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跳转至
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Hello 算法
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8.3. Top-K 问题
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0. 前言
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0. 前言
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0.1. 关于本书
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0.2. 如何使用本书
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0.3. 小结
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1. 初识算法
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1. 初识算法
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1.1. 算法无处不在
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1.2. 算法是什么
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1.3. 小结
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2. 复杂度
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2. 复杂度
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2.1. 算法效率评估
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2.2. 时间复杂度
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2.3. 空间复杂度
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2.4. 小结
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< a href = "../../chapter_data_structure/" class = "md-nav__link " >
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3. 数据结构
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3. 数据结构
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3.1. 数据结构分类
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< a href = "../../chapter_data_structure/basic_data_types/" class = "md-nav__link" >
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3.2. 基本数据类型
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< a href = "../../chapter_data_structure/number_encoding/" class = "md-nav__link" >
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3.3. 数字编码 *
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< a href = "../../chapter_data_structure/character_encoding/" class = "md-nav__link" >
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3.4. 字符编码 *
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3.5. 小结
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< a href = "../../chapter_array_and_linkedlist/" class = "md-nav__link " >
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4. 数组与链表
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4. 数组与链表
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4.1. 数组
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4.2. 链表
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4.3. 列表
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4.4. 小结
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_stack_and_queue/" class = "md-nav__link " >
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5. 栈与队列
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5. 栈与队列
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5.1. 栈
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5.2. 队列
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5.3. 双向队列
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5.4. 小结
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< a href = "../../chapter_hashing/" class = "md-nav__link " >
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6. 散列表
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6. 散列表
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< li class = "md-nav__item" >
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6.1. 哈希表
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< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
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6.2. 哈希冲突
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< a href = "../../chapter_hashing/hash_algorithm/" class = "md-nav__link" >
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6.3. 哈希算法
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6.4. 小结
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< a href = "../../chapter_tree/" class = "md-nav__link " >
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7. 树
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< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
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7. 树
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7.1. 二叉树
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7.2. 二叉树遍历
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7.3. 二叉树数组表示
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7.4. 二叉搜索树
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7.5. AVL 树 *
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7.6. 小结
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< div class = "md-nav__link md-nav__container" >
< a href = "../" class = "md-nav__link " >
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8. 堆
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< / label >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_9_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_9" >
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8. 堆
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< a href = "../heap/" class = "md-nav__link" >
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8.1. 堆
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8.2. 建堆操作
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8.3. Top-K 问题
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8.3. Top-K 问题
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目录
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< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
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< a href = "#831" class = "md-nav__link" >
8.3.1. 方法一：遍历选择
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< a href = "#832" class = "md-nav__link" >
8.3.2. 方法二：排序
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< a href = "#833" class = "md-nav__link" >
8.3.3. 方法三：堆
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< a href = "../summary/" class = "md-nav__link" >
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8.4. 小结
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_graph/" class = "md-nav__link " >
< 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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9. 图
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9. 图
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9.1. 图
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9.2. 图基础操作
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9.3. 图的遍历
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9.4. 小结
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< div class = "md-nav__link md-nav__container" >
< a href = "../../chapter_searching/" class = "md-nav__link " >
< 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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10. 搜索
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10. 搜索
