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<a href="../binary_tree/" class="md-nav__link">
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7.1 Binary tree
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<span class="md-ellipsis">
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7.2 Binary tree traversal
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7.3 Array Representation of tree
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<span class="md-nav__icon md-icon"></span>
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7.3 Array Representation of tree
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</a>
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Table of contents
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<span class="md-ellipsis">
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7.3.1 Representing perfect binary trees
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<a href="#732-representing-any-binary-tree" class="md-nav__link">
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<span class="md-ellipsis">
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7.3.2 Representing any binary tree
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7.3.3 Advantages and limitations
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7.4 Binary Search tree
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7.5 AVL tree *
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7.6 Summary
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Chapter 8. Heap
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</a>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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Chapter 8. Heap
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<span class="md-ellipsis">
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8.1 Heap
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<span class="md-ellipsis">
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8.2 Building a heap
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8.3 Top-k problem
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<a href="../../chapter_heap/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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8.4 Summary
|
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
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<span class="md-ellipsis">
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Chapter 9. Graph
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</a>
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<label class="md-nav__title" for="__nav_11">
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<span class="md-nav__icon md-icon"></span>
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Chapter 9. Graph
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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9.1 Graph
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<span class="md-ellipsis">
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9.2 Basic graph operations
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<span class="md-ellipsis">
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9.3 Graph traversal
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</span>
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9.4 Summary
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<a href="../../chapter_searching/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
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<span class="md-ellipsis">
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Chapter 10. Searching
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</a>
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<label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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Chapter 10. Searching
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
|
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10.1 Binary search
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</span>
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</li>
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<span class="md-ellipsis">
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10.2 Binary search insertion
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</span>
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<span class="md-ellipsis">
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10.3 Binary search boundaries
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
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<span class="md-ellipsis">
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10.4 Hashing optimization strategies
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</span>
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</a>
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<span class="md-ellipsis">
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10.5 Search algorithms revisited
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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_searching/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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10.6 Summary
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</span>
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</a>
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</li>
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<span class="md-ellipsis">
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Chapter 11. Sorting
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<span class="md-nav__icon md-icon"></span>
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Chapter 11. Sorting
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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11.1 Sorting algorithms
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</span>
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</a>
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<a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.2 Selection sort
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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_sorting/bubble_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.3 Bubble sort
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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_sorting/insertion_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.4 Insertion sort
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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_sorting/quick_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.5 Quick sort
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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_sorting/merge_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.6 Merge sort
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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_sorting/heap_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.7 Heap sort
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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_sorting/bucket_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.8 Bucket sort
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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_sorting/counting_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.9 Counting sort
|
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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_sorting/radix_sort/" class="md-nav__link">
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<span class="md-ellipsis">
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11.10 Radix sort
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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_sorting/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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11.11 Summary
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</a>
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</li>
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<span class="md-ellipsis">
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Chapter 12. Divide and conquer
|
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</span>
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</a>
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<label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
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<span class="md-nav__icon md-icon"></span>
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Chapter 12. Divide and conquer
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
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<span class="md-ellipsis">
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12.1 Divide and conquer algorithms
|
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</span>
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</a>
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<a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
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<span class="md-ellipsis">
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12.2 Divide and conquer search strategy
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<a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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12.3 Building binary tree problem
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12.4 Tower of Hanoi Problem
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12.5 Summary
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</span>
