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Hello 算法
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11.5. 归并排序
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0. 写在前面
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0. 写在前面
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0.2. 如何使用本书
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0.4. 一起参与创作
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1. 引言
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1. 引言
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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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2. 计算复杂度
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2. 计算复杂度
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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. 权衡时间与空间
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2.5. 小结
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< label class = "md-nav__link" for = "__nav_4" id = "__nav_4_label" tabindex = "0" >
3. 数据结构简介
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< / label >
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< label class = "md-nav__title" for = "__nav_4" >
< span class = "md-nav__icon md-icon" > < / span >
3. 数据结构简介
< / label >
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< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/data_and_memory/" class = "md-nav__link" >
3.1. 数据与内存
< / a >
< / li >
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< a href = "../../chapter_data_structure/classification_of_data_structure/" class = "md-nav__link" >
3.2. 数据结构分类
< / a >
< / li >
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< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
3.3. 小结
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< / ul >
< / nav >
< / li >
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< label class = "md-nav__link" for = "__nav_5" id = "__nav_5_label" tabindex = "0" >
4. 数组与链表
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< / label >
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< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
4. 数组与链表
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
4.1. 数组（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
4.2. 链表（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
4.3. 列表（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/summary/" class = "md-nav__link" >
4.4. 小结
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< / ul >
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< label class = "md-nav__link" for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
5. 栈与队列
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< / label >
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< label class = "md-nav__title" for = "__nav_6" >
< span class = "md-nav__icon md-icon" > < / span >
5. 栈与队列
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
5.1. 栈（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/queue/" class = "md-nav__link" >
5.2. 队列（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/deque/" class = "md-nav__link" >
5.3. 双向队列（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
5.4. 小结
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< / li >
< / ul >
< / nav >
< / li >
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_7" >
< label class = "md-nav__link" for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
6. 散列表
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_7_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_7" >
< span class = "md-nav__icon md-icon" > < / span >
6. 散列表
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_map/" class = "md-nav__link" >
6.1. 哈希表（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
6.2. 哈希冲突处理
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
6.3. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_8" >
< label class = "md-nav__link" for = "__nav_8" id = "__nav_8_label" tabindex = "0" >
7. 二叉树
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_8_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_8" >
< span class = "md-nav__icon md-icon" > < / span >
7. 二叉树
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree/" class = "md-nav__link" >
7.1. 二叉树（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_tree_traversal/" class = "md-nav__link" >
7.2. 二叉树遍历
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/binary_search_tree/" class = "md-nav__link" >
7.3. 二叉搜索树
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
7.4. AVL 树 *
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
7.5. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_9" >
< label class = "md-nav__link" for = "__nav_9" id = "__nav_9_label" tabindex = "0" >
8. 堆
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_9_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_9" >
< span class = "md-nav__icon md-icon" > < / span >
8. 堆
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
8.1. 堆（ ）
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
< label class = "md-nav__link" for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
9. 图
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_10_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_10" >
< span class = "md-nav__icon md-icon" > < / span >
9. 图
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph/" class = "md-nav__link" >
9.1. 图（ ）
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
9.2. 图基础操作
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_graph/graph_traversal/" class = "md-nav__link" >
9.3. 图的遍历
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_11" >
< label class = "md-nav__link" for = "__nav_11" id = "__nav_11_label" tabindex = "0" >
10. 查找算法
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_11_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
10. 查找算法
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/linear_search/" class = "md-nav__link" >
10.1. 线性查找
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
10.2. 二分查找
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/hashing_search/" class = "md-nav__link" >
10.3. 哈希查找
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
10.4. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--active md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" checked >
< label class = "md-nav__link" for = "__nav_12" id = "__nav_12_label" tabindex = "0" >
11. 排序算法
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_12_label" aria-expanded = "true" >
< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
11. 排序算法
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "../intro_to_sort/" class = "md-nav__link" >
11.1. 排序简介
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../bubble_sort/" class = "md-nav__link" >
11.2. 冒泡排序
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../insertion_sort/" class = "md-nav__link" >
11.3. 插入排序
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "../quick_sort/" class = "md-nav__link" >
11.4. 快速排序
< / a >
< / li >
< li class = "md-nav__item md-nav__item--active" >
< input class = "md-nav__toggle md-toggle" type = "checkbox" id = "__toc" >
< label class = "md-nav__link md-nav__link--active" for = "__toc" >
11.5. 归并排序
< span class = "md-nav__icon md-icon" > < / span >
< / label >
< a href = "./" class = "md-nav__link md-nav__link--active" >
11.5. 归并排序
< / a >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#1151" class = "md-nav__link" >
11.5.1. 算法流程
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#1152" class = "md-nav__link" >
11.5.2. 算法特性
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#1153" class = "md-nav__link" >
11.5.3. 链表排序 *
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item" >
< a href = "../summary/" class = "md-nav__link" >
11.6. 小结
< / a >
< / li >
< / ul >
< / nav >
< / li >
< li class = "md-nav__item md-nav__item--section md-nav__item--nested" >
< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_13" >
< div class = "md-nav__link md-nav__link--index " >
< a href = "../../chapter_reference/" > 参考文献< / a >
< / div >
< nav class = "md-nav" data-md-level = "1" aria-labelledby = "__nav_13_label" aria-expanded = "false" >
< label class = "md-nav__title" for = "__nav_13" >
< span class = "md-nav__icon md-icon" > < / span >
参考文献
< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< / ul >
< / nav >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-sidebar md-sidebar--secondary" data-md-component = "sidebar" data-md-type = "toc" >
< div class = "md-sidebar__scrollwrap" >
< div class = "md-sidebar__inner" >
< nav class = "md-nav md-nav--secondary" aria-label = "目录" >
< label class = "md-nav__title" for = "__toc" >
< span class = "md-nav__icon md-icon" > < / span >
目录
< / label >
< ul class = "md-nav__list" data-md-component = "toc" data-md-scrollfix >
< li class = "md-nav__item" >
< a href = "#1151" class = "md-nav__link" >
11.5.1. 算法流程
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#1152" class = "md-nav__link" >
11.5.2. 算法特性
< / a >
< / li >
< li class = "md-nav__item" >
< a href = "#1153" class = "md-nav__link" >
11.5.3. 链表排序 *
< / a >
< / li >
< / ul >
< / nav >
< / div >
< / div >
< / div >
< div class = "md-content" data-md-component = "content" >
< article class = "md-content__inner md-typeset" >
< a href = "https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/merge_sort.md" title = "编辑此页" class = "md-content__button md-icon" >
< 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 >
< / a >
< h1 id = "115" > 11.5. 归并排序< a class = "headerlink" href = "#115" title = "Permanent link" > ¶ < / a > < / h1 >
< p > 「归并排序 Merge Sort」是算法中“分治思想”的典型体现， ： < / p >
< ol >
< li > < strong > 划分阶段< / strong > ：通过递归不断 < strong > 将数组从中点位置划分开< / strong > ，将长数组的排序问题转化为短数组的排序问题；< / li >
< li > < strong > 合并阶段< / strong > ：划分到子数组长度为 1 时，开始向上合并，不断将 < strong > 左、右两个短排序数组< / strong > 合并为 < strong > 一个长排序数组< / strong > ，直至合并至原数组时完成排序；< / li >
< / ol >
< p > < img alt = "归并排序的划分与合并阶段" src = "../merge_sort.assets/merge_sort_overview.png" / > < / p >
