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11.4 插入排序
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krahets/hello-algo
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第 0 章 前言
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0.1 关于本书
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0.2 如何使用本书
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0.3 小结
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第 1 章 初识算法
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1.1 算法无处不在
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1.2 算法是什么
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1.3 小结
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第 2 章 时空复杂度
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2.1 算法效率评估
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2.2 迭代与递归
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2.3 时间复杂度
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2.4 空间复杂度
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2.5 小结
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第 3 章 数据结构
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<span class="md-nav__icon md-icon"></span>
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第 3 章 数据结构
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<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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<span class="md-ellipsis">
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3.1 数据结构分类
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<span class="md-ellipsis">
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3.2 基本数据类型
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<span class="md-ellipsis">
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3.3 数字编码 *
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<span class="md-ellipsis">
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3.4 字符编码 *
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3.5 小结
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</a>
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
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<a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
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<span class="md-ellipsis">
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第 4 章 数组与链表
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</a>
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<label class="md-nav__link " for="__nav_5">
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<span class="md-nav__icon md-icon"></span>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 4 章 数组与链表
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
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<span class="md-ellipsis">
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4.1 数组
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
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<span class="md-ellipsis">
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4.2 链表
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<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
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<span class="md-ellipsis">
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4.3 列表
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<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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4.4 小结
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_stack_and_queue/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
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<span class="md-ellipsis">
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第 5 章 栈与队列
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</span>
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</a>
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<label class="md-nav__link " for="__nav_6">
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<span class="md-nav__icon md-icon"></span>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_6">
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<span class="md-nav__icon md-icon"></span>
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第 5 章 栈与队列
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
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<span class="md-ellipsis">
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5.1 栈
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
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<span class="md-ellipsis">
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5.2 队列
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
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<span class="md-ellipsis">
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5.3 双向队列
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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5.4 小结
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</span>
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</a>
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</li>
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</nav>
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<span class="md-ellipsis">
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第 6 章 哈希表
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</a>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 6 章 哈希表
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
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<span class="md-ellipsis">
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6.1 哈希表
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</span>
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
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<span class="md-ellipsis">
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6.2 哈希冲突
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
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<span class="md-ellipsis">
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6.3 哈希算法
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_hashing/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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6.4 小结
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</span>
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</a>
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</li>
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</nav>
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<span class="md-ellipsis">
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第 7 章 树
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第 7 章 树
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<span class="md-ellipsis">
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7.1 二叉树
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<span class="md-ellipsis">
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7.2 二叉树遍历
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7.3 二叉树数组表示
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<span class="md-ellipsis">
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7.4 二叉搜索树
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7.5 AVL 树 *
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7.6 小结
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</a>
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<span class="md-ellipsis">
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第 8 章 堆
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</span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 8 章 堆
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<span class="md-ellipsis">
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8.1 堆
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</span>
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</a>
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<a href="../../chapter_heap/build_heap/" class="md-nav__link">
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<span class="md-ellipsis">
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8.2 建堆操作
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</a>
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8.3 Top-K 问题
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8.4 小结
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</span>
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</a>
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</li>
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<a href="../../chapter_graph/" class="md-nav__link ">
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<span class="md-ellipsis">
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第 9 章 图
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
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<span class="md-nav__icon md-icon"></span>
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第 9 章 图
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<span class="md-ellipsis">
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9.1 图
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</span>
