1869 lines
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_preface/installation/" class="md-nav__link">
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编程环境安装
|
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|
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</li>
|
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|
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|
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|
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|
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<li class="md-nav__item">
|
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<a href="../../chapter_preface/contribution/" class="md-nav__link">
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一起参与创作
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|
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</ul>
|
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</nav>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<label class="md-nav__link" for="__nav_2">
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<nav class="md-nav" aria-label="引言" data-md-level="1">
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</label>
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<label class="md-nav__link" for="__nav_3">
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数据与内存
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数组与链表
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<a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
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数组（Array）
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链表（LinkedList）
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
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列表（List）
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|
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<a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
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小结
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<label class="md-nav__link" for="__nav_6">
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栈与队列
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" aria-label="栈与队列" data-md-level="1">
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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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<li class="md-nav__item">
|
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<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
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栈（Stack）
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</a>
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|
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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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队列（Queue）
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</a>
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</li>
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|
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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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双向队列（Deque）
|
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</a>
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</li>
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|
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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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小结
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<label class="md-nav__link" for="__nav_7">
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散列表
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<span class="md-nav__icon md-icon"></span>
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<nav class="md-nav" aria-label="散列表" data-md-level="1">
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<span class="md-nav__icon md-icon"></span>
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散列表
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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|
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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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哈希表（HashMap）
|
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</a>
|
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</li>
|
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|
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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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哈希冲突处理
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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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小结
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<label class="md-nav__link" for="__nav_8">
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二叉树
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" aria-label="二叉树" data-md-level="1">
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<label class="md-nav__title" for="__nav_8">
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二叉树
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
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二叉树（Binary Tree）
|
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</a>
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</li>
|
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_tree_types/" class="md-nav__link">
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二叉树常见类型
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<li class="md-nav__item">
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<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
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二叉搜索树
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
|
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AVL 树 *
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</a>
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</li>
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|
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<li class="md-nav__item">
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<a href="../../chapter_tree/summary/" class="md-nav__link">