< h2 id = "1151" > 11.5.1. 算法流程< a class = "headerlink" href = "#1151" title = "Permanent link" > ¶ < / a > < / h2 >
< p > < strong > 「递归划分」< / strong > 从顶至底递归地 < strong > 将数组从中点切为两个子数组< / strong > ，直至长度为 1 ； < / p >
< ol >
< li > 计算数组中点 < code > mid< / code > ，递归划分左子数组（区间 < code > [left, mid]< / code > ）和右子数组（区间 < code > [mid + 1, right]< / code > ） ； < / li >
< li > 递归执行 < code > 1.< / code > 步骤，直至子数组区间长度为 1 时，终止递归划分；< / li >
< / ol >
< p > < strong > 「回溯合并」< / strong > 从底至顶地将左子数组和右子数组合并为一个 < strong > 有序数组< / strong > ； < / p >
< p > 需要注意，由于从长度为 1 的子数组开始合并，所以 < strong > 每个子数组都是有序的< / strong > 。因此，合并任务本质是要 < strong > 将两个有序子数组合并为一个有序数组< / strong > 。< / p >
< div class = "tabbed-set tabbed-alternate" data-tabs = "1:10" > < 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" / > < 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 > < label for = "__tabbed_1_10" > < 10> < / label > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step1" src = "../merge_sort.assets/merge_sort_step1.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step2" src = "../merge_sort.assets/merge_sort_step2.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step3" src = "../merge_sort.assets/merge_sort_step3.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step4" src = "../merge_sort.assets/merge_sort_step4.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step5" src = "../merge_sort.assets/merge_sort_step5.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step6" src = "../merge_sort.assets/merge_sort_step6.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step7" src = "../merge_sort.assets/merge_sort_step7.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step8" src = "../merge_sort.assets/merge_sort_step8.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step9" src = "../merge_sort.assets/merge_sort_step9.png" / > < / p >
< / div >
< div class = "tabbed-block" >
< p > < img alt = "merge_sort_step10" src = "../merge_sort.assets/merge_sort_step10.png" / > < / p >
< / div >
< / div >
< / div >
< p > 观察发现，归并排序的递归顺序就是二叉树的「后序遍历」。< / p >
< ul >
< li > < strong > 后序遍历< / strong > ：先递归左子树、再递归右子树、最后处理根结点。< / li >
< li > < strong > 归并排序< / strong > ：先递归左子树、再递归右子树、最后处理合并。< / li >
< / ul >
< div class = "tabbed-set tabbed-alternate" data-tabs = "2:10" > < 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" / > < 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 > < / div >
< div class = "tabbed-content" >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.java< / span > < pre > < span > < / span > < code > < a id = "__codelineno-0-1" name = "__codelineno-0-1" href = "#__codelineno-0-1" > < / a > < span class = "cm" > /* 合并左子数组和右子数组 */< / span >
< a id = "__codelineno-0-2" name = "__codelineno-0-2" href = "#__codelineno-0-2" > < / a > < span class = "c1" > // 左子数组区间 [left, mid]< / span >
< a id = "__codelineno-0-3" name = "__codelineno-0-3" href = "#__codelineno-0-3" > < / a > < span class = "c1" > // 右子数组区间 [mid + 1, right]< / span >
< a id = "__codelineno-0-4" name = "__codelineno-0-4" href = "#__codelineno-0-4" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > merge< / 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" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-5" name = "__codelineno-0-5" href = "#__codelineno-0-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化辅助数组< / span >
< a id = "__codelineno-0-6" name = "__codelineno-0-6" href = "#__codelineno-0-6" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "o" > []< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > Arrays< / span > < span class = "p" > .< / span > < span class = "na" > copyOfRange< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > right< / 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 >
< a id = "__codelineno-0-7" name = "__codelineno-0-7" href = "#__codelineno-0-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左子数组的起始索引和结束索引 < / span >
< a id = "__codelineno-0-8" name = "__codelineno-0-8" href = "#__codelineno-0-8" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > leftStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > leftEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-9" name = "__codelineno-0-9" href = "#__codelineno-0-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右子数组的起始索引和结束索引 < / span >
< a id = "__codelineno-0-10" name = "__codelineno-0-10" href = "#__codelineno-0-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > rightStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-11" name = "__codelineno-0-11" href = "#__codelineno-0-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // i, j 分别指向左子数组、右子数组的首元素< / span >
< a id = "__codelineno-0-12" name = "__codelineno-0-12" href = "#__codelineno-0-12" > < / a > < span class = "w" > < / 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" > leftStart< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rightStart< / span > < span class = "p" > ;< / span > < span class = "w" > < / span >
< a id = "__codelineno-0-13" name = "__codelineno-0-13" href = "#__codelineno-0-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过覆盖原数组 nums 来合并左子数组和右子数组< / span >
< a id = "__codelineno-0-14" name = "__codelineno-0-14" href = "#__codelineno-0-14" > < / 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" > k< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > k< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > k< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < 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 = "c1" > // 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-0-16" name = "__codelineno-0-16" href = "#__codelineno-0-16" > < / 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 = "n" > leftEnd< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-17" name = "__codelineno-0-17" href = "#__codelineno-0-17" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > k< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ++]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-18" name = "__codelineno-0-18" href = "#__codelineno-0-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“右子数组已全部合并完”或“左子数组元素 < = 右子数组元素”，则选取左子数组元素，并且 i++< / span >
< a id = "__codelineno-0-19" name = "__codelineno-0-19" href = "#__codelineno-0-19" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > tmp< / 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" > tmp< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ]< / span > < span class = "p" > )< / span >
< a id = "__codelineno-0-20" name = "__codelineno-0-20" href = "#__codelineno-0-20" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > k< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "o" > [< / span > < span class = "n" > i< / span > < span class = "o" > ++]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-21" name = "__codelineno-0-21" href = "#__codelineno-0-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-0-22" name = "__codelineno-0-22" href = "#__codelineno-0-22" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-0-23" name = "__codelineno-0-23" href = "#__codelineno-0-23" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "o" > [< / span > < span class = "n" > k< / span > < span class = "o" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "o" > [< / span > < span class = "n" > j< / span > < span class = "o" > ++]< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-0-24" name = "__codelineno-0-24" href = "#__codelineno-0-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-0-25" name = "__codelineno-0-25" href = "#__codelineno-0-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-0-26" name = "__codelineno-0-26" href = "#__codelineno-0-26" > < / a >
< a id = "__codelineno-0-27" name = "__codelineno-0-27" href = "#__codelineno-0-27" > < / a > < span class = "cm" > /* 归并排序 */< / span >
< a id = "__codelineno-0-28" name = "__codelineno-0-28" href = "#__codelineno-0-28" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > mergeSort< / 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" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-0-29" name = "__codelineno-0-29" href = "#__codelineno-0-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-0-30" name = "__codelineno-0-30" href = "#__codelineno-0-30" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 当子数组长度为 1 时终止递归< / span >
< a id = "__codelineno-0-31" name = "__codelineno-0-31" href = "#__codelineno-0-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 划分阶段< / span >
< a id = "__codelineno-0-32" name = "__codelineno-0-32" href = "#__codelineno-0-32" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 计算中点< / span >
< a id = "__codelineno-0-33" name = "__codelineno-0-33" href = "#__codelineno-0-33" > < / a > < span class = "w" > < / span > < span class = "n" > mergeSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归左子数组< / span >
< a id = "__codelineno-0-34" name = "__codelineno-0-34" href = "#__codelineno-0-34" > < / a > < span class = "w" > < / span > < span class = "n" > mergeSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > mid< / 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 = "n" > right< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归右子数组< / span >
< a id = "__codelineno-0-35" name = "__codelineno-0-35" href = "#__codelineno-0-35" > < / a > < span class = "w" > < / span > < span class = "c1" > // 合并阶段< / span >
< a id = "__codelineno-0-36" name = "__codelineno-0-36" href = "#__codelineno-0-36" > < / a > < span class = "w" > < / span > < span class = "n" > merge< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-0-37" name = "__codelineno-0-37" href = "#__codelineno-0-37" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.cpp< / span > < pre > < span > < / span > < code > < a id = "__codelineno-1-1" name = "__codelineno-1-1" href = "#__codelineno-1-1" > < / a > < span class = "cm" > /* 合并左子数组和右子数组 */< / span >
< a id = "__codelineno-1-2" name = "__codelineno-1-2" href = "#__codelineno-1-2" > < / a > < span class = "c1" > // 左子数组区间 [left, mid]< / span >
< a id = "__codelineno-1-3" name = "__codelineno-1-3" href = "#__codelineno-1-3" > < / a > < span class = "c1" > // 右子数组区间 [mid + 1, right]< / span >