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</a>
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<span class="md-ellipsis">
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Chapter 13. Backtracking
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</span>
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</a>
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<span class="md-nav__icon md-icon"></span>
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Chapter 13. Backtracking
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
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<span class="md-ellipsis">
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13.1 Backtracking algorithms
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</span>
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</a>
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<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
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13.2 Permutation problem
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</span>
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</a>
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<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
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13.3 Subset sum problem
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</span>
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</a>
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<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
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13.4 n queens problem
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</span>
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</a>
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<span class="md-ellipsis">
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13.5 Summary
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</span>
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</a>
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</nav>
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<span class="md-ellipsis">
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Chapter 14. Dynamic programming
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</span>
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</a>
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<h1 id="73-array-representation-of-binary-trees">7.3 Array representation of binary trees<a class="headerlink" href="#73-array-representation-of-binary-trees" title="Permanent link">¶</a></h1>
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<p>Under the linked list representation, the storage unit of a binary tree is a node <code>TreeNode</code>, with nodes connected by pointers. The basic operations of binary trees under the linked list representation were introduced in the previous section.</p>
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<p>So, can we use an array to represent a binary tree? The answer is yes.</p>
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<h2 id="731-representing-perfect-binary-trees">7.3.1 Representing perfect binary trees<a class="headerlink" href="#731-representing-perfect-binary-trees" title="Permanent link">¶</a></h2>
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<p>Let's analyze a simple case first. Given a perfect binary tree, we store all nodes in an array according to the order of level-order traversal, where each node corresponds to a unique array index.</p>
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<p>Based on the characteristics of level-order traversal, we can deduce a "mapping formula" between the index of a parent node and its children: <strong>If a node's index is <span class="arithmatex">\(i\)</span>, then the index of its left child is <span class="arithmatex">\(2i + 1\)</span> and the right child is <span class="arithmatex">\(2i + 2\)</span></strong>. Figure 7-12 shows the mapping relationship between the indices of various nodes.</p>
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<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Array representation of a perfect binary tree" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_binary_tree.png" /></a></p>
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<p align="center"> Figure 7-12 Array representation of a perfect binary tree </p>
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<p><strong>The mapping formula plays a role similar to the node references (pointers) in linked lists</strong>. Given any node in the array, we can access its left (right) child node using the mapping formula.</p>
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<h2 id="732-representing-any-binary-tree">7.3.2 Representing any binary tree<a class="headerlink" href="#732-representing-any-binary-tree" title="Permanent link">¶</a></h2>
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<p>Perfect binary trees are a special case; there are often many <code>None</code> values in the middle levels of a binary tree. Since the sequence of level-order traversal does not include these <code>None</code> values, we cannot solely rely on this sequence to deduce the number and distribution of <code>None</code> values. <strong>This means that multiple binary tree structures can match the same level-order traversal sequence</strong>.</p>
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<p>As shown in Figure 7-13, given a non-perfect binary tree, the above method of array representation fails.</p>
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<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_without_empty.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Level-order traversal sequence corresponds to multiple binary tree possibilities" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_without_empty.png" /></a></p>
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<p align="center"> Figure 7-13 Level-order traversal sequence corresponds to multiple binary tree possibilities </p>
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<p>To solve this problem, <strong>we can consider explicitly writing out all <code>None</code> values in the level-order traversal sequence</strong>. As shown in Figure 7-14, after this treatment, the level-order traversal sequence can uniquely represent a binary tree. Example code is as follows:</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_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"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># Array representation of a binary tree</span>
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># Using None to represent empty slots</span>
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">tree</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">15</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"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* Array representation of a binary tree */</span>
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<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// Using the maximum integer value INT_MAX to mark empty slots</span>
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<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></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">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</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">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">15</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"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* Array representation of a binary tree */</span>
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<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// Using the Integer wrapper class allows for using null to mark empty slots</span>
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<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</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><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="w"> </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"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* Array representation of a binary tree */</span>
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<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// Using nullable int (int?) allows for using null to mark empty slots</span>
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<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kt">int?</span><span class="p">[]</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">1</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">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</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"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* Array representation of a binary tree */</span>
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<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Using an any type slice, allowing for nil to mark empty slots</span>
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<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="nx">tree</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="p">{</span><span class="mi">1</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">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</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"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* Array representation of a binary tree */</span>
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<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Using optional Int (Int?) allows for using nil to mark empty slots</span>