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</a>
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9.2 图基础操作
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</span>
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</a>
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<span class="md-ellipsis">
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9.3 图的遍历
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</span>
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</a>
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9.4 小结
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</span>
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</a>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_searching/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
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<span class="md-ellipsis">
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第 10 章 搜索
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</span>
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</a>
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<label class="md-nav__link " for="__nav_11">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_11">
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<span class="md-nav__icon md-icon"></span>
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第 10 章 搜索
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search/" class="md-nav__link">
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<span class="md-ellipsis">
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10.1 二分查找
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
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<span class="md-ellipsis">
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10.2 二分查找插入点
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</span>
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<span class="md-status md-status--new" title="最近添加">
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
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<span class="md-ellipsis">
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10.3 二分查找边界
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</span>
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<span class="md-status md-status--new" title="最近添加">
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
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<span class="md-ellipsis">
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10.4 哈希优化策略
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
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<span class="md-ellipsis">
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10.5 重识搜索算法
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</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_searching/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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10.6 小结
|
|
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</span>
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--active md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
|
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<div class="md-nav__link md-nav__container">
|
|
|
<a href="../" class="md-nav__link ">
|
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|
|
|
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
|
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<span class="md-ellipsis">
|
|
|
第 11 章 排序
|
|
|
</span>
|
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|
</a>
|
|
|
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|
<label class="md-nav__link " for="__nav_12">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
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|
|
</div>
|
|
|
|
|
|
<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>
|
|
|
第 11 章 排序
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
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|
<a href="../sorting_algorithm/" class="md-nav__link">
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|
<span class="md-ellipsis">
|
|
|
11.1 排序算法
|
|
|
</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../selection_sort/" class="md-nav__link">
|
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|
<span class="md-ellipsis">
|
|
|
11.2 选择排序
|
|
|
</span>
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../bubble_sort/" class="md-nav__link">
|
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|
<span class="md-ellipsis">
|
|
|
11.3 冒泡排序
|
|
|
</span>
|
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</a>
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</li>
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<li class="md-nav__item md-nav__item--active">
|
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|
<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
|
|
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|
<label class="md-nav__link md-nav__link--active" for="__toc">
|
|
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|
|
<span class="md-ellipsis">
|
|
|
11.4 插入排序
|
|
|
</span>
|
|
|
|
|
|
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<a href="./" class="md-nav__link md-nav__link--active">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.4 插入排序
|
|
|
</span>
|
|
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|
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|
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|
|
</a>
|
|
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|
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|
|
<nav class="md-nav md-nav--secondary" aria-label="目录">
|
|
|
|
|
|
|
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|
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|
|
<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>
|
|
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|
|
<li class="md-nav__item">
|
|
|
<a href="#1141" class="md-nav__link">
|
|
|
11.4.1 算法流程
|
|
|
</a>
|
|
|
|
|
|
</li>
|
|
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|
|
<li class="md-nav__item">
|
|
|
<a href="#1142" class="md-nav__link">
|
|
|
11.4.2 算法特性
|
|
|
</a>
|
|
|
|
|
|
</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="#1143" class="md-nav__link">
|
|
|
11.4.3 插入排序优势
|
|
|
</a>
|
|
|
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|
</li>
|
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|
</ul>
|
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|
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|
</nav>
|
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</li>
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<li class="md-nav__item">
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<a href="../quick_sort/" class="md-nav__link">
|
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|
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|
<span class="md-ellipsis">
|
|
|
11.5 快速排序
|
|
|
</span>
|
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../merge_sort/" class="md-nav__link">
|
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|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.6 归并排序
|
|
|
</span>
|
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../heap_sort/" class="md-nav__link">
|
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|
|
|
<span class="md-ellipsis">
|
|
|
11.7 堆排序
|
|
|
</span>
|
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</a>
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</li>
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<li class="md-nav__item">
|
|
|
<a href="../bucket_sort/" class="md-nav__link">
|
|
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|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.8 桶排序
|
|
|
</span>
|
|
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</a>
|
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</li>
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<li class="md-nav__item">
|
|
|
<a href="../counting_sort/" class="md-nav__link">
|
|
|
|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.9 计数排序
|
|
|
</span>
|
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</a>
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</li>
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<li class="md-nav__item">
|
|
|
<a href="../radix_sort/" class="md-nav__link">
|
|
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|
|
|
|
|
|
<span class="md-ellipsis">
|
|
|
11.10 基数排序
|
|
|
</span>
|
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</a>
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</li>
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<li class="md-nav__item">
|
|
|
<a href="../summary/" class="md-nav__link">
|
|
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|
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|
<span class="md-ellipsis">
|
|
|
11.11 小结
|
|
|
</span>
|
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|
</a>
|
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</li>
|
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
|
|
|