< a id = "__codelineno-1-4" name = "__codelineno-1-4" href = "#__codelineno-1-4" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > merge< / 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" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-5" name = "__codelineno-1-5" href = "#__codelineno-1-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化辅助数组< / span >
< a id = "__codelineno-1-6" name = "__codelineno-1-6" href = "#__codelineno-1-6" > < / 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" > tmp< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > begin< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > .< / span > < span class = "n" > begin< / span > < span class = "p" > ()< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > right< / 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 >
< a id = "__codelineno-1-7" name = "__codelineno-1-7" href = "#__codelineno-1-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左子数组的起始索引和结束索引 < / span >
< a id = "__codelineno-1-8" name = "__codelineno-1-8" href = "#__codelineno-1-8" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > leftStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > leftEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-9" name = "__codelineno-1-9" href = "#__codelineno-1-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右子数组的起始索引和结束索引 < / span >
< a id = "__codelineno-1-10" name = "__codelineno-1-10" href = "#__codelineno-1-10" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > rightStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mi" > 1< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-1-11" name = "__codelineno-1-11" href = "#__codelineno-1-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // i, j 分别指向左子数组、右子数组的首元素< / span >
< a id = "__codelineno-1-12" name = "__codelineno-1-12" href = "#__codelineno-1-12" > < / a > < span class = "w" > < / 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" > leftStart< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rightStart< / span > < span class = "p" > ;< / span > < span class = "w" > < / span >
< a id = "__codelineno-1-13" name = "__codelineno-1-13" href = "#__codelineno-1-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过覆盖原数组 nums 来合并左子数组和右子数组< / span >
< a id = "__codelineno-1-14" name = "__codelineno-1-14" href = "#__codelineno-1-14" > < / 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" > k< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > k< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > k< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < 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 = "c1" > // 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-1-16" name = "__codelineno-1-16" href = "#__codelineno-1-16" > < / 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 = "n" > leftEnd< / span > < span class = "p" > )< / span >
< a id = "__codelineno-1-17" name = "__codelineno-1-17" href = "#__codelineno-1-17" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-1-18" name = "__codelineno-1-18" href = "#__codelineno-1-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“右子数组已全部合并完”或“左子数组元素 < = 右子数组元素”，则选取左子数组元素，并且 i++< / span >
< a id = "__codelineno-1-19" name = "__codelineno-1-19" href = "#__codelineno-1-19" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > tmp< / 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" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-1-20" name = "__codelineno-1-20" href = "#__codelineno-1-20" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-1-21" name = "__codelineno-1-21" href = "#__codelineno-1-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-1-22" name = "__codelineno-1-22" href = "#__codelineno-1-22" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-1-23" name = "__codelineno-1-23" href = "#__codelineno-1-23" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-1-24" name = "__codelineno-1-24" href = "#__codelineno-1-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-1-25" name = "__codelineno-1-25" href = "#__codelineno-1-25" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-1-26" name = "__codelineno-1-26" href = "#__codelineno-1-26" > < / a >
< a id = "__codelineno-1-27" name = "__codelineno-1-27" href = "#__codelineno-1-27" > < / a > < span class = "cm" > /* 归并排序 */< / span >
< a id = "__codelineno-1-28" name = "__codelineno-1-28" href = "#__codelineno-1-28" > < / a > < span class = "kt" > void< / span > < span class = "w" > < / span > < span class = "nf" > mergeSort< / 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" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-1-29" name = "__codelineno-1-29" href = "#__codelineno-1-29" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-1-30" name = "__codelineno-1-30" href = "#__codelineno-1-30" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 当子数组长度为 1 时终止递归< / span >
< a id = "__codelineno-1-31" name = "__codelineno-1-31" href = "#__codelineno-1-31" > < / a > < span class = "w" > < / span > < span class = "c1" > // 划分阶段< / span >
< a id = "__codelineno-1-32" name = "__codelineno-1-32" href = "#__codelineno-1-32" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 计算中点< / span >
< a id = "__codelineno-1-33" name = "__codelineno-1-33" href = "#__codelineno-1-33" > < / a > < span class = "w" > < / span > < span class = "n" > mergeSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归左子数组< / span >
< a id = "__codelineno-1-34" name = "__codelineno-1-34" href = "#__codelineno-1-34" > < / a > < span class = "w" > < / span > < span class = "n" > mergeSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > mid< / 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 = "n" > right< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归右子数组< / span >
< a id = "__codelineno-1-35" name = "__codelineno-1-35" href = "#__codelineno-1-35" > < / a > < span class = "w" > < / span > < span class = "c1" > // 合并阶段< / span >
< a id = "__codelineno-1-36" name = "__codelineno-1-36" href = "#__codelineno-1-36" > < / a > < span class = "w" > < / span > < span class = "n" > merge< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-1-37" name = "__codelineno-1-37" href = "#__codelineno-1-37" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.py< / span > < pre > < span > < / span > < code > < a id = "__codelineno-2-1" name = "__codelineno-2-1" href = "#__codelineno-2-1" > < / a > < span class = "sd" > " " " 合并左子数组和右子数组 " " " < / span >
< a id = "__codelineno-2-2" name = "__codelineno-2-2" href = "#__codelineno-2-2" > < / a > < span class = "c1" > # 左子数组区间 [left, mid]< / span >
< a id = "__codelineno-2-3" name = "__codelineno-2-3" href = "#__codelineno-2-3" > < / a > < span class = "c1" > # 右子数组区间 [mid + 1, right]< / span >
< a id = "__codelineno-2-4" name = "__codelineno-2-4" href = "#__codelineno-2-4" > < / a > < span class = "k" > def< / span > < span class = "nf" > merge< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > mid< / span > < span class = "p" > ,< / span > < span class = "n" > right< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-5" name = "__codelineno-2-5" href = "#__codelineno-2-5" > < / a > < span class = "c1" > # 初始化辅助数组 借助 copy模块< / span >
< a id = "__codelineno-2-6" name = "__codelineno-2-6" href = "#__codelineno-2-6" > < / a > < span class = "n" > tmp< / span > < span class = "o" > =< / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > left< / span > < span class = "p" > :< / span > < span class = "n" > right< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-2-7" name = "__codelineno-2-7" href = "#__codelineno-2-7" > < / a > < span class = "c1" > # 左子数组的起始索引和结束索引< / span >
< a id = "__codelineno-2-8" name = "__codelineno-2-8" href = "#__codelineno-2-8" > < / a > < span class = "n" > left_start< / span > < span class = "p" > ,< / span > < span class = "n" > left_end< / span > < span class = "o" > =< / span > < span class = "n" > left< / span > < span class = "o" > -< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > mid< / span > < span class = "o" > -< / span > < span class = "n" > left< / span >
< a id = "__codelineno-2-9" name = "__codelineno-2-9" href = "#__codelineno-2-9" > < / a > < span class = "c1" > # 右子数组的起始索引和结束索引< / span >
< a id = "__codelineno-2-10" name = "__codelineno-2-10" href = "#__codelineno-2-10" > < / a > < span class = "n" > right_start< / span > < span class = "p" > ,< / span > < span class = "n" > right_end< / span > < span class = "o" > =< / span > < span class = "n" > mid< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "o" > -< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > right< / span > < span class = "o" > -< / span > < span class = "n" > left< / span >
< a id = "__codelineno-2-11" name = "__codelineno-2-11" href = "#__codelineno-2-11" > < / a > < span class = "c1" > # i, j 分别指向左子数组、右子数组的首元素< / span >
< a id = "__codelineno-2-12" name = "__codelineno-2-12" href = "#__codelineno-2-12" > < / a > < span class = "n" > i< / span > < span class = "p" > ,< / span > < span class = "n" > j< / span > < span class = "o" > =< / span > < span class = "n" > left_start< / span > < span class = "p" > ,< / span > < span class = "n" > right_start< / span >
< a id = "__codelineno-2-13" name = "__codelineno-2-13" href = "#__codelineno-2-13" > < / a > < span class = "c1" > # 通过覆盖原数组 nums 来合并左子数组和右子数组< / span >
< a id = "__codelineno-2-14" name = "__codelineno-2-14" href = "#__codelineno-2-14" > < / a > < span class = "k" > for< / span > < span class = "n" > k< / span > < span class = "ow" > in< / span > < span class = "nb" > range< / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > right< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-15" name = "__codelineno-2-15" href = "#__codelineno-2-15" > < / a > < span class = "c1" > # 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-2-16" name = "__codelineno-2-16" href = "#__codelineno-2-16" > < / a > < span class = "k" > if< / span > < span class = "n" > i< / span > < span class = "o" > > < / span > < span class = "n" > left_end< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-17" name = "__codelineno-2-17" href = "#__codelineno-2-17" > < / a > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-2-18" name = "__codelineno-2-18" href = "#__codelineno-2-18" > < / a > < span class = "n" > j< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-2-19" name = "__codelineno-2-19" href = "#__codelineno-2-19" > < / a > < span class = "c1" > # 否则，若“右子数组已全部合并完”或“左子数组元素 < = 右子数组元素”，则选取左子数组元素，并且 i++< / span >