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10.1. 二分查找
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10.2. 二分查找边界
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10.3. 哈希优化策略
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10.4. 重识搜索算法
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10.5. 小结
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< a href = "../../chapter_sorting/" class = "md-nav__link " >
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11. 排序
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11. 排序
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11.1. 排序算法
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11.2. 选择排序
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11.3. 冒泡排序
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11.4. 插入排序
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11.5. 快速排序
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11.6. 归并排序
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11.7. 堆排序
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11.8. 桶排序
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11.9. 计数排序
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11.10. 基数排序
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11.11. 小结
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< a href = "../../chapter_divide_and_conquer/" class = "md-nav__link " >
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12. 分治
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12. 分治
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12.1. 分治算法
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12.2. 分治搜索策略
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< a href = "../../chapter_divide_and_conquer/build_binary_tree_problem/" class = "md-nav__link" >
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12.3. 构建树问题
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< a href = "../../chapter_divide_and_conquer/hanota_problem/" class = "md-nav__link" >
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12.4. 汉诺塔问题
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12.5. 小结
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< a href = "../../chapter_backtracking/" class = "md-nav__link " >
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13. 回溯
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13. 回溯
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13.1. 回溯算法
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13.2. 全排列问题
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13.3. 子集和问题
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13.4. N 皇后问题
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13.5. 小结
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< a href = "../../chapter_dynamic_programming/" class = "md-nav__link " >
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14. 动态规划
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14. 动态规划
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14.1. 初探动态规划
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14.2. DP 问题特性
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14.3. DP 解题思路
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14.4. 0-1 背包问题
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14.5. 完全背包问题
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14.6. 编辑距离问题
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14.7. 小结
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< a href = "../../chapter_appendix/" class = "md-nav__link " >
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15. 附录
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15. 附录
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15.1. 编程环境安装
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15.2. 一起参与创作
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参考文献
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参考文献
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目录
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8.3.1. 方法一：遍历选择
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8.3.2. 方法二：排序
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8.3.3. 方法三：堆
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< svg xmlns = "http://www.w3.org/2000/svg" viewBox = "0 0 24 24" > < path d = "M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z" / > < / svg >
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< h1 id = "83-top-k" > 8.3. Top-K 问题< a class = "headerlink" href = "#83-top-k" title = "Permanent link" > ¶ < / a > < / h1 >
< div class = "admonition question" >
< p class = "admonition-title" > Question< / p >
< p > 给定一个长度为 < span class = "arithmatex" > \(n\)< / span > 无序数组 < code > nums< / code > ，请返回数组中前 < span class = "arithmatex" > \(k\)< / span > 大的元素。< / p >
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< p > 对于该问题，我们先介绍两种思路比较直接的解法，再介绍效率更高的堆解法。< / p >
< h2 id = "831" > 8.3.1. 方法一：遍历选择< a class = "headerlink" href = "#831" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 我们可以进行 < span class = "arithmatex" > \(k\)< / span > 轮遍历，分别在每轮中提取第 < span class = "arithmatex" > \(1\)< / span > , < span class = "arithmatex" > \(2\)< / span > , < span class = "arithmatex" > \(\cdots\)< / span > , < span class = "arithmatex" > \(k\)< / span > 大的元素，时间复杂度为 < span class = "arithmatex" > \(O(nk)\)< / span > 。< / p >
< p > 该方法只适用于 < span class = "arithmatex" > \(k \ll n\)< / span > 的情况，因为当 < span class = "arithmatex" > \(k\)< / span > 与 < span class = "arithmatex" > \(n\)< / span > 比较接近时，其时间复杂度趋向于 < span class = "arithmatex" > \(O(n^2)\)< / span > ，非常耗时。< / p >
< p > < img alt = "遍历寻找最大的 k 个元素" src = "../top_k.assets/top_k_traversal.png" / > < / p >
< p align = "center" > Fig. 遍历寻找最大的 k 个元素 < / p >
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< p class = "admonition-title" > Tip< / p >
< p > 当 < span class = "arithmatex" > \(k = n\)< / span > 时，我们可以得到从大到小的序列，等价于「选择排序」算法。 < / p >
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< h2 id = "832" > 8.3.2. 方法二：排序< a class = "headerlink" href = "#832" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 我们可以对数组 < code > nums< / code > 进行排序，并返回最右边的 < span class = "arithmatex" > \(k\)< / span > 个元素，时间复杂度为 < span class = "arithmatex" > \(O(n \log n)\)< / span > 。< / p >
< p > 显然，该方法“超额”完成任务了，因为我们只需要找出最大的 < span class = "arithmatex" > \(k\)< / span > 个元素即可，而不需要排序其他元素。< / p >
< p > < img alt = "排序寻找最大的 k 个元素" src = "../top_k.assets/top_k_sorting.png" / > < / p >
< p align = "center" > Fig. 排序寻找最大的 k 个元素 < / p >
< h2 id = "833" > 8.3.3. 方法三：堆< a class = "headerlink" href = "#833" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 我们可以基于堆更加高效地解决 Top-K 问题，流程如下：< / p >
< ol >
< li > 初始化一个小顶堆，其堆顶元素最小；< / li >
< li > 先将数组的前 < span class = "arithmatex" > \(k\)< / span > 个元素依次入堆；< / li >
< li > 从第 < span class = "arithmatex" > \(k + 1\)< / span > 个元素开始，若当前元素大于堆顶元素，则将堆顶元素出堆，并将当前元素入堆；< / li >