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|
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|
|
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|
|
<div class="md-nav__link md-nav__container">
|
|
|
<a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
|
|
|
|
|
|
|
|
|
<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
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<span class="md-ellipsis">
|
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第 12 章 分治
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<span class="md-nav__icon md-icon"></span>
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第 12 章 分治
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<span class="md-ellipsis">
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12.1 分治算法
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12.2 分治搜索策略
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12.3 构建树问题
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<span class="md-ellipsis">
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12.4 汉诺塔问题
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<a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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12.5 小结
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<div class="md-nav__link md-nav__container">
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<a href="../../chapter_backtracking/" class="md-nav__link ">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
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第 13 章 回溯
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</a>
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<label class="md-nav__link " for="__nav_14">
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_14">
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<span class="md-nav__icon md-icon"></span>
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第 13 章 回溯
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
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13.1 回溯算法
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<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
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13.2 全排列问题
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<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
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13.3 子集和问题
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<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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13.4 N 皇后问题
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<a href="../../chapter_backtracking/summary/" class="md-nav__link">
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<span class="md-ellipsis">
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13.5 小结
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<a href="../../chapter_dynamic_programming/" class="md-nav__link ">
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第 14 章 动态规划
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<span class="md-nav__icon md-icon"></span>
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第 14 章 动态规划
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<span class="md-ellipsis">
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14.1 初探动态规划
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<span class="md-ellipsis">
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14.2 DP 问题特性
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<span class="md-ellipsis">
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14.3 DP 解题思路
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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14.4 0-1 背包问题
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</span>
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<li class="md-nav__item">
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<a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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14.5 完全背包问题
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</span>
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<a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
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<span class="md-ellipsis">
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14.6 编辑距离问题
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</span>
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14.7 小结
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15.1 贪心算法
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15.3 最大容量问题
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15.4 最大切分乘积问题
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15.5 小结
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16.1 编程环境安装
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16.2 一起参与创作
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<a href="#1141" class="md-nav__link">
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11.4.1 算法流程
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<a href="#1142" class="md-nav__link">
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11.4.2 算法特性
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<a href="#1143" class="md-nav__link">
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11.4.3 插入排序优势
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_sorting/insertion_sort.md" title="编辑此页" class="md-content__button md-icon">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
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<h1 id="114">11.4 插入排序<a class="headerlink" href="#114" title="Permanent link">¶</a></h1>
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<p>「插入排序 insertion sort」是一种简单的排序算法，它的工作原理与手动整理一副牌的过程非常相似。</p>
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<p>具体来说，我们在未排序区间选择一个基准元素，将该元素与其左侧已排序区间的元素逐一比较大小，并将该元素插入到正确的位置。</p>
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<p>图 11-6 展示了数组插入元素的操作流程。设基准元素为 <code>base</code> ，我们需要将从目标索引到 <code>base</code> 之间的所有元素向右移动一位，然后再将 <code>base</code> 赋值给目标索引。</p>
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<p><img alt="单次插入操作" src="../insertion_sort.assets/insertion_operation.png" /></p>
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<p align="center"> 图 11-6 单次插入操作 </p>
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<h2 id="1141">11.4.1 算法流程<a class="headerlink" href="#1141" title="Permanent link">¶</a></h2>
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<p>插入排序的整体流程如图 11-7 所示。</p>
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<ol>
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<li>初始状态下，数组的第 1 个元素已完成排序。</li>
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<li>选取数组的第 2 个元素作为 <code>base</code> ，将其插入到正确位置后，<strong>数组的前 2 个元素已排序</strong>。</li>
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<li>选取第 3 个元素作为 <code>base</code> ，将其插入到正确位置后，<strong>数组的前 3 个元素已排序</strong>。</li>
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<li>以此类推，在最后一轮中，选取最后一个元素作为 <code>base</code> ，将其插入到正确位置后，<strong>所有元素均已排序</strong>。</li>
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</ol>
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<p><img alt="插入排序流程" src="../insertion_sort.assets/insertion_sort_overview.png" /></p>
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<p align="center"> 图 11-7 插入排序流程 </p>
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<div class="highlight"><span class="filename">insertion_sort.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insertionSort</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="p">{</span>
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<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w"> </span><span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</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">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
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<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="k">while</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="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
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<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="highlight"><span class="filename">insertion_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insertionSort</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="o">&</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w"> </span><span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">base</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">i</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">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
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<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="k">while</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="mi">0</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">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
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<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="k">def</span> <span class="nf">insertion_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