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小结
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</ul>
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</nav>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle" data-md-toggle="__nav_9" type="checkbox" id="__nav_9" >
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|
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|
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|
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|
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<label class="md-nav__link" for="__nav_9">
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查找算法
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" aria-label="查找算法" data-md-level="1">
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查找算法
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<a href="../../chapter_searching/linear_search/" class="md-nav__link">
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线性查找
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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/" class="md-nav__link">
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二分查找
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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="https://github.com/krahets/hello-algo/tree/master/docs/chapter_sorting/merge_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="M20.71 7.04c.39-.39.39-1.04 0-1.41l-2.34-2.34c-.37-.39-1.02-.39-1.41 0l-1.84 1.83 3.75 3.75M3 17.25V21h3.75L17.81 9.93l-3.75-3.75L3 17.25Z"/></svg>
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<h1 id="_1">归并排序<a class="headerlink" href="#_1" title="Permanent link">¶</a></h1>
|
||
<p>「归并排序 Merge Sort」是算法中 “分治思想” 的典型体现，其有「划分」和「合并」两个阶段：</p>
|
||
<ol>
|
||
<li><strong>划分阶段：</strong> 通过递归不断 <strong>将数组从中点位置划分开</strong>，将长数组的排序问题转化为短数组的排序问题；</li>
|
||
<li><strong>合并阶段：</strong> 划分到子数组长度为 1 时，开始向上合并，不断将 <strong>左、右两个短排序数组</strong> 合并为 <strong>一个长排序数组</strong>，直至合并至原数组时完成排序；</li>
|
||
</ol>
|
||
<p><img alt="merge_sort_preview" src="../merge_sort.assets/merge_sort_preview.png" /></p>
|
||
<p align="center"> Fig. 归并排序两阶段：划分与合并 </p>
|
||
|
||
<h2 id="_2">算法流程<a class="headerlink" href="#_2" title="Permanent link">¶</a></h2>
|
||
<p><strong>「递归划分」</strong> 从顶至底递归地 <strong>将数组从中点切为两个子数组</strong> ，直至长度为 1 ；</p>
|
||
<ol>
|
||
<li>计算数组中点 <code>mid</code> ，递归划分左子数组（区间 <code>[left, mid]</code> ）和右子数组（区间 <code>[mid + 1, right]</code> ）；</li>
|
||
<li>递归执行 <code>1.</code> 步骤，直至子数组区间长度为 1 时，终止递归划分；</li>
|
||
</ol>
|
||
<p><strong>「回溯合并」</strong> 从底至顶地将左子数组和右子数组合并为一个 <strong>有序数组</strong> ；</p>
|
||
<p>需要注意，由于从长度为 1 的子数组开始合并，所以 <strong>每个子数组都是有序的</strong> 。因此，合并任务本质是要 <strong>将两个有序子数组合并为一个有序数组</strong> 。</p>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="1:10"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Step1</label><label for="__tabbed_1_2">Step2</label><label for="__tabbed_1_3">Step3</label><label for="__tabbed_1_4">Step4</label><label for="__tabbed_1_5">Step5</label><label for="__tabbed_1_6">Step6</label><label for="__tabbed_1_7">Step7</label><label for="__tabbed_1_8">Step8</label><label for="__tabbed_1_9">Step9</label><label for="__tabbed_1_10">Step10</label></div>
|
||
<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step1" src="../merge_sort.assets/merge_sort_step1.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step2" src="../merge_sort.assets/merge_sort_step2.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step3" src="../merge_sort.assets/merge_sort_step3.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step4" src="../merge_sort.assets/merge_sort_step4.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step5" src="../merge_sort.assets/merge_sort_step5.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step6" src="../merge_sort.assets/merge_sort_step6.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step7" src="../merge_sort.assets/merge_sort_step7.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step8" src="../merge_sort.assets/merge_sort_step8.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step9" src="../merge_sort.assets/merge_sort_step9.png" /></p>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<p><img alt="merge_sort_step10" src="../merge_sort.assets/merge_sort_step10.png" /></p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>观察发现，归并排序的递归顺序就是二叉树的「后序遍历」。</p>
|
||
<ul>
|
||
<li><strong>后序遍历：</strong> 先递归左子树、再递归右子树、最后处理根结点。</li>
|
||
<li><strong>归并排序：</strong> 先递归左子树、再递归右子树、最后处理合并。</li>
|
||
</ul>
|
||
<div class="tabbed-set tabbed-alternate" data-tabs="2:8"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Java</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Python</label><label for="__tabbed_2_4">Go</label><label for="__tabbed_2_5">JavaScript</label><label for="__tabbed_2_6">TypeScript</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label></div>
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<div class="tabbed-content">
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">merge_sort.java</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="cm">/**</span>
|
||
<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="cm"> * 合并左子数组和右子数组</span>
|
||
<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="cm"> * 左子数组区间 [left, mid]</span>
|
||
<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="cm"> * 右子数组区间 [mid + 1, right]</span>
|
||
<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="cm"> */</span><span class="w"></span>
|
||
<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w"> </span><span class="c1">// 初始化辅助数组</span><span class="w"></span>
|
||
<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">copyOfRange</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span>
|
||
<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引 </span><span class="w"></span>
|
||
<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引 </span><span class="w"></span>
|
||
<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span><span class="w"></span>
|
||
<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftStart</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightStart</span><span class="p">;</span><span class="w"> </span>
|
||
<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span><span class="w"></span>
|
||
<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="w"> </span><span class="c1">// 若 “左子数组已全部合并完”，则选取右子数组元素，并且 j++</span><span class="w"></span>
