap it with the largest child. Then repeat this operation until passing the leaf node or encountering a node that does not need to be swapped.</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="6:10"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1"><1></label><label for="__tabbed_6_2"><2></label><label for="__tabbed_6_3"><3></label><label for="__tabbed_6_4"><4></label><label for="__tabbed_6_5"><5></label><label for="__tabbed_6_6"><6></label><label for="__tabbed_6_7"><7></label><label for="__tabbed_6_8"><8></label><label for="__tabbed_6_9"><9></label><label for="__tabbed_6_10"><10></label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Steps of removing the top element from the heap" class="animation-figure" src="../heap.assets/heap_pop_step1.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step2" class="animation-figure" src="../heap.assets/heap_pop_step2.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step3" class="animation-figure" src="../heap.assets/heap_pop_step3.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step4" class="animation-figure" src="../heap.assets/heap_pop_step4.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step5" class="animation-figure" src="../heap.assets/heap_pop_step5.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step6" class="animation-figure" src="../heap.assets/heap_pop_step6.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step7" class="animation-figure" src="../heap.assets/heap_pop_step7.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step8" class="animation-figure" src="../heap.assets/heap_pop_step8.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step9" class="animation-figure" src="../heap.assets/heap_pop_step9.png" /></a></p>
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</div>
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<div class="tabbed-block">
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<p><a class="glightbox" href="../heap.assets/heap_pop_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step10" class="animation-figure" src="../heap.assets/heap_pop_step10.png" /></a></p>
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</div>
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</div>
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</div>
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<p align="center"> Figure 8-4 Steps of removing the top element from the heap </p>
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<p>Similar to the element insertion operation, the time complexity of the top element removal operation is also <span class="arithmatex">\(O(\log n)\)</span>. The code is as follows:</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
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<div class="tabbed-content">
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="k">def</span> <span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">int</span><span class="p">:</span>
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<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="w"> </span><span class="sd">"""元素出堆"""</span>
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<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a> <span class="c1"># 判空处理</span>
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<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
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<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a> <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">"堆为空"</span><span class="p">)</span>
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<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a> <span class="c1"># 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a> <span class="c1"># 删除节点</span>
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<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a> <span class="n">val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
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<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a> <span class="c1"># 从顶至底堆化</span>
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<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a> <span class="bp">self</span><span class="o">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
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<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a> <span class="c1"># 返回堆顶元素</span>
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<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a> <span class="k">return</span> <span class="n">val</span>
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<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a>
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<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a><span class="k">def</span> <span class="nf">sift_down</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
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<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="w"> </span><span class="sd">"""从节点 i 开始，从顶至底堆化"""</span>
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<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a> <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
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<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a> <span class="c1"># 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a> <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">ma</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">i</span>
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<a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a> <span class="k">if</span> <span class="n">l</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
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<a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a> <span class="n">ma</span> <span class="o">=</span> <span class="n">l</span>
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<a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a> <span class="k">if</span> <span class="n">r</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
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<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></a> <span class="n">ma</span> <span class="o">=</span> <span class="n">r</span>
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<a id="__codelineno-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></a> <span class="c1"># 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a> <span class="k">if</span> <span class="n">ma</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
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<a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a> <span class="k">break</span>
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<a id="__codelineno-56-27" name="__codelineno-56-27" href="#__codelineno-56-27"></a> <span class="c1"># 交换两节点</span>
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<a id="__codelineno-56-28" name="__codelineno-56-28" href="#__codelineno-56-28"></a> <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">ma</span><span class="p">)</span>
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<a id="__codelineno-56-29" name="__codelineno-56-29" href="#__codelineno-56-29"></a> <span class="c1"># 循环向下堆化</span>
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<a id="__codelineno-56-30" name="__codelineno-56-30" href="#__codelineno-56-30"></a> <span class="n">i</span> <span class="o">=</span> <span class="n">ma</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">"堆为空"</span><span class="p">);</span>
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<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
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<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
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<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="p">}</span>
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<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a>
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<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
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<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
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<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