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<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">let</span> <span class="nv">tree</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">?]</span> <span class="p">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="kc">nil</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="kc">nil</span><span class="p">,</span> <span class="kc">nil</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="kc">nil</span><span class="p">,</span> <span class="kc">nil</span><span class="p">,</span> <span class="mi">15</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"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* Array representation of a binary tree */</span>
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<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// Using null to represent empty slots</span>
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<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">15</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"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* Array representation of a binary tree */</span>
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<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// Using null to represent empty slots</span>
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<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">tree</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">15</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"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* Array representation of a binary tree */</span>
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<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// Using nullable int (int?) allows for using null to mark empty slots</span>
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<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">?></span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">1</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">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</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"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* Array representation of a binary tree */</span>
|
|
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// Using None to mark empty slots</span>
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<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nb">Some</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">4</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">6</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">7</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">8</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">9</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">12</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">15</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"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* Array representation of a binary tree */</span>
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<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="c1">// Using the maximum int value to mark empty slots, therefore, node values must not be INT_MAX</span>
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<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="kt">int</span><span class="w"> </span><span class="n">tree</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</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">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">};</span>
|
|
</code></pre></div>
|
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</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* Array representation of a binary tree */</span>
|
|
<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// Using null to represent empty slots</span>
|
|
<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="p">(</span><span class="w"> </span><span class="m">1</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">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</span><span class="w"> </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"><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"><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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<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_with_empty.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Array representation of any type of binary tree" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_with_empty.png" /></a></p>
|
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<p align="center"> Figure 7-14 Array representation of any type of binary tree </p>
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<p>It's worth noting that <strong>complete binary trees are very suitable for array representation</strong>. Recalling the definition of a complete binary tree, <code>None</code> appears only at the bottom level and towards the right, <strong>meaning all <code>None</code> values definitely appear at the end of the level-order traversal sequence</strong>.</p>
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<p>This means that when using an array to represent a complete binary tree, it's possible to omit storing all <code>None</code> values, which is very convenient. Figure 7-15 gives an example.</p>
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<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Array representation of a complete binary tree" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" /></a></p>
|
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<p align="center"> Figure 7-15 Array representation of a complete binary tree </p>
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<p>The following code implements a binary tree based on array representation, including the following operations:</p>
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<ul>
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<li>Given a node, obtain its value, left (right) child node, and parent node.</li>
|
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<li>Obtain the pre-order, in-order, post-order, and level-order traversal sequences.</li>
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</ul>
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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">array_binary_tree.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">class</span> <span class="nc">ArrayBinaryTree</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">"""Array-based binary tree class"""</span>
|
|
<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>
|
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<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]):</span>
|
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<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w"> </span><span class="sd">"""Constructor"""</span>
|
|
<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a> <span class="bp">self</span><span class="o">.</span><span class="n">_tree</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
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<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>
|
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<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a> <span class="k">def</span> <span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
|
|
<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w"> </span><span class="sd">"""List capacity"""</span>
|
|
<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a> <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_tree</span><span class="p">)</span>
|
|
<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>
|
|
<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a> <span class="k">def</span> <span class="nf">val</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="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
|
<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w"> </span><span class="sd">"""Get the value of the node at index i"""</span>
|
|
<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a> <span class="c1"># If the index is out of bounds, return None, representing a vacancy</span>
|
|
<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a> <span class="k">if</span> <span class="n">i</span> <span class="o"><</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">>=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">():</span>
|
|
<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a> <span class="k">return</span> <span class="kc">None</span>
|
|
<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_tree</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
|
<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>
|
|
<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></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="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
|
<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w"> </span><span class="sd">"""Get the index of the left child of the node at index i"""</span>
|
|
<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></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>
|
|
<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>
|
|
<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></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="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
|
<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w"> </span><span class="sd">"""Get the index of the right child of the node at index i"""</span>
|
|