|
||
<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">leftEnd</span><span class="p">)</span><span class="w"></span>
|
||
<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="w"> </span><span class="c1">// 否则，若 “右子数组已全部合并完” 或 “左子数组元素 < 右子数组元素”，则选取左子数组元素，并且 i++</span><span class="w"></span>
|
||
<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"></span>
|
||
<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w"> </span><span class="c1">// 否则，若 “左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span><span class="w"></span>
|
||
<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="w"> </span><span class="k">else</span><span class="w"></span>
|
||
<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>
|
||
<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="cm">/* 归并排序 */</span><span class="w"></span>
|
||
<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="w"> </span><span class="c1">// 终止条件</span><span class="w"></span>
|
||
<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span><span class="w"></span>
|
||
<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a><span class="w"> </span><span class="c1">// 递归划分</span><span class="w"></span>
|
||
<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计算数组中点</span><span class="w"></span>
|
||
<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span><span class="w"></span>
|
||
<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span><span class="w"></span>
|
||
<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a><span class="w"> </span><span class="c1">// 回溯合并</span><span class="w"></span>
|
||
<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"></span>
|
||
<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a><span class="p">}</span><span class="w"></span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">merge_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/**</span>
|
||
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="cm"> * 合并左子数组和右子数组</span>
|
||
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="cm"> * 左子数组区间 [left, mid]</span>
|
||
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm"> * 右子数组区间 [mid + 1, right]</span>
|
||
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="cm"> */</span><span class="w"></span>
|
||
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">>&</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w"> </span><span class="c1">// 初始化辅助数组</span>
|
||
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w"> </span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">></span><span class="w"> </span><span class="n">tmp</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span>
|
||
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引 </span>
|
||
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引 </span>
|
||
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span>
|
||
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftStart</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightStart</span><span class="p">;</span><span class="w"> </span>
|
||
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
||
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w"> </span><span class="c1">// 若 “左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
||
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">leftEnd</span><span class="p">)</span><span class="w"></span>
|
||
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span><span class="w"></span>
|
||
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w"> </span><span class="c1">// 否则，若 “右子数组已全部合并完” 或 “左子数组元素 < 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
||
<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="n">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"></span>
|
||
<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span><span class="w"></span>
|
||
<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w"> </span><span class="c1">// 否则，若 “左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
||
<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w"> </span><span class="k">else</span><span class="w"></span>
|
||
<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span><span class="w"></span>
|
||
<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a>
|
||
<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="cm">/* 归并排序 */</span><span class="w"></span>
|
||
<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="n">vector</span><span class="o"><</span><span class="kt">int</span><span class="o">>&</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w"> </span><span class="c1">// 终止条件</span>
|
||
<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span>
|
||
<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w"> </span><span class="c1">// 划分阶段</span>
|
||
<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 计算中点</span>
|
||
<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span>
|
||
<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w"> </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span>
|
||
<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w"> </span><span class="c1">// 合并阶段</span>
|
||
<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w"> </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"></span>
|
||
<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="p">}</span><span class="w"></span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">merge_sort.py</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="sd">"""</span>
|
||
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="sd">合并左子数组和右子数组</span>
|
||
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="sd">左子数组区间 [left, mid]</span>
|
||
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="sd">右子数组区间 [mid + 1, right]</span>
|
||
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="sd">"""</span>
|
||
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="k">def</span> <span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
|
||
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a> <span class="c1"># 初始化辅助数组 借助 copy模块</span>
|
||
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a> <span class="n">tmp</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">:</span><span class="n">right</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