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<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
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<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
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<a id="__codelineno-57-24" name="__codelineno-57-24" href="#__codelineno-57-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-57-25" name="__codelineno-57-25" href="#__codelineno-57-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
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<a id="__codelineno-57-26" name="__codelineno-57-26" href="#__codelineno-57-26"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-57-27" name="__codelineno-57-27" href="#__codelineno-57-27"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
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<a id="__codelineno-57-28" name="__codelineno-57-28" href="#__codelineno-57-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-57-29" name="__codelineno-57-29" href="#__codelineno-57-29"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
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<a id="__codelineno-57-30" name="__codelineno-57-30" href="#__codelineno-57-30"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-57-31" name="__codelineno-57-31" href="#__codelineno-57-31"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
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<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
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<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
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<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="p">}</span>
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<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a>
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<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
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<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
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<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
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<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
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<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
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<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-58-26" name="__codelineno-58-26" href="#__codelineno-58-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
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<a id="__codelineno-58-27" name="__codelineno-58-27" href="#__codelineno-58-27"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-58-28" name="__codelineno-58-28" href="#__codelineno-58-28"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-58-29" name="__codelineno-58-29" href="#__codelineno-58-29"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
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<a id="__codelineno-58-30" name="__codelineno-58-30" href="#__codelineno-58-30"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-58-31" name="__codelineno-58-31" href="#__codelineno-58-31"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
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<a id="__codelineno-58-32" name="__codelineno-58-32" href="#__codelineno-58-32"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-58-33" name="__codelineno-58-33" href="#__codelineno-58-33"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span>
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<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="nf">IndexOutOfRangeException</span><span class="p">();</span>
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<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="w"> </span><span class="n">Swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
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<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Last</span><span class="p">();</span>
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<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
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<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-59-12" name="__codelineno-59-12" href="#__codelineno-59-12"></a><span class="w"> </span><span class="n">SiftDown</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
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<a id="__codelineno-59-13" name="__codelineno-59-13" href="#__codelineno-59-13"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-59-14" name="__codelineno-59-14" href="#__codelineno-59-14"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
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<a id="__codelineno-59-15" name="__codelineno-59-15" href="#__codelineno-59-15"></a><span class="p">}</span>
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<a id="__codelineno-59-16" name="__codelineno-59-16" href="#__codelineno-59-16"></a>
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<a id="__codelineno-59-17" name="__codelineno-59-17" href="#__codelineno-59-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-59-18" name="__codelineno-59-18" href="#__codelineno-59-18"></a><span class="k">void</span><span class="w"> </span><span class="nf">SiftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-59-19" name="__codelineno-59-19" href="#__codelineno-59-19"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="k">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-59-20" name="__codelineno-59-20" href="#__codelineno-59-20"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-59-21" name="__codelineno-59-21" href="#__codelineno-59-21"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
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<a id="__codelineno-59-22" name="__codelineno-59-22" href="#__codelineno-59-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
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<a id="__codelineno-59-23" name="__codelineno-59-23" href="#__codelineno-59-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
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<a id="__codelineno-59-24" name="__codelineno-59-24" href="#__codelineno-59-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">Size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
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<a id="__codelineno-59-25" name="__codelineno-59-25" href="#__codelineno-59-25"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
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<a id="__codelineno-59-26" name="__codelineno-59-26" href="#__codelineno-59-26"></a><span class="w"> </span><span class="c1">// 若“节点 i 最大”或“越过叶节点”，则结束堆化</span>
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<a id="__codelineno-59-27" name="__codelineno-59-27" href="#__codelineno-59-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-59-28" name="__codelineno-59-28" href="#__codelineno-59-28"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-59-29" name="__codelineno-59-29" href="#__codelineno-59-29"></a><span class="w"> </span><span class="n">Swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
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<a id="__codelineno-59-30" name="__codelineno-59-30" href="#__codelineno-59-30"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-59-31" name="__codelineno-59-31" href="#__codelineno-59-31"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
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<a id="__codelineno-59-32" name="__codelineno-59-32" href="#__codelineno-59-32"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-59-33" name="__codelineno-59-33" href="#__codelineno-59-33"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="w"> </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="s">"error"</span><span class="p">)</span>
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<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">nil</span>
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<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
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<a id="__codelineno-60-12" name="__codelineno-60-12" href="#__codelineno-60-12"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