<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></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>
|
|
<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>
|
|
<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></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="o">|</span> <span class="kc">None</span><span class="p">:</span>
|
|
<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w"> </span><span class="sd">"""Get the index of the parent of the node at index i"""</span>
|
|
<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></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>
|
|
<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a>
|
|
<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a> <span class="k">def</span> <span class="nf">level_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
|
|
<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w"> </span><span class="sd">"""Level-order traversal"""</span>
|
|
<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
|
|
<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a> <span class="c1"># Traverse array</span>
|
|
<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
|
|
<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
|
<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
|
|
<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
|
|
<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a>
|
|
<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a> <span class="k">def</span> <span class="nf">dfs</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="n">order</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
|
|
<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w"> </span><span class="sd">"""Depth-first traversal"""</span>
|
|
<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a> <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
|
|
<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a> <span class="k">return</span>
|
|
<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a> <span class="c1"># Pre-order traversal</span>
|
|
<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a> <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">"pre"</span><span class="p">:</span>
|
|
<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
|
|
<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</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="n">order</span><span class="p">)</span>
|
|
<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a> <span class="c1"># In-order traversal</span>
|
|
<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a> <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">"in"</span><span class="p">:</span>
|
|
<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
|
|
<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</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">order</span><span class="p">)</span>
|
|
<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a> <span class="c1"># Post-order traversal</span>
|
|
<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a> <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">"post"</span><span class="p">:</span>
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|
<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
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<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a>
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<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a> <span class="k">def</span> <span class="nf">pre_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
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<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w"> </span><span class="sd">"""Pre-order traversal"""</span>
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<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
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<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">"pre"</span><span class="p">)</span>
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<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
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<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a>
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<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a> <span class="k">def</span> <span class="nf">in_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
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<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w"> </span><span class="sd">"""In-order traversal"""</span>
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<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
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<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">"in"</span><span class="p">)</span>
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<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
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<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a>
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<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a> <span class="k">def</span> <span class="nf">post_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-></span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
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<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w"> </span><span class="sd">"""Post-order traversal"""</span>
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<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a> <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
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<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">"post"</span><span class="p">)</span>
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<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a> <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</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">array_binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* Array-based binary tree class */</span>
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<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</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">public</span><span class="o">:</span>
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<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w"> </span><span class="cm">/* Constructor */</span>
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<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w"> </span><span class="n">ArrayBinaryTree</span><span class="p">(</span><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">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
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<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><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>
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<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w"> </span><span class="cm">/* List capacity */</span>
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<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
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<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><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>
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<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
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<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</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-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w"> </span><span class="c1">// If index is out of bounds, return INT_MAX, representing a null</span>
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<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w"> </span><span class="k">if</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">0</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="n">size</span><span class="p">())</span>
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<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></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-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
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<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w"> </span><span class="p">}</span>
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|
<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a>
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<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w"> </span><span class="cm">/* Get the index of the left child of the node at index i */</span>
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<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w"> </span><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>
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<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></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-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w"> </span><span class="p">}</span>
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|
<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a>
|
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<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w"> </span><span class="cm">/* Get the index of the right child of the node at index i */</span>
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<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w"> </span><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>