|
||
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a> <span class="c1"># 左子数组的起始索引和结束索引</span>
|
||
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a> <span class="n">left_start</span><span class="p">,</span> <span class="n">left_end</span> <span class="o">=</span> <span class="n">left</span> <span class="o">-</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span> <span class="o">-</span> <span class="n">left</span>
|
||
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a> <span class="c1"># 右子数组的起始索引和结束索引</span>
|
||
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a> <span class="n">right_start</span><span class="p">,</span> <span class="n">right_end</span> <span class="o">=</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span> <span class="o">-</span> <span class="n">left</span>
|
||
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a> <span class="c1"># i, j 分别指向左子数组、右子数组的首元素</span>
|
||
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">left_start</span><span class="p">,</span> <span class="n">right_start</span>
|
||
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a> <span class="c1"># 通过覆盖原数组 nums 来合并左子数组和右子数组</span>
|
||
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a> <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">right</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
|
||
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a> <span class="c1"># 若 “左子数组已全部合并完”，则选取右子数组元素，并且 j++</span>
|
||
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a> <span class="k">if</span> <span class="n">i</span> <span class="o">></span> <span class="n">left_end</span><span class="p">:</span>
|
||
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
|
||
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a> <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a> <span class="c1"># 否则，若 “右子数组已全部合并完” 或 “左子数组元素 < 右子数组元素”，则选取左子数组元素，并且 i++</span>
|
||
<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a> <span class="k">elif</span> <span class="n">j</span> <span class="o">></span> <span class="n">right_end</span> <span class="ow">or</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]:</span>
|
||
<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
||
<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a> <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a> <span class="c1"># 否则，若 “左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span>
|
||
<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a> <span class="k">else</span><span class="p">:</span>
|
||
<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
|
||
<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a> <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
|
||
<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a>
|
||
<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="sd">""" 归并排序 """</span>
|
||
<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="k">def</span> <span class="nf">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">):</span>
|
||
<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a> <span class="c1"># 终止条件</span>
|
||
<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a> <span class="k">if</span> <span class="n">left</span> <span class="o">>=</span> <span class="n">right</span><span class="p">:</span>
|
||
<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a> <span class="k">return</span> <span class="c1"># 当子数组长度为 1 时终止递归</span>
|
||
<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a> <span class="c1"># 划分阶段</span>
|
||
<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a> <span class="n">mid</span> <span class="o">=</span> <span class="p">(</span><span class="n">left</span> <span class="o">+</span> <span class="n">right</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="c1"># 计算中点</span>
|
||
<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a> <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">)</span> <span class="c1"># 递归左子数组</span>
|
||
<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a> <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span> <span class="c1"># 递归右子数组</span>
|
||
<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a> <span class="c1"># 合并阶段</span>
|
||
<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a> <span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">merge_sort.go</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">merge_sort.js</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/**</span>
|
||
<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="cm"> * 合并左子数组和右子数组</span>
|
||
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="cm"> * 左子数组区间 [left, mid]</span>
|
||
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="cm"> * 右子数组区间 [mid + 1, right]</span>
|
||
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm"> */</span><span class="w"></span>
|
||
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w"> </span><span class="c1">// 初始化辅助数组</span><span class="w"></span>
|
||
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">slice</span><span class="p">(</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"> </span>
|
||
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引 </span><span class="w"></span>
|
||
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引 </span><span class="w"></span>
|
||
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span><span class="w"></span>
|
||
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">leftStart</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">rightStart</span><span class="p">;</span><span class="w"> </span>
|
||
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span><span class="w"></span>
|
||
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w"> </span><span class="c1">// 若 “左子数组已全部合并完”，则选取右子数组元素，并且 j++</span><span class="w"></span>
|
||
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">leftEnd</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span><span class="w"></span>
|
||
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w"> </span><span class="c1">// 否则，若 “右子数组已全部合并完” 或 “左子数组元素 < 右子数组元素”，则选取左子数组元素，并且 i++</span><span class="w"></span>
|
||
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">];</span><span class="w"></span>
|
||