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<a id="__codelineno-60-13" name="__codelineno-60-13" href="#__codelineno-60-13"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-60-14" name="__codelineno-60-14" href="#__codelineno-60-14"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
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<a id="__codelineno-60-15" name="__codelineno-60-15" href="#__codelineno-60-15"></a>
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<a id="__codelineno-60-16" name="__codelineno-60-16" href="#__codelineno-60-16"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-60-17" name="__codelineno-60-17" href="#__codelineno-60-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span>
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<a id="__codelineno-60-18" name="__codelineno-60-18" href="#__codelineno-60-18"></a><span class="p">}</span>
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<a id="__codelineno-60-19" name="__codelineno-60-19" href="#__codelineno-60-19"></a>
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<a id="__codelineno-60-20" name="__codelineno-60-20" href="#__codelineno-60-20"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-60-21" name="__codelineno-60-21" href="#__codelineno-60-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-60-22" name="__codelineno-60-22" href="#__codelineno-60-22"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="kc">true</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-60-23" name="__codelineno-60-23" href="#__codelineno-60-23"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 max</span>
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<a id="__codelineno-60-24" name="__codelineno-60-24" href="#__codelineno-60-24"></a><span class="w"> </span><span class="nx">l</span><span class="p">,</span><span class="w"> </span><span class="nx">r</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span><span class="w"> </span><span class="nx">i</span>
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<a id="__codelineno-60-25" name="__codelineno-60-25" href="#__codelineno-60-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">l</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-60-26" name="__codelineno-60-26" href="#__codelineno-60-26"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">l</span>
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<a id="__codelineno-60-27" name="__codelineno-60-27" href="#__codelineno-60-27"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-60-28" name="__codelineno-60-28" href="#__codelineno-60-28"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">r</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">data</span><span class="p">[</span><span class="nx">max</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-60-29" name="__codelineno-60-29" href="#__codelineno-60-29"></a><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">r</span>
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<a id="__codelineno-60-30" name="__codelineno-60-30" href="#__codelineno-60-30"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-60-31" name="__codelineno-60-31" href="#__codelineno-60-31"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-60-32" name="__codelineno-60-32" href="#__codelineno-60-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="nx">max</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-60-33" name="__codelineno-60-33" href="#__codelineno-60-33"></a><span class="w"> </span><span class="k">break</span>
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<a id="__codelineno-60-34" name="__codelineno-60-34" href="#__codelineno-60-34"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-60-35" name="__codelineno-60-35" href="#__codelineno-60-35"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-60-36" name="__codelineno-60-36" href="#__codelineno-60-36"></a><span class="w"> </span><span class="nx">h</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">max</span><span class="p">)</span>
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<a id="__codelineno-60-37" name="__codelineno-60-37" href="#__codelineno-60-37"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-60-38" name="__codelineno-60-38" href="#__codelineno-60-38"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">max</span>
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<a id="__codelineno-60-39" name="__codelineno-60-39" href="#__codelineno-60-39"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-60-40" name="__codelineno-60-40" href="#__codelineno-60-40"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="kd">func</span> <span class="nf">pop</span><span class="p">()</span> <span class="p">-></span> <span class="nb">Int</span> <span class="p">{</span>
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<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a> <span class="c1">// 判空处理</span>
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<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a> <span class="k">if</span> <span class="bp">isEmpty</span><span class="p">()</span> <span class="p">{</span>
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<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a> <span class="bp">fatalError</span><span class="p">(</span><span class="s">"堆为空"</span><span class="p">)</span>
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<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a> <span class="p">}</span>
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<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a> <span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a> <span class="c1">// 删除节点</span>
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<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a> <span class="kd">let</span> <span class="nv">val</span> <span class="p">=</span> <span class="n">maxHeap</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span> <span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
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<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a> <span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-61-12" name="__codelineno-61-12" href="#__codelineno-61-12"></a> <span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
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<a id="__codelineno-61-13" name="__codelineno-61-13" href="#__codelineno-61-13"></a> <span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-61-14" name="__codelineno-61-14" href="#__codelineno-61-14"></a> <span class="k">return</span> <span class="n">val</span>
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<a id="__codelineno-61-15" name="__codelineno-61-15" href="#__codelineno-61-15"></a><span class="p">}</span>
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<a id="__codelineno-61-16" name="__codelineno-61-16" href="#__codelineno-61-16"></a>
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<a id="__codelineno-61-17" name="__codelineno-61-17" href="#__codelineno-61-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-61-18" name="__codelineno-61-18" href="#__codelineno-61-18"></a><span class="kd">func</span> <span class="nf">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">Int</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-61-19" name="__codelineno-61-19" href="#__codelineno-61-19"></a> <span class="kd">var</span> <span class="nv">i</span> <span class="p">=</span> <span class="n">i</span>
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<a id="__codelineno-61-20" name="__codelineno-61-20" href="#__codelineno-61-20"></a> <span class="k">while</span> <span class="kc">true</span> <span class="p">{</span>
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<a id="__codelineno-61-21" name="__codelineno-61-21" href="#__codelineno-61-21"></a> <span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-61-22" name="__codelineno-61-22" href="#__codelineno-61-22"></a> <span class="kd">let</span> <span class="nv">l</span> <span class="p">=</span> <span class="kr">left</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
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<a id="__codelineno-61-23" name="__codelineno-61-23" href="#__codelineno-61-23"></a> <span class="kd">let</span> <span class="nv">r</span> <span class="p">=</span> <span class="kr">right</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">)</span>