< a id = "__codelineno-2-20" name = "__codelineno-2-20" href = "#__codelineno-2-20" > < / a > < span class = "k" > elif< / span > < span class = "n" > j< / span > < span class = "o" > > < / span > < span class = "n" > right_end< / span > < span class = "ow" > or< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > < =< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]:< / span >
< a id = "__codelineno-2-21" name = "__codelineno-2-21" href = "#__codelineno-2-21" > < / a > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-2-22" name = "__codelineno-2-22" href = "#__codelineno-2-22" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-2-23" name = "__codelineno-2-23" href = "#__codelineno-2-23" > < / a > < span class = "c1" > # 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-2-24" name = "__codelineno-2-24" href = "#__codelineno-2-24" > < / a > < span class = "k" > else< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-25" name = "__codelineno-2-25" href = "#__codelineno-2-25" > < / a > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "o" > =< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-2-26" name = "__codelineno-2-26" href = "#__codelineno-2-26" > < / a > < span class = "n" > j< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-2-27" name = "__codelineno-2-27" href = "#__codelineno-2-27" > < / a >
< a id = "__codelineno-2-28" name = "__codelineno-2-28" href = "#__codelineno-2-28" > < / a > < span class = "sd" > " " " 归并排序 " " " < / span >
< a id = "__codelineno-2-29" name = "__codelineno-2-29" href = "#__codelineno-2-29" > < / a > < span class = "k" > def< / span > < span class = "nf" > merge_sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > right< / span > < span class = "p" > ):< / span >
< a id = "__codelineno-2-30" name = "__codelineno-2-30" href = "#__codelineno-2-30" > < / a > < span class = "c1" > # 终止条件< / span >
< a id = "__codelineno-2-31" name = "__codelineno-2-31" href = "#__codelineno-2-31" > < / a > < span class = "k" > if< / span > < span class = "n" > left< / span > < span class = "o" > > =< / span > < span class = "n" > right< / span > < span class = "p" > :< / span >
< a id = "__codelineno-2-32" name = "__codelineno-2-32" href = "#__codelineno-2-32" > < / a > < span class = "k" > return< / span > < span class = "c1" > # 当子数组长度为 1 时终止递归< / span >
< a id = "__codelineno-2-33" name = "__codelineno-2-33" href = "#__codelineno-2-33" > < / a > < span class = "c1" > # 划分阶段< / span >
< a id = "__codelineno-2-34" name = "__codelineno-2-34" href = "#__codelineno-2-34" > < / a > < span class = "n" > mid< / span > < span class = "o" > =< / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "o" > +< / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "o" > //< / span > < span class = "mi" > 2< / span > < span class = "c1" > # 计算中点< / span >
< a id = "__codelineno-2-35" name = "__codelineno-2-35" href = "#__codelineno-2-35" > < / a > < span class = "n" > merge_sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > mid< / span > < span class = "p" > )< / span > < span class = "c1" > # 递归左子数组< / span >
< a id = "__codelineno-2-36" name = "__codelineno-2-36" href = "#__codelineno-2-36" > < / a > < span class = "n" > merge_sort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > mid< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "c1" > # 递归右子数组< / span >
< a id = "__codelineno-2-37" name = "__codelineno-2-37" href = "#__codelineno-2-37" > < / a > < span class = "c1" > # 合并阶段< / span >
< a id = "__codelineno-2-38" name = "__codelineno-2-38" href = "#__codelineno-2-38" > < / a > < span class = "n" > merge< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "n" > mid< / span > < span class = "p" > ,< / span > < span class = "n" > right< / span > < span class = "p" > )< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.go< / span > < pre > < span > < / span > < code > < a id = "__codelineno-3-1" name = "__codelineno-3-1" href = "#__codelineno-3-1" > < / a > < span class = "cm" > /*< / span >
< a id = "__codelineno-3-2" name = "__codelineno-3-2" href = "#__codelineno-3-2" > < / a > < span class = "cm" > 合并左子数组和右子数组< / span >
< a id = "__codelineno-3-3" name = "__codelineno-3-3" href = "#__codelineno-3-3" > < / a > < span class = "cm" > 左子数组区间 [left, mid]< / span >
< a id = "__codelineno-3-4" name = "__codelineno-3-4" href = "#__codelineno-3-4" > < / a > < span class = "cm" > 右子数组区间 [mid + 1, right]< / span >
< a id = "__codelineno-3-5" name = "__codelineno-3-5" href = "#__codelineno-3-5" > < / a > < span class = "cm" > */< / span >
< a id = "__codelineno-3-6" name = "__codelineno-3-6" href = "#__codelineno-3-6" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > merge< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-7" name = "__codelineno-3-7" href = "#__codelineno-3-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化辅助数组 借助 copy 模块< / span >
< a id = "__codelineno-3-8" name = "__codelineno-3-8" href = "#__codelineno-3-8" > < / a > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nb" > make< / span > < span class = "p" > ([]< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "o" > -< / span > < span class = "nx" > left< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-9" name = "__codelineno-3-9" href = "#__codelineno-3-9" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-10" name = "__codelineno-3-10" href = "#__codelineno-3-10" > < / a > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "o" > -< / span > < span class = "nx" > left< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-11" name = "__codelineno-3-11" href = "#__codelineno-3-11" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-12" name = "__codelineno-3-12" href = "#__codelineno-3-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左子数组的起始索引和结束索引< / span >
< a id = "__codelineno-3-13" name = "__codelineno-3-13" href = "#__codelineno-3-13" > < / a > < span class = "w" > < / span > < span class = "nx" > leftStart< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > leftEnd< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "o" > -< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "o" > -< / span > < span class = "nx" > left< / span >
< a id = "__codelineno-3-14" name = "__codelineno-3-14" href = "#__codelineno-3-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右子数组的起始索引和结束索引< / span >
< a id = "__codelineno-3-15" name = "__codelineno-3-15" href = "#__codelineno-3-15" > < / a > < span class = "w" > < / span > < span class = "nx" > rightStart< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "o" > -< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "o" > -< / span > < span class = "nx" > left< / span >
< a id = "__codelineno-3-16" name = "__codelineno-3-16" href = "#__codelineno-3-16" > < / a > < span class = "w" > < / span > < span class = "c1" > // i, j 分别指向左子数组、右子数组的首元素< / span >
< a id = "__codelineno-3-17" name = "__codelineno-3-17" href = "#__codelineno-3-17" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > leftStart< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > rightStart< / span >
< a id = "__codelineno-3-18" name = "__codelineno-3-18" href = "#__codelineno-3-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过覆盖原数组 nums 来合并左子数组和右子数组< / span >
< a id = "__codelineno-3-19" name = "__codelineno-3-19" href = "#__codelineno-3-19" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "nx" > k< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > k< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > k< / span > < span class = "o" > ++< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-20" name = "__codelineno-3-20" href = "#__codelineno-3-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-3-21" name = "__codelineno-3-21" href = "#__codelineno-3-21" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nx" > leftEnd< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-22" name = "__codelineno-3-22" href = "#__codelineno-3-22" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-23" name = "__codelineno-3-23" href = "#__codelineno-3-23" > < / a > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-3-24" name = "__codelineno-3-24" href = "#__codelineno-3-24" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“右子数组已全部合并完”或“左子数组元素 < = 右子数组元素”，则选取左子数组元素，并且 i++< / span >
< a id = "__codelineno-3-25" name = "__codelineno-3-25" href = "#__codelineno-3-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "p" > > < / span > < span class = "w" > < / span > < span class = "nx" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-26" name = "__codelineno-3-26" href = "#__codelineno-3-26" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-27" name = "__codelineno-3-27" href = "#__codelineno-3-27" > < / a > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-3-28" name = "__codelineno-3-28" href = "#__codelineno-3-28" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-3-29" name = "__codelineno-3-29" href = "#__codelineno-3-29" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-30" name = "__codelineno-3-30" href = "#__codelineno-3-30" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "p" > =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-3-31" name = "__codelineno-3-31" href = "#__codelineno-3-31" > < / a > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span >