< li > 遍历完成后，堆中保存的就是最大的 < span class = "arithmatex" > \(k\)< / span > 个元素；< / li >
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< div class = "tabbed-set tabbed-alternate" data-tabs = "1:9" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_1_1" > < 1> < / label > < label for = "__tabbed_1_2" > < 2> < / label > < label for = "__tabbed_1_3" > < 3> < / label > < label for = "__tabbed_1_4" > < 4> < / label > < label for = "__tabbed_1_5" > < 5> < / label > < label for = "__tabbed_1_6" > < 6> < / label > < label for = "__tabbed_1_7" > < 7> < / label > < label for = "__tabbed_1_8" > < 8> < / label > < label for = "__tabbed_1_9" > < 9> < / label > < / div >
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< p > < img alt = "基于堆寻找最大的 k 个元素" src = "../top_k.assets/top_k_heap_step1.png" / > < / p >
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< p > < img alt = "top_k_heap_step2" src = "../top_k.assets/top_k_heap_step2.png" / > < / p >
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< p > < img alt = "top_k_heap_step3" src = "../top_k.assets/top_k_heap_step3.png" / > < / p >
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< p > < img alt = "top_k_heap_step4" src = "../top_k.assets/top_k_heap_step4.png" / > < / p >
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< p > < img alt = "top_k_heap_step5" src = "../top_k.assets/top_k_heap_step5.png" / > < / p >
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< p > < img alt = "top_k_heap_step6" src = "../top_k.assets/top_k_heap_step6.png" / > < / p >
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< p > 总共执行了 < span class = "arithmatex" > \(n\)< / span > 轮入堆和出堆，堆的最大长度为 < span class = "arithmatex" > \(k\)< / span > ，因此时间复杂度为 < span class = "arithmatex" > \(O(n \log k)\)< / span > 。该方法的效率很高，当 < span class = "arithmatex" > \(k\)< / span > 较小时，时间复杂度趋向 < span class = "arithmatex" > \(O(n)\)< / span > ；当 < span class = "arithmatex" > \(k\)< / span > 较大时，时间复杂度不会超过 < span class = "arithmatex" > \(O(n \log n)\)< / span > 。< / p >
< p > 另外，该方法适用于动态数据流的使用场景。在不断加入数据时，我们可以持续维护堆内的元素，从而实现最大 < span class = "arithmatex" > \(k\)< / span > 个元素的动态更新。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:11" > < 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" / > < div class = "tabbed-labels" > < label for = "__tabbed_2_1" > Java< / label > < label for = "__tabbed_2_2" > C++< / label > < label for = "__tabbed_2_3" > Python< / label > < label for = "__tabbed_2_4" > Go< / label > < label for = "__tabbed_2_5" > JavaScript< / label > < label for = "__tabbed_2_6" > TypeScript< / label > < label for = "__tabbed_2_7" > C< / label > < label for = "__tabbed_2_8" > C#< / label > < label for = "__tabbed_2_9" > Swift< / label > < label for = "__tabbed_2_10" > Zig< / label > < label for = "__tabbed_2_11" > Dart< / label > < / div >
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< div class = "highlight" > < span class = "filename" > top_k.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 基于堆查找数组中最大的 k 个元素 */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "n" > Queue< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nf" > topKHeap< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > k< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "w" > < / span > < span class = "n" > Queue< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "k" > new< / span > < span class = "w" > < / span > < span class = "n" > PriorityQueue< / span > < span class = "o" > < < / span > < span class = "n" > Integer< / span > < span class = "o" > > < / span > < span class = "p" > ();< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将数组的前 k 个元素入堆< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / 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" > k< / 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-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从第 k+1 个元素开始，保持堆的长度为 k< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / 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 = "n" > k< / 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" > nums< / span > < span class = "p" > .< / span > < span class = "na" > length< / 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-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若当前元素大于堆顶元素，则将堆顶元素出堆、当前元素入堆< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "na" > peek< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "na" > poll< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "na" > add< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ]< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-15" name = "__codelineno-0-15" href = "#__codelineno-0-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "p" > }< / span >
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< div class = "highlight" > < span class = "filename" > top_k.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 基于堆查找数组中最大的 k 个元素 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "n" > priority_queue< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > greater< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > topKHeap< / 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 = "o" > & < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > k< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "w" > < / span > < span class = "n" > priority_queue< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > vector< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > < / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > greater< / span > < span class = "o" > < < / span > < span class = "kt" > int< / span > < span class = "o" > > > < / span > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "w" > < / span > < span class = "c1" > // 将数组的前 k 个元素入堆< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / 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" > k< / 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-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / a > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 从第 k+1 个元素开始，保持堆的长度为 k< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / 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 = "n" > k< / 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" > nums< / span > < span class = "p" > .< / 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-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若当前元素大于堆顶元素，则将堆顶元素出堆、当前元素入堆< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > nums< / 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" > heap< / span > < span class = "p" > .< / span > < span class = "n" > top< / span > < span class = "p" > ())< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "n" > pop< / span > < span class = "p" > ();< / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "n" > push< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]);< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-15" name = "__codelineno-1-15" href = "#__codelineno-1-15" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "w" > < / span > < span class = "n" > heap< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > top_k.