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<a id="__codelineno-61-24" name="__codelineno-61-24" href="#__codelineno-61-24"></a> <span class="kd">var</span> <span class="nv">ma</span> <span class="p">=</span> <span class="n">i</span>
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<a id="__codelineno-61-25" name="__codelineno-61-25" href="#__codelineno-61-25"></a> <span class="k">if</span> <span class="n">l</span> <span class="o"><</span> <span class="n">size</span><span class="p">(),</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">></span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="p">{</span>
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<a id="__codelineno-61-26" name="__codelineno-61-26" href="#__codelineno-61-26"></a> <span class="n">ma</span> <span class="p">=</span> <span class="n">l</span>
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<a id="__codelineno-61-27" name="__codelineno-61-27" href="#__codelineno-61-27"></a> <span class="p">}</span>
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<a id="__codelineno-61-28" name="__codelineno-61-28" href="#__codelineno-61-28"></a> <span class="k">if</span> <span class="n">r</span> <span class="o"><</span> <span class="n">size</span><span class="p">(),</span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">></span> <span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="p">{</span>
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<a id="__codelineno-61-29" name="__codelineno-61-29" href="#__codelineno-61-29"></a> <span class="n">ma</span> <span class="p">=</span> <span class="n">r</span>
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<a id="__codelineno-61-30" name="__codelineno-61-30" href="#__codelineno-61-30"></a> <span class="p">}</span>
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<a id="__codelineno-61-31" name="__codelineno-61-31" href="#__codelineno-61-31"></a> <span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-61-32" name="__codelineno-61-32" href="#__codelineno-61-32"></a> <span class="k">if</span> <span class="n">ma</span> <span class="p">==</span> <span class="n">i</span> <span class="p">{</span>
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<a id="__codelineno-61-33" name="__codelineno-61-33" href="#__codelineno-61-33"></a> <span class="k">break</span>
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<a id="__codelineno-61-34" name="__codelineno-61-34" href="#__codelineno-61-34"></a> <span class="p">}</span>
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<a id="__codelineno-61-35" name="__codelineno-61-35" href="#__codelineno-61-35"></a> <span class="c1">// 交换两节点</span>
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<a id="__codelineno-61-36" name="__codelineno-61-36" href="#__codelineno-61-36"></a> <span class="bp">swap</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="n">ma</span><span class="p">)</span>
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<a id="__codelineno-61-37" name="__codelineno-61-37" href="#__codelineno-61-37"></a> <span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-61-38" name="__codelineno-61-38" href="#__codelineno-61-38"></a> <span class="n">i</span> <span class="p">=</span> <span class="n">ma</span>
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<a id="__codelineno-61-39" name="__codelineno-61-39" href="#__codelineno-61-39"></a> <span class="p">}</span>
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<a id="__codelineno-61-40" name="__codelineno-61-40" href="#__codelineno-61-40"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">Error</span><span class="p">(</span><span class="s1">'堆为空'</span><span class="p">);</span>
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<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
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<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
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<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
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<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-62-12" name="__codelineno-62-12" href="#__codelineno-62-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
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<a id="__codelineno-62-13" name="__codelineno-62-13" href="#__codelineno-62-13"></a><span class="p">}</span>
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<a id="__codelineno-62-14" name="__codelineno-62-14" href="#__codelineno-62-14"></a>
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<a id="__codelineno-62-15" name="__codelineno-62-15" href="#__codelineno-62-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-62-16" name="__codelineno-62-16" href="#__codelineno-62-16"></a><span class="err">#</span><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-62-17" name="__codelineno-62-17" href="#__codelineno-62-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-62-18" name="__codelineno-62-18" href="#__codelineno-62-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-62-19" name="__codelineno-62-19" href="#__codelineno-62-19"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
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<a id="__codelineno-62-20" name="__codelineno-62-20" href="#__codelineno-62-20"></a><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
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<a id="__codelineno-62-21" name="__codelineno-62-21" href="#__codelineno-62-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
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<a id="__codelineno-62-22" name="__codelineno-62-22" href="#__codelineno-62-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
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<a id="__codelineno-62-23" name="__codelineno-62-23" href="#__codelineno-62-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
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<a id="__codelineno-62-24" name="__codelineno-62-24" href="#__codelineno-62-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-62-25" name="__codelineno-62-25" href="#__codelineno-62-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-62-26" name="__codelineno-62-26" href="#__codelineno-62-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-62-27" name="__codelineno-62-27" href="#__codelineno-62-27"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
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<a id="__codelineno-62-28" name="__codelineno-62-28" href="#__codelineno-62-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-62-29" name="__codelineno-62-29" href="#__codelineno-62-29"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
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<a id="__codelineno-62-30" name="__codelineno-62-30" href="#__codelineno-62-30"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-62-31" name="__codelineno-62-31" href="#__codelineno-62-31"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a><span class="nx">pop</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="ne">RangeError</span><span class="p">(</span><span class="s1">'Heap is empty.'</span><span class="p">);</span>
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<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
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<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
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<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">siftDown</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
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<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-63-12" name="__codelineno-63-12" href="#__codelineno-63-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
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<a id="__codelineno-63-13" name="__codelineno-63-13" href="#__codelineno-63-13"></a><span class="p">}</span>
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<a id="__codelineno-63-14" name="__codelineno-63-14" href="#__codelineno-63-14"></a>