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<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></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-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a>
|
|
<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w"> </span><span class="cm">/* Get the index of the parent of the node at index i */</span>
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<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w"> </span><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-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></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>
|
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<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a>
|
|
<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
|
|
<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w"> </span><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">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w"> </span><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">res</span><span class="p">;</span>
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<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w"> </span><span class="c1">// Traverse array</span>
|
|
<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</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="p">;</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">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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">INT_MAX</span><span class="p">)</span>
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|
<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
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<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
|
<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a>
|
|
<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w"> </span><span class="cm">/* Pre-order traversal */</span>
|
|
<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w"> </span><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">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w"> </span><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">res</span><span class="p">;</span>
|
|
<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
|
<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a>
|
|
<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w"> </span><span class="cm">/* In-order traversal */</span>
|
|
<a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w"> </span><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">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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|
<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w"> </span><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">res</span><span class="p">;</span>
|
|
<a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
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|
<a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
|
<a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a>
|
|
<a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></a><span class="w"> </span><span class="cm">/* Post-order traversal */</span>
|
|
<a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></a><span class="w"> </span><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">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-15-64" name="__codelineno-15-64" href="#__codelineno-15-64"></a><span class="w"> </span><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">res</span><span class="p">;</span>
|
|
<a id="__codelineno-15-65" name="__codelineno-15-65" href="#__codelineno-15-65"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-15-66" name="__codelineno-15-66" href="#__codelineno-15-66"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
|
<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-15-68" name="__codelineno-15-68" href="#__codelineno-15-68"></a>
|
|
<a id="__codelineno-15-69" name="__codelineno-15-69" href="#__codelineno-15-69"></a><span class="w"> </span><span class="k">private</span><span class="o">:</span>
|
|
<a id="__codelineno-15-70" name="__codelineno-15-70" href="#__codelineno-15-70"></a><span class="w"> </span><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">tree</span><span class="p">;</span>
|
|
<a id="__codelineno-15-71" name="__codelineno-15-71" href="#__codelineno-15-71"></a>
|
|
<a id="__codelineno-15-72" name="__codelineno-15-72" href="#__codelineno-15-72"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
|
|
<a id="__codelineno-15-73" name="__codelineno-15-73" href="#__codelineno-15-73"></a><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</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="n">string</span><span class="w"> </span><span class="n">order</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="w"> </span><span class="o">&</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-15-74" name="__codelineno-15-74" href="#__codelineno-15-74"></a><span class="w"> </span><span class="c1">// If it is an empty spot, return</span>
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<a id="__codelineno-15-75" name="__codelineno-15-75" href="#__codelineno-15-75"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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">INT_MAX</span><span class="p">)</span>
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<a id="__codelineno-15-76" name="__codelineno-15-76" href="#__codelineno-15-76"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-15-77" name="__codelineno-15-77" href="#__codelineno-15-77"></a><span class="w"> </span><span class="c1">// Pre-order traversal</span>
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|
<a id="__codelineno-15-78" name="__codelineno-15-78" href="#__codelineno-15-78"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"pre"</span><span class="p">)</span>
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<a id="__codelineno-15-79" name="__codelineno-15-79" href="#__codelineno-15-79"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
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|
<a id="__codelineno-15-80" name="__codelineno-15-80" href="#__codelineno-15-80"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</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">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-15-81" name="__codelineno-15-81" href="#__codelineno-15-81"></a><span class="w"> </span><span class="c1">// In-order traversal</span>
|
|
<a id="__codelineno-15-82" name="__codelineno-15-82" href="#__codelineno-15-82"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"in"</span><span class="p">)</span>
|
|
<a id="__codelineno-15-83" name="__codelineno-15-83" href="#__codelineno-15-83"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
|
<a id="__codelineno-15-84" name="__codelineno-15-84" href="#__codelineno-15-84"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</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">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-15-85" name="__codelineno-15-85" href="#__codelineno-15-85"></a><span class="w"> </span><span class="c1">// Post-order traversal</span>
|
|
<a id="__codelineno-15-86" name="__codelineno-15-86" href="#__codelineno-15-86"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">"post"</span><span class="p">)</span>
|
|
<a id="__codelineno-15-87" name="__codelineno-15-87" href="#__codelineno-15-87"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
|
<a id="__codelineno-15-88" name="__codelineno-15-88" href="#__codelineno-15-88"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-15-89" name="__codelineno-15-89" href="#__codelineno-15-89"></a><span class="p">};</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
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<div class="highlight"><span class="filename">array_binary_tree.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* Array-based binary tree class */</span>
|
|
<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">class</span> <span class="nc">ArrayBinaryTree</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="kd">private</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">tree</span><span class="p">;</span>
|
|
<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a>
|
|
<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w"> </span><span class="cm">/* Constructor */</span>
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<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayBinaryTree</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w"> </span><span class="n">tree</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">ArrayList</span><span class="o"><></span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
|
|
<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a>
|
|
<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w"> </span><span class="cm">/* List capacity */</span>
|
|
<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
|
|
<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a>
|
|
<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w"> </span><span class="cm">/* Get the value of the node at index i */</span>
|
|
<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">val</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-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w"> </span><span class="c1">// If the index is out of bounds, return null, representing an empty spot</span>
|
|
<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w"> </span><span class="k">if</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">0</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="n">size</span><span class="p">())</span>