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<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="w"> </span><span class="sd">"""插入排序"""</span>
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<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a> <span class="c1"># 外循环：已排序区间为 [0, i-1]</span>
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<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
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<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a> <span class="n">base</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
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<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a> <span class="n">j</span> <span class="o">=</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span>
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<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a> <span class="c1"># 内循环：将 base 插入到已排序区间 [0, i-1] 中的正确位置</span>
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<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a> <span class="k">while</span> <span class="n">j</span> <span class="o">>=</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">></span> <span class="n">base</span><span class="p">:</span>
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<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="c1"># 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a> <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
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<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">base</span> <span class="c1"># 将 base 赋值到正确位置</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">insertionSort</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="p">{</span>
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<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w"> </span><span class="c1">// 外循环：未排序区间为 [0, i]</span>
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<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></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="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p"><</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</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>
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<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w"> </span><span class="nx">base</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">i</span><span class="p">]</span>
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<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span>
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<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">></span><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</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">j</span><span class="p">]</span><span class="w"> </span><span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w"> </span><span class="nx">j</span><span class="o">--</span>
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<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="o">+</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">base</span><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.js</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insertionSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w"> </span><span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></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">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</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">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">base</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">i</span><span class="p">],</span>
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<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
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<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="k">while</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="mf">0</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">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="nx">j</span><span class="o">--</span><span class="p">;</span>
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<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.ts</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">insertionSort</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="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w"> </span><span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></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">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</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">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w"> </span><span class="kd">const</span><span class="w"> </span><span class="nx">base</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">i</span><span class="p">];</span>
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<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">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span>
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<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="k">while</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="mf">0</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">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="nx">j</span><span class="o">--</span><span class="p">;</span>
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<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insertionSort</span><span class="p">(</span><span class="kt">int</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">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w"> </span><span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">base</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">i</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">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
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<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w"> </span><span class="k">while</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="mi">0</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">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w"> </span><span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
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<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
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<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span>
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<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">insertionSort</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="p">{</span>
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<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w"> </span><span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">bas</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">i</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">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
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<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w"> </span><span class="k">while</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="m">0</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">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">bas</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
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<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bas</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.swift</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">func</span> <span class="nf">insertionSort</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="p">{</span>
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<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a> <span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a> <span class="k">for</span> <span class="n">i</span> <span class="k">in</span> <span class="bp">stride</span><span class="p">(</span><span class="n">from</span><span class="p">:</span> <span class="mi">1</span><span class="p">,</span> <span class="n">to</span><span class="p">:</span> <span class="n">nums</span><span class="p">.</span><span class="bp">count</span><span class="p">,</span> <span class="n">by</span><span class="p">:</span> <span class="mi">1</span><span class="p">)</span> <span class="p">{</span>
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<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a> <span class="kd">let</span> <span class="nv">base</span> <span class="p">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
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<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a> <span class="kd">var</span> <span class="nv">j</span> <span class="p">=</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span>