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<a id="__codelineno-63-15" name="__codelineno-63-15" href="#__codelineno-63-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-63-16" name="__codelineno-63-16" href="#__codelineno-63-16"></a><span class="nx">siftDown</span><span class="p">(</span><span class="nx">i</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-17" name="__codelineno-63-17" href="#__codelineno-63-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-63-18" name="__codelineno-63-18" href="#__codelineno-63-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-63-19" name="__codelineno-63-19" href="#__codelineno-63-19"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="p">(</span><span class="nx">i</span><span class="p">),</span>
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<a id="__codelineno-63-20" name="__codelineno-63-20" href="#__codelineno-63-20"></a><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="p">(</span><span class="nx">i</span><span class="p">);</span>
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<a id="__codelineno-63-21" name="__codelineno-63-21" href="#__codelineno-63-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="p">;</span>
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<a id="__codelineno-63-22" name="__codelineno-63-22" href="#__codelineno-63-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">l</span><span class="p">;</span>
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<a id="__codelineno-63-23" name="__codelineno-63-23" href="#__codelineno-63-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">maxHeap</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
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<a id="__codelineno-63-24" name="__codelineno-63-24" href="#__codelineno-63-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-63-25" name="__codelineno-63-25" href="#__codelineno-63-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-63-26" name="__codelineno-63-26" href="#__codelineno-63-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-63-27" name="__codelineno-63-27" href="#__codelineno-63-27"></a><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="nx">swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">ma</span><span class="p">);</span>
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<a id="__codelineno-63-28" name="__codelineno-63-28" href="#__codelineno-63-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-63-29" name="__codelineno-63-29" href="#__codelineno-63-29"></a><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">ma</span><span class="p">;</span>
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<a id="__codelineno-63-30" name="__codelineno-63-30" href="#__codelineno-63-30"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-63-31" name="__codelineno-63-31" href="#__codelineno-63-31"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">Exception</span><span class="p">(</span><span class="s1">'堆为空'</span><span class="p">);</span>
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<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
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<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
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<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
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<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-64-12" name="__codelineno-64-12" href="#__codelineno-64-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
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<a id="__codelineno-64-13" name="__codelineno-64-13" href="#__codelineno-64-13"></a><span class="p">}</span>
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<a id="__codelineno-64-14" name="__codelineno-64-14" href="#__codelineno-64-14"></a>
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<a id="__codelineno-64-15" name="__codelineno-64-15" href="#__codelineno-64-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-64-16" name="__codelineno-64-16" href="#__codelineno-64-16"></a><span class="kt">void</span><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-64-17" name="__codelineno-64-17" href="#__codelineno-64-17"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-64-18" name="__codelineno-64-18" href="#__codelineno-64-18"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-64-19" name="__codelineno-64-19" href="#__codelineno-64-19"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_left</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-64-20" name="__codelineno-64-20" href="#__codelineno-64-20"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">_right</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-64-21" name="__codelineno-64-21" href="#__codelineno-64-21"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
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<a id="__codelineno-64-22" name="__codelineno-64-22" href="#__codelineno-64-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
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<a id="__codelineno-64-23" name="__codelineno-64-23" href="#__codelineno-64-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">_maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
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<a id="__codelineno-64-24" name="__codelineno-64-24" href="#__codelineno-64-24"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-64-25" name="__codelineno-64-25" href="#__codelineno-64-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-64-26" name="__codelineno-64-26" href="#__codelineno-64-26"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-64-27" name="__codelineno-64-27" href="#__codelineno-64-27"></a><span class="w"> </span><span class="n">_swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
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<a id="__codelineno-64-28" name="__codelineno-64-28" href="#__codelineno-64-28"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-64-29" name="__codelineno-64-29" href="#__codelineno-64-29"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
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<a id="__codelineno-64-30" name="__codelineno-64-30" href="#__codelineno-64-30"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-64-31" name="__codelineno-64-31" href="#__codelineno-64-31"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="k">fn</span> <span class="nf">pop</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">)</span><span class="w"> </span>-> <span class="kt">i32</span> <span class="p">{</span>
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<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">is_empty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a><span class="w"> </span><span class="fm">panic!</span><span class="p">(</span><span class="s">"index out of bounds"</span><span class="p">);</span>
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<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-65-10" name="__codelineno-65-10" href="#__codelineno-65-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-65-12" name="__codelineno-65-12" href="#__codelineno-65-12"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-65-13" name="__codelineno-65-13" href="#__codelineno-65-13"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-65-14" name="__codelineno-65-14" href="#__codelineno-65-14"></a><span class="w"> </span><span class="n">val</span>
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<a id="__codelineno-65-15" name="__codelineno-65-15" href="#__codelineno-65-15"></a><span class="p">}</span>
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<a id="__codelineno-65-16" name="__codelineno-65-16" href="#__codelineno-65-16"></a>
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<a id="__codelineno-65-17" name="__codelineno-65-17" href="#__codelineno-65-17"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-65-18" name="__codelineno-65-18" href="#__codelineno-65-18"></a><span class="k">fn</span> <span class="nf">sift_down</span><span class="p">(</span><span class="o">&</span><span class="k">mut</span><span class="w"> </span><span class="bp">self</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">i</span>: <span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-65-19" name="__codelineno-65-19" href="#__codelineno-65-19"></a><span class="w"> </span><span class="k">loop</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-65-20" name="__codelineno-65-20" href="#__codelineno-65-20"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-65-21" name="__codelineno-65-21" href="#__codelineno-65-21"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="bp">Self</span>::<span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="bp">Self</span>::<span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-65-22" name="__codelineno-65-22" href="#__codelineno-65-22"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-65-23" name="__codelineno-65-23" href="#__codelineno-65-23"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