|
|
<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
|
|
<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
|
|
<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a>
|
|
<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w"> </span><span class="cm">/* Get the index of the left child of the node at index i */</span>
|
|
<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</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>
|
|
<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></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-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a>
|
|
<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w"> </span><span class="cm">/* Get the index of the right child of the node at index i */</span>
|
|
<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</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>
|
|
<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></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-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a>
|
|
<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w"> </span><span class="cm">/* Get the index of the parent of the node at index i */</span>
|
|
<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</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>
|
|
<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></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-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a>
|
|
<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w"> </span><span class="cm">/* Level-order traversal */</span>
|
|
<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">res</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">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
|
<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w"> </span><span class="c1">// Traverse array</span>
|
|
<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</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="p">;</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">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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="kc">null</span><span class="p">)</span>
|
|
<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
|
<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
|
<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a>
|
|
<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w"> </span><span class="cm">/* Depth-first traversal */</span>
|
|
<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w"> </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">Integer</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w"> </span><span class="c1">// If it is an empty spot, return</span>
|
|
<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</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="kc">null</span><span class="p">)</span>
|
|
<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w"> </span><span class="k">return</span><span class="p">;</span>
|
|
<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w"> </span><span class="c1">// Pre-order traversal</span>
|
|
<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">"pre"</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
|
|
<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
|
<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</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">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-16-58" name="__codelineno-16-58" href="#__codelineno-16-58"></a><span class="w"> </span><span class="c1">// In-order traversal</span>
|
|
<a id="__codelineno-16-59" name="__codelineno-16-59" href="#__codelineno-16-59"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">"in"</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
|
|
<a id="__codelineno-16-60" name="__codelineno-16-60" href="#__codelineno-16-60"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
|
<a id="__codelineno-16-61" name="__codelineno-16-61" href="#__codelineno-16-61"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</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">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-16-62" name="__codelineno-16-62" href="#__codelineno-16-62"></a><span class="w"> </span><span class="c1">// Post-order traversal</span>
|
|
<a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">"post"</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
|
|
<a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
|
|
<a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a>
|
|
<a id="__codelineno-16-67" name="__codelineno-16-67" href="#__codelineno-16-67"></a><span class="w"> </span><span class="cm">/* Pre-order traversal */</span>
|
|
<a id="__codelineno-16-68" name="__codelineno-16-68" href="#__codelineno-16-68"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="nf">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-69" name="__codelineno-16-69" href="#__codelineno-16-69"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">res</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">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
|
<a id="__codelineno-16-70" name="__codelineno-16-70" href="#__codelineno-16-70"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"pre"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-16-71" name="__codelineno-16-71" href="#__codelineno-16-71"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
|
<a id="__codelineno-16-72" name="__codelineno-16-72" href="#__codelineno-16-72"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-73" name="__codelineno-16-73" href="#__codelineno-16-73"></a>
|
|
<a id="__codelineno-16-74" name="__codelineno-16-74" href="#__codelineno-16-74"></a><span class="w"> </span><span class="cm">/* In-order traversal */</span>
|
|
<a id="__codelineno-16-75" name="__codelineno-16-75" href="#__codelineno-16-75"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="nf">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-76" name="__codelineno-16-76" href="#__codelineno-16-76"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">res</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">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
|
<a id="__codelineno-16-77" name="__codelineno-16-77" href="#__codelineno-16-77"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"in"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-16-78" name="__codelineno-16-78" href="#__codelineno-16-78"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
|
<a id="__codelineno-16-79" name="__codelineno-16-79" href="#__codelineno-16-79"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-80" name="__codelineno-16-80" href="#__codelineno-16-80"></a>
|
|
<a id="__codelineno-16-81" name="__codelineno-16-81" href="#__codelineno-16-81"></a><span class="w"> </span><span class="cm">/* Post-order traversal */</span>
|
|
<a id="__codelineno-16-82" name="__codelineno-16-82" href="#__codelineno-16-82"></a><span class="w"> </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="nf">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
|
|
<a id="__codelineno-16-83" name="__codelineno-16-83" href="#__codelineno-16-83"></a><span class="w"> </span><span class="n">List</span><span class="o"><</span><span class="n">Integer</span><span class="o">></span><span class="w"> </span><span class="n">res</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">ArrayList</span><span class="o"><></span><span class="p">();</span>
|
|
<a id="__codelineno-16-84" name="__codelineno-16-84" href="#__codelineno-16-84"></a><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">"post"</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
|
|
<a id="__codelineno-16-85" name="__codelineno-16-85" href="#__codelineno-16-85"></a><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
|
|
<a id="__codelineno-16-86" name="__codelineno-16-86" href="#__codelineno-16-86"></a><span class="w"> </span><span class="p">}</span>
|
|
<a id="__codelineno-16-87" name="__codelineno-16-87" href="#__codelineno-16-87"></a><span class="p">}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.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">ArrayBinaryTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
<div class="tabbed-block">
|
|
<div class="highlight"><span class="filename">array_binary_tree.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
|
|
</code></pre></div>
|
|
</div>
|
|
</div>
|
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</div>
|
|
<h2 id="733-advantages-and-limitations">7.3.3 Advantages and limitations<a class="headerlink" href="#733-advantages-and-limitations" title="Permanent link">¶</a></h2>
|
|
<p>The array representation of binary trees has the following advantages:</p>
|
|
<ul>
|
|
<li>Arrays are stored in contiguous memory spaces, which is cache-friendly and allows for faster access and traversal.</li>
|
|
<li>It does not require storing pointers, which saves space.</li>
|
|
<li>It allows random access to nodes.</li>
|
|
</ul>
|
|
<p>However, the array representation also has some limitations:</p>
|
|
<ul>
|
|
<li>Array storage requires contiguous memory space, so it is not suitable for storing trees with a large amount of data.</li>
|
|
<li>Adding or deleting nodes requires array insertion and deletion operations, which are less efficient.</li>
|
|
<li>When there are many <code>None</code> values in the binary tree, the proportion of node data contained in the array is low, leading to lower space utilization.</li>
|
|
</ul>
|
|
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