< a id = "__codelineno-3-32" name = "__codelineno-3-32" href = "#__codelineno-3-32" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-33" name = "__codelineno-3-33" href = "#__codelineno-3-33" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-34" name = "__codelineno-3-34" href = "#__codelineno-3-34" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-3-35" name = "__codelineno-3-35" href = "#__codelineno-3-35" > < / a >
< a id = "__codelineno-3-36" name = "__codelineno-3-36" href = "#__codelineno-3-36" > < / a > < span class = "kd" > func< / span > < span class = "w" > < / span > < span class = "nx" > mergeSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "w" > < / span > < span class = "p" > []< / span > < span class = "kt" > int< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-37" name = "__codelineno-3-37" href = "#__codelineno-3-37" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-3-38" name = "__codelineno-3-38" href = "#__codelineno-3-38" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-3-39" name = "__codelineno-3-39" href = "#__codelineno-3-39" > < / a > < span class = "w" > < / span > < span class = "k" > return< / span >
< a id = "__codelineno-3-40" name = "__codelineno-3-40" href = "#__codelineno-3-40" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-3-41" name = "__codelineno-3-41" href = "#__codelineno-3-41" > < / a > < span class = "w" > < / span > < span class = "c1" > // 划分阶段< / span >
< a id = "__codelineno-3-42" name = "__codelineno-3-42" href = "#__codelineno-3-42" > < / a > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "w" > < / span > < span class = "o" > :=< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "mi" > 2< / span >
< a id = "__codelineno-3-43" name = "__codelineno-3-43" href = "#__codelineno-3-43" > < / a > < span class = "w" > < / span > < span class = "nx" > mergeSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-44" name = "__codelineno-3-44" href = "#__codelineno-3-44" > < / a > < span class = "w" > < / span > < span class = "nx" > mergeSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-45" name = "__codelineno-3-45" href = "#__codelineno-3-45" > < / a > < span class = "w" > < / span > < span class = "c1" > // 合并阶段< / span >
< a id = "__codelineno-3-46" name = "__codelineno-3-46" href = "#__codelineno-3-46" > < / a > < span class = "w" > < / span > < span class = "nx" > merge< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-3-47" name = "__codelineno-3-47" href = "#__codelineno-3-47" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.js< / span > < pre > < span > < / span > < code > < a id = "__codelineno-4-1" name = "__codelineno-4-1" href = "#__codelineno-4-1" > < / a > < span class = "cm" > /* 合并左子数组和右子数组 */< / span >
< a id = "__codelineno-4-2" name = "__codelineno-4-2" href = "#__codelineno-4-2" > < / a > < span class = "c1" > // 左子数组区间 [left, mid]< / span >
< a id = "__codelineno-4-3" name = "__codelineno-4-3" href = "#__codelineno-4-3" > < / a > < span class = "c1" > // 右子数组区间 [mid + 1, right]< / span >
< a id = "__codelineno-4-4" name = "__codelineno-4-4" href = "#__codelineno-4-4" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > merge< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-5" name = "__codelineno-4-5" href = "#__codelineno-4-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化辅助数组< / span >
< a id = "__codelineno-4-6" name = "__codelineno-4-6" href = "#__codelineno-4-6" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > slice< / span > < span class = "p" > (< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > );< / span > < span class = "w" > < / span >
< a id = "__codelineno-4-7" name = "__codelineno-4-7" href = "#__codelineno-4-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左子数组的起始索引和结束索引 < / span >
< a id = "__codelineno-4-8" name = "__codelineno-4-8" href = "#__codelineno-4-8" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > leftStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > leftEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-9" name = "__codelineno-4-9" href = "#__codelineno-4-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右子数组的起始索引和结束索引 < / span >
< a id = "__codelineno-4-10" name = "__codelineno-4-10" href = "#__codelineno-4-10" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > rightStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-4-11" name = "__codelineno-4-11" href = "#__codelineno-4-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // i, j 分别指向左子数组、右子数组的首元素< / span >
< a id = "__codelineno-4-12" name = "__codelineno-4-12" href = "#__codelineno-4-12" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > leftStart< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > rightStart< / span > < span class = "p" > ;< / span > < span class = "w" > < / span >
< a id = "__codelineno-4-13" name = "__codelineno-4-13" href = "#__codelineno-4-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过覆盖原数组 nums 来合并左子数组和右子数组< / span >
< a id = "__codelineno-4-14" name = "__codelineno-4-14" href = "#__codelineno-4-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > k< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > k< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > k< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-15" name = "__codelineno-4-15" href = "#__codelineno-4-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-4-16" name = "__codelineno-4-16" href = "#__codelineno-4-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > leftEnd< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-17" name = "__codelineno-4-17" href = "#__codelineno-4-17" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-4-18" name = "__codelineno-4-18" href = "#__codelineno-4-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“右子数组已全部合并完”或“左子数组元素 < = 右子数组元素”，则选取左子数组元素，并且 i++< / span >
< a id = "__codelineno-4-19" name = "__codelineno-4-19" href = "#__codelineno-4-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-20" name = "__codelineno-4-20" href = "#__codelineno-4-20" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-4-21" name = "__codelineno-4-21" href = "#__codelineno-4-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-4-22" name = "__codelineno-4-22" href = "#__codelineno-4-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-23" name = "__codelineno-4-23" href = "#__codelineno-4-23" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-4-24" name = "__codelineno-4-24" href = "#__codelineno-4-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-25" name = "__codelineno-4-25" href = "#__codelineno-4-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-4-26" name = "__codelineno-4-26" href = "#__codelineno-4-26" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-4-27" name = "__codelineno-4-27" href = "#__codelineno-4-27" > < / a >
< a id = "__codelineno-4-28" name = "__codelineno-4-28" href = "#__codelineno-4-28" > < / a > < span class = "cm" > /* 归并排序 */< / span >
< a id = "__codelineno-4-29" name = "__codelineno-4-29" href = "#__codelineno-4-29" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > mergeSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-4-30" name = "__codelineno-4-30" href = "#__codelineno-4-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-4-31" name = "__codelineno-4-31" href = "#__codelineno-4-31" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 当子数组长度为 1 时终止递归< / span >
< a id = "__codelineno-4-32" name = "__codelineno-4-32" href = "#__codelineno-4-32" > < / a > < span class = "w" > < / span > < span class = "c1" > // 划分阶段< / span >
< a id = "__codelineno-4-33" name = "__codelineno-4-33" href = "#__codelineno-4-33" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Math< / span > < span class = "p" > .< / span > < span class = "nx" > floor< / span > < span class = "p" > ((< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 计算中点< / span >
< a id = "__codelineno-4-34" name = "__codelineno-4-34" href = "#__codelineno-4-34" > < / a > < span class = "w" > < / span > < span class = "nx" > mergeSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归左子数组< / span >
< a id = "__codelineno-4-35" name = "__codelineno-4-35" href = "#__codelineno-4-35" > < / a > < span class = "w" > < / span > < span class = "nx" > mergeSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归右子数组< / span >
< a id = "__codelineno-4-36" name = "__codelineno-4-36" href = "#__codelineno-4-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 合并阶段< / span >
< a id = "__codelineno-4-37" name = "__codelineno-4-37" href = "#__codelineno-4-37" > < / a > < span class = "w" > < / span > < span class = "nx" > merge< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-4-38" name = "__codelineno-4-38" href = "#__codelineno-4-38" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.ts< / span > < pre > < span > < / span > < code > < a id = "__codelineno-5-1" name = "__codelineno-5-1" href = "#__codelineno-5-1" > < / a > < span class = "cm" > /* 合并左子数组和右子数组 */< / span >
< a id = "__codelineno-5-2" name = "__codelineno-5-2" href = "#__codelineno-5-2" > < / a > < span class = "c1" > // 左子数组区间 [left, mid]< / span >
< a id = "__codelineno-5-3" name = "__codelineno-5-3" href = "#__codelineno-5-3" > < / a > < span class = "c1" > // 右子数组区间 [mid + 1, right]< / span >
< a id = "__codelineno-5-4" name = "__codelineno-5-4" href = "#__codelineno-5-4" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > merge< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-5" name = "__codelineno-5-5" href = "#__codelineno-5-5" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化辅助数组< / span >
< a id = "__codelineno-5-6" name = "__codelineno-5-6" href = "#__codelineno-5-6" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > .< / span > < span class = "nx" > slice< / span > < span class = "p" > (< / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-7" name = "__codelineno-5-7" href = "#__codelineno-5-7" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左子数组的起始索引和结束索引< / span >
< a id = "__codelineno-5-8" name = "__codelineno-5-8" href = "#__codelineno-5-8" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > leftStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > leftEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-9" name = "__codelineno-5-9" href = "#__codelineno-5-9" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右子数组的起始索引和结束索引< / span >