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<a id="__codelineno-65-24" name="__codelineno-65-24" href="#__codelineno-65-24"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-65-25" name="__codelineno-65-25" href="#__codelineno-65-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-65-26" name="__codelineno-65-26" href="#__codelineno-65-26"></a><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
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<a id="__codelineno-65-27" name="__codelineno-65-27" href="#__codelineno-65-27"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-65-28" name="__codelineno-65-28" href="#__codelineno-65-28"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-65-29" name="__codelineno-65-29" href="#__codelineno-65-29"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-65-30" name="__codelineno-65-30" href="#__codelineno-65-30"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-65-31" name="__codelineno-65-31" href="#__codelineno-65-31"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-65-32" name="__codelineno-65-32" href="#__codelineno-65-32"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-65-33" name="__codelineno-65-33" href="#__codelineno-65-33"></a><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
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<a id="__codelineno-65-34" name="__codelineno-65-34" href="#__codelineno-65-34"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-65-35" name="__codelineno-65-35" href="#__codelineno-65-35"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
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<a id="__codelineno-65-36" name="__codelineno-65-36" href="#__codelineno-65-36"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-65-37" name="__codelineno-65-37" href="#__codelineno-65-37"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">"heap is empty!"</span><span class="p">);</span>
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<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
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<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-66-8" name="__codelineno-66-8" href="#__codelineno-66-8"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-66-9" name="__codelineno-66-9" href="#__codelineno-66-9"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-66-10" name="__codelineno-66-10" href="#__codelineno-66-10"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
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<a id="__codelineno-66-12" name="__codelineno-66-12" href="#__codelineno-66-12"></a><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
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<a id="__codelineno-66-13" name="__codelineno-66-13" href="#__codelineno-66-13"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-66-14" name="__codelineno-66-14" href="#__codelineno-66-14"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-66-15" name="__codelineno-66-15" href="#__codelineno-66-15"></a>
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<a id="__codelineno-66-16" name="__codelineno-66-16" href="#__codelineno-66-16"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-66-17" name="__codelineno-66-17" href="#__codelineno-66-17"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
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<a id="__codelineno-66-18" name="__codelineno-66-18" href="#__codelineno-66-18"></a><span class="p">}</span>
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<a id="__codelineno-66-19" name="__codelineno-66-19" href="#__codelineno-66-19"></a>
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<a id="__codelineno-66-20" name="__codelineno-66-20" href="#__codelineno-66-20"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-66-21" name="__codelineno-66-21" href="#__codelineno-66-21"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="n">MaxHeap</span><span class="w"> </span><span class="o">*</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-66-22" name="__codelineno-66-22" href="#__codelineno-66-22"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-66-23" name="__codelineno-66-23" href="#__codelineno-66-23"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 max</span>
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<a id="__codelineno-66-24" name="__codelineno-66-24" href="#__codelineno-66-24"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-66-25" name="__codelineno-66-25" href="#__codelineno-66-25"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-66-26" name="__codelineno-66-26" href="#__codelineno-66-26"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
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<a id="__codelineno-66-27" name="__codelineno-66-27" href="#__codelineno-66-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">max</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-66-28" name="__codelineno-66-28" href="#__codelineno-66-28"></a><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
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<a id="__codelineno-66-29" name="__codelineno-66-29" href="#__codelineno-66-29"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-66-30" name="__codelineno-66-30" href="#__codelineno-66-30"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="o">-></span><span class="n">data</span><span class="p">[</span><span class="n">max</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-66-31" name="__codelineno-66-31" href="#__codelineno-66-31"></a><span class="w"> </span><span class="n">max</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
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<a id="__codelineno-66-32" name="__codelineno-66-32" href="#__codelineno-66-32"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-66-33" name="__codelineno-66-33" href="#__codelineno-66-33"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-66-34" name="__codelineno-66-34" href="#__codelineno-66-34"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">max</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-66-35" name="__codelineno-66-35" href="#__codelineno-66-35"></a><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-66-36" name="__codelineno-66-36" href="#__codelineno-66-36"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-66-37" name="__codelineno-66-37" href="#__codelineno-66-37"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-66-38" name="__codelineno-66-38" href="#__codelineno-66-38"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">max</span><span class="p">);</span>
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<a id="__codelineno-66-39" name="__codelineno-66-39" href="#__codelineno-66-39"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-66-40" name="__codelineno-66-40" href="#__codelineno-66-40"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">;</span>
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<a id="__codelineno-66-41" name="__codelineno-66-41" href="#__codelineno-66-41"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-66-42" name="__codelineno-66-42" href="#__codelineno-66-42"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 元素出堆 */</span>
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<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">pop</span><span class="p">():</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w"> </span><span class="c1">// 判空处理</span>
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<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">throw</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">()</span>
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<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
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<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">removeAt</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">)</span>