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<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a> <span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a> <span class="k">while</span> <span class="n">j</span> <span class="o">>=</span> <span class="mi">0</span><span class="p">,</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">></span> <span class="n">base</span> <span class="p">{</span>
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<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="p">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a> <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
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<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a> <span class="p">}</span>
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<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="p">=</span> <span class="n">base</span> <span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a> <span class="p">}</span>
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<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.zig</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// 插入排序</span>
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<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">insertionSort</span><span class="p">(</span><span class="n">nums</span><span class="o">:</span><span class="w"> </span><span class="p">[]</span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w"> </span><span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
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<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w"> </span><span class="k">while</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">nums</span><span class="p">.</span><span class="n">len</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">base</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">i</span><span class="p">];</span>
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<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w"> </span><span class="kr">var</span><span class="w"> </span><span class="n">j</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
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<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w"> </span><span class="k">while</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="mi">1</span><span class="w"> </span><span class="k">and</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="o">:</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="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</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">j</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="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.dart</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">insertionSort</span><span class="p">(</span><span class="n">List</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w"> </span><span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o"><</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">base</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">i</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">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">;</span>
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<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w"> </span><span class="k">while</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="m">0</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">j</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
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<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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<div class="tabbed-block">
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<div class="highlight"><span class="filename">insertion_sort.rs</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 插入排序 */</span>
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<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="k">fn</span> <span class="nf">insertion_sort</span><span class="p">(</span><span class="n">nums</span>: <span class="kp">&</span><span class="nc">mut</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w"> </span><span class="c1">// 外循环：已排序元素数量为 1, 2, ..., n</span>
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<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">1</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="p">(</span><span class="n">base</span><span class="p">,</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">i32</span><span class="p">);</span>
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<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="w"> </span><span class="c1">// 内循环：将 base 插入到已排序部分的正确位置</span>
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<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="w"> </span><span class="k">while</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&&</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="p">{</span>
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<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="w"> </span><span class="n">nums</span><span class="p">[(</span><span class="n">j</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="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</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">j</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span><span class="w"> </span><span class="c1">// 将 nums[j] 向右移动一位</span>
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<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
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<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w"> </span><span class="n">nums</span><span class="p">[(</span><span class="n">j</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="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// 将 base 赋值到正确位置</span>
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<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w"> </span><span class="p">}</span>
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<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="p">}</span>
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</code></pre></div>
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</div>
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</div>
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</div>
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<h2 id="1142">11.4.2 算法特性<a class="headerlink" href="#1142" title="Permanent link">¶</a></h2>
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<ul>
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<li><strong>时间复杂度 <span class="arithmatex">\(O(n^2)\)</span>、自适应排序</strong>：最差情况下，每次插入操作分别需要循环 <span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(n-2\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> 次，求和得到 <span class="arithmatex">\((n - 1) n / 2\)</span> ，因此时间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> 。在遇到有序数据时，插入操作会提前终止。当输入数组完全有序时，插入排序达到最佳时间复杂度 <span class="arithmatex">\(O(n)\)</span> 。</li>
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<li><strong>空间复杂度 <span class="arithmatex">\(O(1)\)</span>、原地排序</strong>：指针 <span class="arithmatex">\(i\)</span> 和 <span class="arithmatex">\(j\)</span> 使用常数大小的额外空间。</li>
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<li><strong>稳定排序</strong>：在插入操作过程中，我们会将元素插入到相等元素的右侧，不会改变它们的顺序。</li>
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</ul>
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<h2 id="1143">11.4.3 插入排序优势<a class="headerlink" href="#1143" title="Permanent link">¶</a></h2>
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<p>插入排序的时间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> ，而我们即将学习的快速排序的时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span> 。尽管插入排序的时间复杂度相比快速排序更高，<strong>但在数据量较小的情况下，插入排序通常更快</strong>。</p>
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<p>这个结论与线性查找和二分查找的适用情况的结论类似。快速排序这类 <span class="arithmatex">\(O(n \log n)\)</span> 的算法属于基于分治的排序算法，往往包含更多单元计算操作。而在数据量较小时，<span class="arithmatex">\(n^2\)</span> 和 <span class="arithmatex">\(n \log n\)</span> 的数值比较接近，复杂度不占主导作用；每轮中的单元操作数量起到决定性因素。</p>
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<p>实际上，许多编程语言（例如 Java）的内置排序函数都采用了插入排序，大致思路为：对于长数组，采用基于分治的排序算法，例如快速排序；对于短数组，直接使用插入排序。</p>
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<p>虽然冒泡排序、选择排序和插入排序的时间复杂度都为 <span class="arithmatex">\(O(n^2)\)</span> ，但在实际情况中，<strong>插入排序的使用频率显著高于冒泡排序和选择排序</strong>，主要有以下原因。</p>
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<ul>
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<li>冒泡排序基于元素交换实现，需要借助一个临时变量，共涉及 3 个单元操作；插入排序基于元素赋值实现，仅需 1 个单元操作。因此，<strong>冒泡排序的计算开销通常比插入排序更高</strong>。</li>
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<li>选择排序在任何情况下的时间复杂度都为 <span class="arithmatex">\(O(n^2)\)</span> 。<strong>如果给定一组部分有序的数据，插入排序通常比选择排序效率更高</strong>。</li>
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<li>选择排序不稳定，无法应用于多级排序。</li>
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