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "k" > def< / span > < span class = "nf" > top_k_heap< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "nb" > list< / span > < span class = "p" > [< / span > < span class = "nb" > int< / span > < span class = "p" > ],< / span > < span class = "n" > k< / span > < span class = "p" > :< / span > < span class = "nb" > int< / 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-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "w" > < / span > < span class = "sd" > " " " 基于堆查找数组中最大的 k 个元素" " " < / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "n" > heap< / span > < span class = "o" > =< / span > < span class = "p" > []< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "c1" > # 将数组的前 k 个元素入堆< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / 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 = "n" > k< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "n" > heapq< / span > < span class = "o" > .< / span > < span class = "n" > heappush< / span > < span class = "p" > (< / span > < span class = "n" > heap< / span > < span class = "p" > ,< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "c1" > # 从第 k+1 个元素开始，保持堆的长度为 k< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / 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 = "n" > k< / span > < span class = "p" > ,< / span > < span class = "nb" > len< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > )):< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "c1" > # 若当前元素大于堆顶元素，则将堆顶元素出堆、当前元素入堆< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "k" > if< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > > < / span > < span class = "n" > heap< / span > < span class = "p" > [< / span > < span class = "mi" > 0< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "n" > heapq< / span > < span class = "o" > .< / span > < span class = "n" > heappop< / span > < span class = "p" > (< / span > < span class = "n" > heap< / span > < span class = "p" > )< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "n" > heapq< / span > < span class = "o" > .< / span > < span class = "n" > heappush< / span > < span class = "p" > (< / span > < span class = "n" > heap< / span > < span class = "p" > ,< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "k" > return< / span > < span class = "n" > heap< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > top_k.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "p" > [< / span > < span class = "nx" > class< / span > < span class = "p" > ]{< / span > < span class = "nx" > maxHeap< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "kd" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > topKHeap< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > top_k.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > topKHeap< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > top_k.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "p" > [< / span > < span class = "kd" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "nx" > func< / span > < span class = "p" > ]{< / span > < span class = "nx" > topKHeap< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > top_k.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{< / span > < span class = "n" > maxHeap< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > topKHeap< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > top_k.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "na" > [class]< / span > < span class = "p" > {< / span > < span class = "n" > top_k< / span > < span class = "p" > }< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > topKHeap< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > top_k.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /* 基于堆查找数组中最大的 k 个元素 */< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "kd" > func< / span > < span class = "nf" > topKHeap< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "n" > k< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > -> < / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "c1" > // 将数组的前 k 个元素入堆< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "kd" > var< / span > < span class = "nv" > heap< / span > < span class = "p" > =< / span > < span class = "nb" > Array< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "kr" > prefix< / span > < span class = "p" > (< / span > < span class = "n" > k< / span > < span class = "p" > ))< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "c1" > // 从第 k+1 个元素开始，保持堆的长度为 k< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "k" > for< / span > < span class = "n" > i< / span > < span class = "k" > in< / span > < span class = "bp" > stride< / span > < span class = "p" > (< / span > < span class = "n" > from< / span > < span class = "p" > :< / span > < span class = "n" > k< / span > < span class = "p" > ,< / span > < span class = "n" > to< / span > < span class = "p" > :< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "bp" > count< / span > < span class = "p" > ,< / span > < span class = "n" > by< / span > < span class = "p" > :< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-7" name = "__codelineno-8-7" href = "#__codelineno-8-7" > < / a > < span class = "c1" > // 若当前元素大于堆顶元素，则将堆顶元素出堆、当前元素入堆< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "k" > if< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > > < / span > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "bp" > first< / span > < span class = "p" > !< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "n" > removeFirst< / span > < span class = "p" > ()< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "n" > heap< / span > < span class = "p" > .< / span > < span class = "bp" > insert< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ],< / span > < span class = "n" > at< / span > < span class = "p" > :< / span > < span class = "mi" > 0< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "k" > return< / span > < span class = "n" > heap< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > top_k.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > topKHeap< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > top_k.dart< / span > < pre > < span > < / span > < code > < a id = "__codelineno-10-1" name = "__codelineno-10-1" href = "#__codelineno-10-1" > < / a > < span class = "p" > [< / span > < span class = "n" > class< / span > < span class = "p" > ]{}< / span > < span class = "o" > -< / span > < span class = "p" > [< / span > < span class = "n" > func< / span > < span class = "p" > ]{< / span > < span class = "n" > top_k_heap< / span > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< h2 id = "__comments" > 评论< / h2 >
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