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<a id="__codelineno-67-9" name="__codelineno-67-9" href="#__codelineno-67-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-67-10" name="__codelineno-67-10" href="#__codelineno-67-10"></a><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
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<a id="__codelineno-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-67-12" name="__codelineno-67-12" href="#__codelineno-67-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">_val</span>
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<a id="__codelineno-67-13" name="__codelineno-67-13" href="#__codelineno-67-13"></a><span class="p">}</span>
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<a id="__codelineno-67-14" name="__codelineno-67-14" href="#__codelineno-67-14"></a>
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<a id="__codelineno-67-15" name="__codelineno-67-15" href="#__codelineno-67-15"></a><span class="cm">/* 从节点 i 开始，从顶至底堆化 */</span>
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<a id="__codelineno-67-16" name="__codelineno-67-16" href="#__codelineno-67-16"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="nb">it</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-67-17" name="__codelineno-67-17" href="#__codelineno-67-17"></a><span class="w"> </span><span class="c1">// Kotlin的函数参数不可变，因此创建临时变量</span>
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<a id="__codelineno-67-18" name="__codelineno-67-18" href="#__codelineno-67-18"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">it</span>
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<a id="__codelineno-67-19" name="__codelineno-67-19" href="#__codelineno-67-19"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-67-20" name="__codelineno-67-20" href="#__codelineno-67-20"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-67-21" name="__codelineno-67-21" href="#__codelineno-67-21"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
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<a id="__codelineno-67-22" name="__codelineno-67-22" href="#__codelineno-67-22"></a><span class="w"> </span><span class="kd">val</span><span class="w"> </span><span class="nv">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
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<a id="__codelineno-67-23" name="__codelineno-67-23" href="#__codelineno-67-23"></a><span class="w"> </span><span class="kd">var</span><span class="w"> </span><span class="nv">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span>
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<a id="__codelineno-67-24" name="__codelineno-67-24" href="#__codelineno-67-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">l</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span>
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<a id="__codelineno-67-25" name="__codelineno-67-25" href="#__codelineno-67-25"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">maxHeap</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span>
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<a id="__codelineno-67-26" name="__codelineno-67-26" href="#__codelineno-67-26"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-67-27" name="__codelineno-67-27" href="#__codelineno-67-27"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span>
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<a id="__codelineno-67-28" name="__codelineno-67-28" href="#__codelineno-67-28"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-67-29" name="__codelineno-67-29" href="#__codelineno-67-29"></a><span class="w"> </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">)</span>
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<a id="__codelineno-67-30" name="__codelineno-67-30" href="#__codelineno-67-30"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-67-31" name="__codelineno-67-31" href="#__codelineno-67-31"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span>
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<a id="__codelineno-67-32" name="__codelineno-67-32" href="#__codelineno-67-32"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-67-33" name="__codelineno-67-33" href="#__codelineno-67-33"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pop</span><span class="p">}</span>
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<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a>
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<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">sift_down</span><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="c1">// 元素出堆</span>
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<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="n">T</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w"> </span><span class="c1">// 判断处理</span>
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<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="k">unreachable</span><span class="p">;</span>
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<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w"> </span><span class="c1">// 交换根节点与最右叶节点（交换首元素与尾元素）</span>
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<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
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<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w"> </span><span class="c1">// 删除节点</span>
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<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
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<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="w"> </span><span class="c1">// 从顶至底堆化</span>
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<a id="__codelineno-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
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<a id="__codelineno-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></a><span class="w"> </span><span class="c1">// 返回堆顶元素</span>
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<a id="__codelineno-69-12" name="__codelineno-69-12" href="#__codelineno-69-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
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<a id="__codelineno-69-13" name="__codelineno-69-13" href="#__codelineno-69-13"></a><span class="p">}</span><span class="w"> </span>
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<a id="__codelineno-69-14" name="__codelineno-69-14" href="#__codelineno-69-14"></a>
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<a id="__codelineno-69-15" name="__codelineno-69-15" href="#__codelineno-69-15"></a><span class="c1">// 从节点 i 开始，从顶至底堆化</span>
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<a id="__codelineno-69-16" name="__codelineno-69-16" href="#__codelineno-69-16"></a><span class="k">fn</span><span class="w"> </span><span class="n">siftDown</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">i_</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-69-17" name="__codelineno-69-17" href="#__codelineno-69-17"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i_</span><span class="p">;</span>
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<a id="__codelineno-69-18" name="__codelineno-69-18" href="#__codelineno-69-18"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-69-19" name="__codelineno-69-19" href="#__codelineno-69-19"></a><span class="w"> </span><span class="c1">// 判断节点 i, l, r 中值最大的节点，记为 ma</span>
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<a id="__codelineno-69-20" name="__codelineno-69-20" href="#__codelineno-69-20"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-69-21" name="__codelineno-69-21" href="#__codelineno-69-21"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
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<a id="__codelineno-69-22" name="__codelineno-69-22" href="#__codelineno-69-22"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
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<a id="__codelineno-69-23" name="__codelineno-69-23" href="#__codelineno-69-23"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
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<a id="__codelineno-69-24" name="__codelineno-69-24" href="#__codelineno-69-24"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">max_heap</span><span class="p">.</span><span class="o">?</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