< a id = "__codelineno-5-10" name = "__codelineno-5-10" href = "#__codelineno-5-10" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > rightStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-11" name = "__codelineno-5-11" href = "#__codelineno-5-11" > < / a > < span class = "w" > < / span > < span class = "c1" > // i, j 分别指向左子数组、右子数组的首元素< / span >
< a id = "__codelineno-5-12" name = "__codelineno-5-12" href = "#__codelineno-5-12" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > leftStart< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > rightStart< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-5-13" name = "__codelineno-5-13" href = "#__codelineno-5-13" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过覆盖原数组 nums 来合并左子数组和右子数组< / span >
< a id = "__codelineno-5-14" name = "__codelineno-5-14" href = "#__codelineno-5-14" > < / a > < span class = "w" > < / span > < span class = "k" > for< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > k< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > k< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "nx" > k< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-15" name = "__codelineno-5-15" href = "#__codelineno-5-15" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-5-16" name = "__codelineno-5-16" href = "#__codelineno-5-16" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > i< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > leftEnd< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-17" name = "__codelineno-5-17" href = "#__codelineno-5-17" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-5-18" name = "__codelineno-5-18" href = "#__codelineno-5-18" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“右子数组已全部合并完”或“左子数组元素 < = 右子数组元素”，则选取左子数组元素，并且 i++< / span >
< a id = "__codelineno-5-19" name = "__codelineno-5-19" href = "#__codelineno-5-19" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > j< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "nx" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "p" > ])< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-20" name = "__codelineno-5-20" href = "#__codelineno-5-20" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-5-21" name = "__codelineno-5-21" href = "#__codelineno-5-21" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-5-22" name = "__codelineno-5-22" href = "#__codelineno-5-22" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-23" name = "__codelineno-5-23" href = "#__codelineno-5-23" > < / a > < span class = "w" > < / span > < span class = "nx" > nums< / span > < span class = "p" > [< / span > < span class = "nx" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nx" > tmp< / span > < span class = "p" > [< / span > < span class = "nx" > j< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-5-24" name = "__codelineno-5-24" href = "#__codelineno-5-24" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-25" name = "__codelineno-5-25" href = "#__codelineno-5-25" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-5-26" name = "__codelineno-5-26" href = "#__codelineno-5-26" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-5-27" name = "__codelineno-5-27" href = "#__codelineno-5-27" > < / a >
< a id = "__codelineno-5-28" name = "__codelineno-5-28" href = "#__codelineno-5-28" > < / a > < span class = "cm" > /* 归并排序 */< / span >
< a id = "__codelineno-5-29" name = "__codelineno-5-29" href = "#__codelineno-5-29" > < / a > < span class = "kd" > function< / span > < span class = "w" > < / span > < span class = "nx" > mergeSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > [],< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "kt" > number< / span > < span class = "p" > )< / span > < span class = "o" > :< / span > < span class = "w" > < / span > < span class = "ow" > void< / span > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-5-30" name = "__codelineno-5-30" href = "#__codelineno-5-30" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-5-31" name = "__codelineno-5-31" href = "#__codelineno-5-31" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 当子数组长度为 1 时终止递归< / span >
< a id = "__codelineno-5-32" name = "__codelineno-5-32" href = "#__codelineno-5-32" > < / a > < span class = "w" > < / span > < span class = "c1" > // 划分阶段< / span >
< a id = "__codelineno-5-33" name = "__codelineno-5-33" href = "#__codelineno-5-33" > < / a > < span class = "w" > < / span > < span class = "kd" > let< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "nb" > Math< / span > < span class = "p" > .< / span > < span class = "nx" > floor< / span > < span class = "p" > ((< / span > < span class = "nx" > left< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "mf" > 2< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 计算中点< / span >
< a id = "__codelineno-5-34" name = "__codelineno-5-34" href = "#__codelineno-5-34" > < / a > < span class = "w" > < / span > < span class = "nx" > mergeSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归左子数组< / span >
< a id = "__codelineno-5-35" name = "__codelineno-5-35" href = "#__codelineno-5-35" > < / a > < span class = "w" > < / span > < span class = "nx" > mergeSort< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "mf" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归右子数组< / span >
< a id = "__codelineno-5-36" name = "__codelineno-5-36" href = "#__codelineno-5-36" > < / a > < span class = "w" > < / span > < span class = "c1" > // 合并阶段< / span >
< a id = "__codelineno-5-37" name = "__codelineno-5-37" href = "#__codelineno-5-37" > < / a > < span class = "w" > < / span > < span class = "nx" > merge< / span > < span class = "p" > (< / span > < span class = "nx" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "nx" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-5-38" name = "__codelineno-5-38" href = "#__codelineno-5-38" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.c< / span > < pre > < span > < / span > < code > < a id = "__codelineno-6-1" name = "__codelineno-6-1" href = "#__codelineno-6-1" > < / a >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.cs< / span > < pre > < span > < / span > < code > < a id = "__codelineno-7-1" name = "__codelineno-7-1" href = "#__codelineno-7-1" > < / a > < span class = "cm" > /* 合并左子数组和右子数组 */< / span >
< a id = "__codelineno-7-2" name = "__codelineno-7-2" href = "#__codelineno-7-2" > < / a > < span class = "c1" > // 左子数组区间 [left, mid]< / span >
< a id = "__codelineno-7-3" name = "__codelineno-7-3" href = "#__codelineno-7-3" > < / a > < span class = "c1" > // 右子数组区间 [mid + 1, right]< / span >
< a id = "__codelineno-7-4" name = "__codelineno-7-4" href = "#__codelineno-7-4" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > merge< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > []< / 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" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-7-5" name = "__codelineno-7-5" href = "#__codelineno-7-5" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-7-6" name = "__codelineno-7-6" href = "#__codelineno-7-6" > < / a > < span class = "w" > < / span > < span class = "c1" > // 初始化辅助数组< / span >
< a id = "__codelineno-7-7" name = "__codelineno-7-7" href = "#__codelineno-7-7" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "p" > []< / span > < span class = "w" > < / span > < span class = "n" > tmp< / 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" > left< / span > < span class = "p" > ..(< / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > )];< / span >
< a id = "__codelineno-7-8" name = "__codelineno-7-8" href = "#__codelineno-7-8" > < / a > < span class = "w" > < / span > < span class = "c1" > // 左子数组的起始索引和结束索引 < / span >
< a id = "__codelineno-7-9" name = "__codelineno-7-9" href = "#__codelineno-7-9" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > leftStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > leftEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-10" name = "__codelineno-7-10" href = "#__codelineno-7-10" > < / a > < span class = "w" > < / span > < span class = "c1" > // 右子数组的起始索引和结束索引 < / span >
< a id = "__codelineno-7-11" name = "__codelineno-7-11" href = "#__codelineno-7-11" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > rightStart< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "w" > < / span > < span class = "o" > -< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-12" name = "__codelineno-7-12" href = "#__codelineno-7-12" > < / a > < span class = "w" > < / span > < span class = "c1" > // i, j 分别指向左子数组、右子数组的首元素< / span >
< a id = "__codelineno-7-13" name = "__codelineno-7-13" href = "#__codelineno-7-13" > < / a > < span class = "w" > < / 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" > leftStart< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > rightStart< / span > < span class = "p" > ;< / span >
< a id = "__codelineno-7-14" name = "__codelineno-7-14" href = "#__codelineno-7-14" > < / a > < span class = "w" > < / span > < span class = "c1" > // 通过覆盖原数组 nums 来合并左子数组和右子数组< / span >
< a id = "__codelineno-7-15" name = "__codelineno-7-15" href = "#__codelineno-7-15" > < / 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" > k< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > k< / span > < span class = "w" > < / span > < span class = "o" > < =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "n" > k< / span > < span class = "o" > ++< / span > < span class = "p" > )< / span >
< a id = "__codelineno-7-16" name = "__codelineno-7-16" href = "#__codelineno-7-16" > < / a > < span class = "w" > < / span > < span class = "p" > {< / span >
< a id = "__codelineno-7-17" name = "__codelineno-7-17" href = "#__codelineno-7-17" > < / a > < span class = "w" > < / span > < span class = "c1" > // 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-7-18" name = "__codelineno-7-18" href = "#__codelineno-7-18" > < / 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 = "n" > leftEnd< / span > < span class = "p" > )< / span >
< a id = "__codelineno-7-19" name = "__codelineno-7-19" href = "#__codelineno-7-19" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-7-20" name = "__codelineno-7-20" href = "#__codelineno-7-20" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“右子数组已全部合并完”或“左子数组元素 < = 右子数组元素”，则选取左子数组元素，并且 i++< / span >
< a id = "__codelineno-7-21" name = "__codelineno-7-21" href = "#__codelineno-7-21" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span > < span class = "w" > < / span > < span class = "nf" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > j< / span > < span class = "w" > < / span > < span class = "o" > > < / span > < span class = "w" > < / span > < span class = "n" > rightEnd< / span > < span class = "w" > < / span > < span class = "o" > ||< / span > < span class = "w" > < / span > < span class = "n" > tmp< / 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" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ])< / span >
< a id = "__codelineno-7-22" name = "__codelineno-7-22" href = "#__codelineno-7-22" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-7-23" name = "__codelineno-7-23" href = "#__codelineno-7-23" > < / a > < span class = "w" > < / span > < span class = "c1" > // 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-7-24" name = "__codelineno-7-24" href = "#__codelineno-7-24" > < / a > < span class = "w" > < / span > < span class = "k" > else< / span >
< a id = "__codelineno-7-25" name = "__codelineno-7-25" href = "#__codelineno-7-25" > < / a > < span class = "w" > < / span > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "o" > ++< / span > < span class = "p" > ];< / span >
< a id = "__codelineno-7-26" name = "__codelineno-7-26" href = "#__codelineno-7-26" > < / a > < span class = "w" > < / span > < span class = "p" > }< / span >
< a id = "__codelineno-7-27" name = "__codelineno-7-27" href = "#__codelineno-7-27" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-7-28" name = "__codelineno-7-28" href = "#__codelineno-7-28" > < / a >
< a id = "__codelineno-7-29" name = "__codelineno-7-29" href = "#__codelineno-7-29" > < / a > < span class = "cm" > /* 归并排序 */< / span >
< a id = "__codelineno-7-30" name = "__codelineno-7-30" href = "#__codelineno-7-30" > < / a > < span class = "k" > void< / span > < span class = "w" > < / span > < span class = "nf" > mergeSort< / span > < span class = "p" > (< / span > < span class = "kt" > int< / span > < span class = "p" > []< / 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" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-7-31" name = "__codelineno-7-31" href = "#__codelineno-7-31" > < / a > < span class = "p" > {< / span >
< a id = "__codelineno-7-32" name = "__codelineno-7-32" href = "#__codelineno-7-32" > < / a > < span class = "w" > < / span > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-7-33" name = "__codelineno-7-33" href = "#__codelineno-7-33" > < / a > < span class = "w" > < / span > < span class = "k" > if< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > > =< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "k" > return< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 当子数组长度为 1 时终止递归< / span >
< a id = "__codelineno-7-34" name = "__codelineno-7-34" href = "#__codelineno-7-34" > < / a > < span class = "w" > < / span > < span class = "c1" > // 划分阶段< / span >
< a id = "__codelineno-7-35" name = "__codelineno-7-35" href = "#__codelineno-7-35" > < / a > < span class = "w" > < / span > < span class = "kt" > int< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > =< / span > < span class = "w" > < / span > < span class = "p" > (< / span > < span class = "n" > left< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > )< / span > < span class = "w" > < / span > < span class = "o" > /< / span > < span class = "w" > < / span > < span class = "m" > 2< / span > < span class = "p" > ;< / span > < span class = "w" > < / span > < span class = "c1" > // 计算中点< / span >
< a id = "__codelineno-7-36" name = "__codelineno-7-36" href = "#__codelineno-7-36" > < / a > < span class = "w" > < / span > < span class = "n" > mergeSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归左子数组< / span >
< a id = "__codelineno-7-37" name = "__codelineno-7-37" href = "#__codelineno-7-37" > < / a > < span class = "w" > < / span > < span class = "n" > mergeSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "w" > < / span > < span class = "o" > +< / span > < span class = "w" > < / span > < span class = "m" > 1< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > );< / span > < span class = "w" > < / span > < span class = "c1" > // 递归右子数组< / span >
< a id = "__codelineno-7-38" name = "__codelineno-7-38" href = "#__codelineno-7-38" > < / a > < span class = "w" > < / span > < span class = "c1" > // 合并阶段< / span >
< a id = "__codelineno-7-39" name = "__codelineno-7-39" href = "#__codelineno-7-39" > < / a > < span class = "w" > < / span > < span class = "n" > merge< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > left< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > mid< / span > < span class = "p" > ,< / span > < span class = "w" > < / span > < span class = "n" > right< / span > < span class = "p" > );< / span >
< a id = "__codelineno-7-40" name = "__codelineno-7-40" href = "#__codelineno-7-40" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.swift< / span > < pre > < span > < / span > < code > < a id = "__codelineno-8-1" name = "__codelineno-8-1" href = "#__codelineno-8-1" > < / a > < span class = "cm" > /**< / span >
< a id = "__codelineno-8-2" name = "__codelineno-8-2" href = "#__codelineno-8-2" > < / a > < span class = "cm" > * 合并左子数组和右子数组< / span >
< a id = "__codelineno-8-3" name = "__codelineno-8-3" href = "#__codelineno-8-3" > < / a > < span class = "cm" > * 左子数组区间 [left, mid]< / span >
< a id = "__codelineno-8-4" name = "__codelineno-8-4" href = "#__codelineno-8-4" > < / a > < span class = "cm" > * 右子数组区间 [mid + 1, right]< / span >
< a id = "__codelineno-8-5" name = "__codelineno-8-5" href = "#__codelineno-8-5" > < / a > < span class = "cm" > */< / span >
< a id = "__codelineno-8-6" name = "__codelineno-8-6" href = "#__codelineno-8-6" > < / a > < span class = "kd" > func< / span > < span class = "nf" > merge< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "kr" > left< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "n" > mid< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "kr" > right< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / 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" > // 初始化辅助数组< / span >
< a id = "__codelineno-8-8" name = "__codelineno-8-8" href = "#__codelineno-8-8" > < / a > < span class = "kd" > let< / span > < span class = "nv" > tmp< / 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" > left< / span > < span class = "p" > ..< / span > < span class = "o" > < < / span > < span class = "p" > (< / span > < span class = "kr" > right< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > )])< / span >
< a id = "__codelineno-8-9" name = "__codelineno-8-9" href = "#__codelineno-8-9" > < / a > < span class = "c1" > // 左子数组的起始索引和结束索引< / span >
< a id = "__codelineno-8-10" name = "__codelineno-8-10" href = "#__codelineno-8-10" > < / a > < span class = "kd" > let< / span > < span class = "nv" > leftStart< / span > < span class = "p" > =< / span > < span class = "kr" > left< / span > < span class = "o" > -< / span > < span class = "kr" > left< / span >
< a id = "__codelineno-8-11" name = "__codelineno-8-11" href = "#__codelineno-8-11" > < / a > < span class = "kd" > let< / span > < span class = "nv" > leftEnd< / span > < span class = "p" > =< / span > < span class = "n" > mid< / span > < span class = "o" > -< / span > < span class = "kr" > left< / span >
< a id = "__codelineno-8-12" name = "__codelineno-8-12" href = "#__codelineno-8-12" > < / a > < span class = "c1" > // 右子数组的起始索引和结束索引< / span >
< a id = "__codelineno-8-13" name = "__codelineno-8-13" href = "#__codelineno-8-13" > < / a > < span class = "kd" > let< / span > < span class = "nv" > rightStart< / span > < span class = "p" > =< / span > < span class = "n" > mid< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "o" > -< / span > < span class = "kr" > left< / span >
< a id = "__codelineno-8-14" name = "__codelineno-8-14" href = "#__codelineno-8-14" > < / a > < span class = "kd" > let< / span > < span class = "nv" > rightEnd< / span > < span class = "p" > =< / span > < span class = "kr" > right< / span > < span class = "o" > -< / span > < span class = "kr" > left< / span >
< a id = "__codelineno-8-15" name = "__codelineno-8-15" href = "#__codelineno-8-15" > < / a > < span class = "c1" > // i, j 分别指向左子数组、右子数组的首元素< / span >
< a id = "__codelineno-8-16" name = "__codelineno-8-16" href = "#__codelineno-8-16" > < / a > < span class = "kd" > var< / span > < span class = "nv" > i< / span > < span class = "p" > =< / span > < span class = "n" > leftStart< / span >
< a id = "__codelineno-8-17" name = "__codelineno-8-17" href = "#__codelineno-8-17" > < / a > < span class = "kd" > var< / span > < span class = "nv" > j< / span > < span class = "p" > =< / span > < span class = "n" > rightStart< / span >
< a id = "__codelineno-8-18" name = "__codelineno-8-18" href = "#__codelineno-8-18" > < / a > < span class = "c1" > // 通过覆盖原数组 nums 来合并左子数组和右子数组< / span >
< a id = "__codelineno-8-19" name = "__codelineno-8-19" href = "#__codelineno-8-19" > < / a > < span class = "k" > for< / span > < span class = "n" > k< / span > < span class = "k" > in< / span > < span class = "kr" > left< / span > < span class = "p" > ...< / span > < span class = "kr" > right< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-20" name = "__codelineno-8-20" href = "#__codelineno-8-20" > < / a > < span class = "c1" > // 若“左子数组已全部合并完”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-8-21" name = "__codelineno-8-21" href = "#__codelineno-8-21" > < / a > < span class = "k" > if< / span > < span class = "n" > i< / span > < span class = "o" > > < / span > < span class = "n" > leftEnd< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-22" name = "__codelineno-8-22" href = "#__codelineno-8-22" > < / a > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-23" name = "__codelineno-8-23" href = "#__codelineno-8-23" > < / a > < span class = "n" > j< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-8-24" name = "__codelineno-8-24" href = "#__codelineno-8-24" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-25" name = "__codelineno-8-25" href = "#__codelineno-8-25" > < / a > < span class = "c1" > // 否则，若“右子数组已全部合并完”或“左子数组元素 < = 右子数组元素”，则选取左子数组元素，并且 i++< / span >