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<a id="__codelineno-69-25" name="__codelineno-69-25" href="#__codelineno-69-25"></a><span class="w"> </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
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<a id="__codelineno-69-26" name="__codelineno-69-26" href="#__codelineno-69-26"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
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<a id="__codelineno-69-27" name="__codelineno-69-27" href="#__codelineno-69-27"></a><span class="w"> </span><span class="c1">// 交换两节点</span>
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<a id="__codelineno-69-28" name="__codelineno-69-28" href="#__codelineno-69-28"></a><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
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<a id="__codelineno-69-29" name="__codelineno-69-29" href="#__codelineno-69-29"></a><span class="w"> </span><span class="c1">// 循环向下堆化</span>
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<a id="__codelineno-69-30" name="__codelineno-69-30" href="#__codelineno-69-30"></a><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
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<a id="__codelineno-69-31" name="__codelineno-69-31" href="#__codelineno-69-31"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-69-32" name="__codelineno-69-32" href="#__codelineno-69-32"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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</div>
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</div>
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<details class="pythontutor">
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<summary>Code Visualization</summary>
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<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=class%20MaxHeap%3A%0A%20%20%20%20%22%22%22%E5%A4%A7%E9%A1%B6%E5%A0%86%22%22%22%0A%0A%20%20%20%20def%20__init__%28self,%20nums%3A%20list%5Bint%5D%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E6%9E%84%E9%80%A0%E6%96%B9%E6%B3%95%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%B0%86%E5%88%97%E8%A1%A8%E5%85%83%E7%B4%A0%E5%8E%9F%E5%B0%81%E4%B8%8D%E5%8A%A8%E6%B7%BB%E5%8A%A0%E8%BF%9B%E5%A0%86%0A%20%20%20%20%20%20%20%20self.max_heap%20%3D%20nums%0A%0A%20%20%20%20def%20left%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%B7%A6%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%201%0A%0A%20%20%20%20def%20right%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%8F%B3%E5%AD%90%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%202%20*%20i%20%2B%202%0A%0A%20%20%20%20def%20parent%28self,%20i%3A%20int%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E7%88%B6%E8%8A%82%E7%82%B9%E7%9A%84%E7%B4%A2%E5%BC%95%22%22%22%0A%20%20%20%20%20%20%20%20return%20%28i%20-%201%29%20//%202%20%20%23%20%E5%90%91%E4%B8%8B%E6%95%B4%E9%99%A4%0A%0A%20%20%20%20def%20swap%28self,%20i%3A%20int,%20j%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BA%A4%E6%8D%A2%E5%85%83%E7%B4%A0%22%22%22%0A%20%20%20%20%20%20%20%20self.max_heap%5Bi%5D,%20self.max_heap%5Bj%5D%20%3D%20self.max_heap%5Bj%5D,%20self.max_heap%5Bi%5D%0A%0A%20%20%20%20def%20size%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E8%8E%B7%E5%8F%96%E5%A0%86%E5%A4%A7%E5%B0%8F%22%22%22%0A%20%20%20%20%20%20%20%20return%20len%28self.max_heap%29%0A%0A%20%20%20%20def%20is_empty%28self%29%20-%3E%20bool%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%88%A4%E6%96%AD%E5%A0%86%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%22%22%22%0A%20%20%20%20%20%20%20%20return%20self.size%28%29%20%3D%3D%200%0A%0A%20%20%20%20def%20pop%28self%29%20-%3E%20int%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E5%85%83%E7%B4%A0%E5%87%BA%E5%A0%86%22%22%22%0A%20%20%20%20%20%20%20%20%23%20%E5%88%A4%E7%A9%BA%E5%A4%84%E7%90%86%0A%20%20%20%20%20%20%20%20if%20self.is_empty%28%29%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20raise%20IndexError%28%22%E5%A0%86%E4%B8%BA%E7%A9%BA%22%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E6%A0%B9%E8%8A%82%E7%82%B9%E4%B8%8E%E6%9C%80%E5%8F%B3%E5%8F%B6%E8%8A%82%E7%82%B9%EF%BC%88%E4%BA%A4%E6%8D%A2%E9%A6%96%E5%85%83%E7%B4%A0%E4%B8%8E%E5%B0%BE%E5%85%83%E7%B4%A0%EF%BC%89%0A%20%20%20%20%20%20%20%20self.swap%280,%20self.size%28%29%20-%201%29%0A%20%20%20%20%20%20%20%20%23%20%E5%88%A0%E9%99%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20val%20%3D%20self.max_heap.pop%28%29%0A%20%20%20%20%20%20%20%20%23%20%E4%BB%8E%E9%A1%B6%E8%87%B3%E5%BA%95%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20self.sift_down%280%29%0A%20%20%20%20%20%20%20%20%23%20%E8%BF%94%E5%9B%9E%E5%A0%86%E9%A1%B6%E5%85%83%E7%B4%A0%0A%20%20%20%20%20%20%20%20return%20val%0A%0A%20%20%20%20def%20sift_down%28self,%20i%3A%20int%29%3A%0A%20%20%20%20%20%20%20%20%22%22%22%E4%BB%8E%E8%8A%82%E7%82%B9%20i%20%E5%BC%80%E5%A7%8B%EF%BC%8C%E4%BB%8E%E9%A1%B6%E8%87%B3%E5%BA%95%E5%A0%86%E5%8C%96%22%22%22%0A%20%20%20%20%20%20%20%20while%20True%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E8%8A%82%E7%82%B9%20i,%20l,%20r%20%E4%B8%AD%E5%80%BC%E6%9C%80%E5%A4%A7%E7%9A%84%E8%8A%82%E7%82%B9%EF%BC%8C%E8%AE%B0%E4%B8%BA%20ma%0A%20%20%20%20%20%20%20%20%20%20%20%20l,%20r,%20ma%20%3D%20self.left%28i%29,%20self.right%28i%29,%20i%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20l%20%3C%20self.size%28%29%20and%20self.max_heap%5Bl%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20l%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20r%20%3C%20self.size%28%29%20and%20self.max_heap%5Br%5D%20%3E%20self.max_heap%5Bma%5D%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20ma%20%3D%20r%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E8%8B%A5%E8%8A%82%E7%82%B9%20i%20%E6%9C%80%E5%A4%A7%E6%88%96%E7%B4%A2%E5%BC%95%20l,%20r%20%E8%B6%8A%E7%95%8C%EF%BC%8C%E5%88%99%E6%97%A0%E9%A1%BB%E7%BB%A7%E7%BB%AD%E5%A0%86%E5%8C%96%EF%BC%8C%E8%B7%B3%E5%87%BA%0A%20%20%20%20%20%20%20%20%20%20%20%20if%20ma%20%3D%3D%20i%3A%0A%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20%20break%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E4%BA%A4%E6%8D%A2%E4%B8%A4%E8%8A%82%E7%82%B9%0A%20%20%20%20%20%20%20%20%20%20%20%20self.swap%28i,%20ma%29%0A%20%20%20%20%20%20%20%20%20%20%20%20%23%20%E5%BE%AA%E7%8E%AF%E5%90%91%E4%B8%8B%E5%A0%86%E5%8C%96%0A%20%20%20%20%20%20%20%20%20%20%20%20i%20%3D%20ma%0A%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%A4%A7%E9%A1%B6%E5%A0%86%0A%20%20%20%20%23%20%E8%AF%B7%E6%B3%A8%E6%84%8F%EF%BC%8C%E8%BE%93%E5%85%A5%E6%95%B0%E7%BB%84%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%B7%B2%E7%BB%8F%E6%98%AF%E4%B8%80%E4%B8%AA%E5%90%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<div style="margin-top: 5px;"><a 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target="_blank" rel="noopener noreferrer">Full Screen ></a></div></p>
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</details>
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<h2 id="813-common-applications-of-heaps">8.1.3 Common applications of heaps<a class="headerlink" href="#813-common-applications-of-heaps" title="Permanent link">¶</a></h2>
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<ul>
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<li><strong>Priority Queue</strong>: Heaps are often the preferred data structure for implementing priority queues, with both enqueue and dequeue operations having a time complexity of <span class="arithmatex">\(O(\log n)\)</span>, and building a queue having a time complexity of <span class="arithmatex">\(O(n)\)</span>, all of which are very efficient.</li>
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<li><strong>Heap Sort</strong>: Given a set of data, we can create a heap from them and then continually perform element removal operations to obtain ordered data. However, we usually use a more elegant method to implement heap sort, as detailed in the "Heap Sort" section.</li>
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<li><strong>Finding the Largest <span class="arithmatex">\(k\)</span> Elements</strong>: This is a classic algorithm problem and also a typical application, such as selecting the top 10 hot news for Weibo hot search, picking the top 10 selling products, etc.</li>
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