< a id = "__codelineno-8-26" name = "__codelineno-8-26" href = "#__codelineno-8-26" > < / a > < span class = "k" > else< / span > < span class = "k" > if< / span > < span class = "n" > j< / span > < span class = "o" > > < / span > < span class = "n" > rightEnd< / span > < span class = "o" > ||< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span > < span class = "o" > < =< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-27" name = "__codelineno-8-27" href = "#__codelineno-8-27" > < / a > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > i< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-28" name = "__codelineno-8-28" href = "#__codelineno-8-28" > < / a > < span class = "n" > i< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-8-29" name = "__codelineno-8-29" href = "#__codelineno-8-29" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-30" name = "__codelineno-8-30" href = "#__codelineno-8-30" > < / a > < span class = "c1" > // 否则，若“左右子数组都未全部合并完”且“左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++< / span >
< a id = "__codelineno-8-31" name = "__codelineno-8-31" href = "#__codelineno-8-31" > < / a > < span class = "k" > else< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-32" name = "__codelineno-8-32" href = "#__codelineno-8-32" > < / a > < span class = "n" > nums< / span > < span class = "p" > [< / span > < span class = "n" > k< / span > < span class = "p" > ]< / span > < span class = "p" > =< / span > < span class = "n" > tmp< / span > < span class = "p" > [< / span > < span class = "n" > j< / span > < span class = "p" > ]< / span >
< a id = "__codelineno-8-33" name = "__codelineno-8-33" href = "#__codelineno-8-33" > < / a > < span class = "n" > j< / span > < span class = "o" > +=< / span > < span class = "mi" > 1< / span >
< a id = "__codelineno-8-34" name = "__codelineno-8-34" href = "#__codelineno-8-34" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-35" name = "__codelineno-8-35" href = "#__codelineno-8-35" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-36" name = "__codelineno-8-36" href = "#__codelineno-8-36" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-37" name = "__codelineno-8-37" href = "#__codelineno-8-37" > < / a >
< a id = "__codelineno-8-38" name = "__codelineno-8-38" href = "#__codelineno-8-38" > < / a > < span class = "cm" > /* 归并排序 */< / span >
< a id = "__codelineno-8-39" name = "__codelineno-8-39" href = "#__codelineno-8-39" > < / a > < span class = "kd" > func< / span > < span class = "nf" > mergeSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "kr" > inout< / span > < span class = "p" > [< / span > < span class = "nb" > Int< / span > < span class = "p" > ],< / span > < span class = "kr" > left< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > ,< / span > < span class = "kr" > right< / span > < span class = "p" > :< / span > < span class = "nb" > Int< / span > < span class = "p" > )< / span > < span class = "p" > {< / span >
< a id = "__codelineno-8-40" name = "__codelineno-8-40" href = "#__codelineno-8-40" > < / a > < span class = "c1" > // 终止条件< / span >
< a id = "__codelineno-8-41" name = "__codelineno-8-41" href = "#__codelineno-8-41" > < / a > < span class = "k" > if< / span > < span class = "kr" > left< / span > < span class = "o" > > =< / span > < span class = "kr" > right< / span > < span class = "p" > {< / span > < span class = "c1" > // 当子数组长度为 1 时终止递归< / span >
< a id = "__codelineno-8-42" name = "__codelineno-8-42" href = "#__codelineno-8-42" > < / a > < span class = "k" > return< / span >
< a id = "__codelineno-8-43" name = "__codelineno-8-43" href = "#__codelineno-8-43" > < / a > < span class = "p" > }< / span >
< a id = "__codelineno-8-44" name = "__codelineno-8-44" href = "#__codelineno-8-44" > < / a > < span class = "c1" > // 划分阶段< / span >
< a id = "__codelineno-8-45" name = "__codelineno-8-45" href = "#__codelineno-8-45" > < / a > < span class = "kd" > let< / span > < span class = "nv" > mid< / span > < span class = "p" > =< / span > < span class = "p" > (< / span > < span class = "kr" > left< / span > < span class = "o" > +< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span > < span class = "o" > /< / span > < span class = "mi" > 2< / span > < span class = "c1" > // 计算中点< / span >
< a id = "__codelineno-8-46" name = "__codelineno-8-46" href = "#__codelineno-8-46" > < / a > < span class = "n" > mergeSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "kr" > left< / span > < span class = "p" > :< / span > < span class = "kr" > left< / span > < span class = "p" > ,< / span > < span class = "kr" > right< / span > < span class = "p" > :< / span > < span class = "n" > mid< / span > < span class = "p" > )< / span > < span class = "c1" > // 递归左子数组< / span >
< a id = "__codelineno-8-47" name = "__codelineno-8-47" href = "#__codelineno-8-47" > < / a > < span class = "n" > mergeSort< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "kr" > left< / span > < span class = "p" > :< / span > < span class = "n" > mid< / span > < span class = "o" > +< / span > < span class = "mi" > 1< / span > < span class = "p" > ,< / span > < span class = "kr" > right< / span > < span class = "p" > :< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span > < span class = "c1" > // 递归右子数组< / span >
< a id = "__codelineno-8-48" name = "__codelineno-8-48" href = "#__codelineno-8-48" > < / a > < span class = "c1" > // 合并阶段< / span >
< a id = "__codelineno-8-49" name = "__codelineno-8-49" href = "#__codelineno-8-49" > < / a > < span class = "n" > merge< / span > < span class = "p" > (< / span > < span class = "n" > nums< / span > < span class = "p" > :< / span > < span class = "p" > & < / span > < span class = "n" > nums< / span > < span class = "p" > ,< / span > < span class = "kr" > left< / span > < span class = "p" > :< / span > < span class = "kr" > left< / span > < span class = "p" > ,< / span > < span class = "n" > mid< / span > < span class = "p" > :< / span > < span class = "n" > mid< / span > < span class = "p" > ,< / span > < span class = "kr" > right< / span > < span class = "p" > :< / span > < span class = "kr" > right< / span > < span class = "p" > )< / span >
< a id = "__codelineno-8-50" name = "__codelineno-8-50" href = "#__codelineno-8-50" > < / a > < span class = "p" > }< / span >
< / code > < / pre > < / div >
< / div >
< div class = "tabbed-block" >
< div class = "highlight" > < span class = "filename" > merge_sort.zig< / span > < pre > < span > < / span > < code > < a id = "__codelineno-9-1" name = "__codelineno-9-1" href = "#__codelineno-9-1" > < / a >
< / code > < / pre > < / div >
< / div >
< / div >
< / div >
< p > 下面重点解释一下合并方法 < code > merge()< / code > 的流程：< / p >
< ol >
< li > 初始化一个辅助数组 < code > tmp< / code > 暂存待合并区间 < code > [left, right]< / code > 内的元素，后续通过覆盖原数组 < code > nums< / code > 的元素来实现合并；< / li >
< li > 初始化指针 < code > i< / code > , < code > j< / code > , < code > k< / code > 分别指向左子数组、右子数组、原数组的首元素；< / li >
< li > 循环判断 < code > tmp[i]< / code > 和 < code > tmp[j]< / code > 的大小，将较小的先覆盖至 < code > nums[k]< / code > ，指针 < code > i< / code > , < code > j< / code > 根据判断结果交替前进（指针 < code > k< / code > 也前进），直至两个子数组都遍历完，即可完成合并。< / li >
< / ol >
< p > 合并方法 < code > merge()< / code > 代码中的主要难点：< / p >
< ul >
< li > < code > nums< / code > 的待合并区间为 < code > [left, right]< / code > ，而因为 < code > tmp< / code > 只复制了 < code > nums< / code > 该区间元素，所以 < code > tmp< / code > 对应区间为 < code > [0, right - left]< / code > ， < strong > 需要特别注意代码中各个变量的含义< / strong > 。< / li >
< li > 判断 < code > tmp[i]< / code > 和 < code > tmp[j]< / code > 的大小的操作中，还 < strong > 需考虑当子数组遍历完成后的索引越界问题< / strong > ，即 < code > i > leftEnd< / code > 和 < code > j > rightEnd< / code > 的情况，索引越界的优先级是最高的，例如如果左子数组已经被合并完了，那么不用继续判断，直接合并右子数组元素即可。< / li >
< / ul >
< h2 id = "1152" > 11.5.2. 算法特性< a class = "headerlink" href = "#1152" title = "Permanent link" > ¶ < / a > < / h2 >
< ul >
< li > < strong > 时间复杂度 < span class = "arithmatex" > \(O(n \log n)\)< / span > < / strong > ：划分形成高度为 < span class = "arithmatex" > \(\log n\)< / span > 的递归树，每层合并的总操作数量为 < span class = "arithmatex" > \(n\)< / span > ，总体使用 < span class = "arithmatex" > \(O(n \log n)\)< / span > 时间。< / li >
< li > < strong > 空间复杂度 < span class = "arithmatex" > \(O(n)\)< / span > < / strong > ：需借助辅助数组实现合并，使用 < span class = "arithmatex" > \(O(n)\)< / span > 大小的额外空间；递归深度为 < span class = "arithmatex" > \(\log n\)< / span > ，使用 < span class = "arithmatex" > \(O(\log n)\)< / span > 大小的栈帧空间。< / li >
< li > < strong > 非原地排序< / strong > ：辅助数组需要使用 < span class = "arithmatex" > \(O(n)\)< / span > 额外空间。< / li >
< li > < strong > 稳定排序< / strong > ：在合并时可保证相等元素的相对位置不变。< / li >
< li > < strong > 非自适应排序< / strong > ：对于任意输入数据，归并排序的时间复杂度皆相同。< / li >
< / ul >
< h2 id = "1153" > 11.5.3. 链表排序 *< a class = "headerlink" href = "#1153" title = "Permanent link" > ¶ < / a > < / h2 >
< p > 归并排序有一个很特别的优势，用于排序链表时有很好的性能表现，< strong > 空间复杂度可被优化至 < span class = "arithmatex" > \(O(1)\)< / span > < / strong > ，这是因为：< / p >
< ul >
< li > 由于链表可仅通过改变指针来实现结点增删，因此“将两个短有序链表合并为一个长有序链表”无需使用额外空间，即回溯合并阶段不用像排序数组一样建立辅助数组 < code > tmp< / code > ； < / li >
< li > 通过使用「迭代」代替「递归划分」，可省去递归使用的栈帧空间；< / li >
< / ul >
< blockquote >
< p > 详情参考：< a href = "https://leetcode-cn.com/problems/sort-list/solution/sort-list-gui-bing-pai-xu-lian-biao-by-jyd/" > 148. 排序链表< / a > < / p >
< / blockquote >
< h2 id = "__comments" > 评论< / h2 >
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