<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w"> </span><span class="c1">// 否则，若 “左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span><span class="w"></span>
|
||
<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span><span class="w"></span>
|
||
<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a>
|
||
<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a><span class="cm">/* 归并排序 */</span><span class="w"></span>
|
||
<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="w"> </span><span class="c1">// 终止条件</span><span class="w"></span>
|
||
<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span><span class="w"></span>
|
||
<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="w"> </span><span class="c1">// 划分阶段</span><span class="w"></span>
|
||
<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 计算中点</span><span class="w"></span>
|
||
<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span><span class="w"></span>
|
||
<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span><span class="w"></span>
|
||
<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w"> </span><span class="c1">// 合并阶段</span><span class="w"></span>
|
||
<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"></span>
|
||
<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a><span class="p">}</span><span class="w"></span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">merge_sort.ts</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/**</span>
|
||
<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="cm"> * 合并左子数组和右子数组</span>
|
||
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="cm"> * 左子数组区间 [left, mid]</span>
|
||
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="cm"> * 右子数组区间 [mid + 1, right]</span>
|
||
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm"> */</span><span class="w"></span>
|
||
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w"> </span><span class="c1">// 初始化辅助数组</span><span class="w"></span>
|
||
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">slice</span><span class="p">(</span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span><span class="w"></span>
|
||
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w"> </span><span class="c1">// 左子数组的起始索引和结束索引</span><span class="w"></span>
|
||
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">leftStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">leftEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w"> </span><span class="c1">// 右子数组的起始索引和结束索引</span><span class="w"></span>
|
||
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">rightStart</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">rightEnd</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w"> </span><span class="c1">// i, j 分别指向左子数组、右子数组的首元素</span><span class="w"></span>
|
||
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">leftStart</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">rightStart</span><span class="p">;</span><span class="w"></span>
|
||
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w"> </span><span class="c1">// 通过覆盖原数组 nums 来合并左子数组和右子数组</span><span class="w"></span>
|
||
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="nx">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w"> </span><span class="c1">// 若 “左子数组已全部合并完”，则选取右子数组元素，并且 j++</span><span class="w"></span>
|
||
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">i</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">leftEnd</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span><span class="w"></span>
|
||
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w"> </span><span class="c1">// 否则，若 “右子数组已全部合并完” 或 “左子数组元素 < 右子数组元素”，则选取左子数组元素，并且 i++</span><span class="w"></span>
|
||
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">j</span><span class="w"> </span><span class="o">></span><span class="w"> </span><span class="nx">rightEnd</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span><span class="w"> </span><span class="o"><=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">i</span><span class="o">++</span><span class="p">];</span><span class="w"></span>
|
||
<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="w"> </span><span class="c1">// 否则，若 “左子数组元素 > 右子数组元素”，则选取右子数组元素，并且 j++</span><span class="w"></span>
|
||
<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="w"> </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">tmp</span><span class="p">[</span><span class="nx">j</span><span class="o">++</span><span class="p">];</span><span class="w"></span>
|
||
<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a><span class="w"> </span><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="p">}</span><span class="w"></span>
|
||
<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a>
|
||
<a id="__codelineno-5-30" name="__codelineno-5-30" href="#__codelineno-5-30"></a><span class="cm">/* 归并排序 */</span><span class="w"></span>
|
||
<a id="__codelineno-5-31" name="__codelineno-5-31" href="#__codelineno-5-31"></a><span class="kd">function</span><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[],</span><span class="w"> </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
|
||
<a id="__codelineno-5-32" name="__codelineno-5-32" href="#__codelineno-5-32"></a><span class="w"> </span><span class="c1">// 终止条件</span><span class="w"></span>
|
||
<a id="__codelineno-5-33" name="__codelineno-5-33" href="#__codelineno-5-33"></a><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">left</span><span class="w"> </span><span class="o">>=</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 当子数组长度为 1 时终止递归</span><span class="w"></span>
|
||
<a id="__codelineno-5-34" name="__codelineno-5-34" href="#__codelineno-5-34"></a><span class="w"> </span><span class="c1">// 划分阶段</span><span class="w"></span>
|
||
<a id="__codelineno-5-35" name="__codelineno-5-35" href="#__codelineno-5-35"></a><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Math</span><span class="p">.</span><span class="nx">floor</span><span class="p">((</span><span class="nx">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 计算中点</span><span class="w"></span>
|
||
<a id="__codelineno-5-36" name="__codelineno-5-36" href="#__codelineno-5-36"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归左子数组</span><span class="w"></span>
|
||
<a id="__codelineno-5-37" name="__codelineno-5-37" href="#__codelineno-5-37"></a><span class="w"> </span><span class="nx">mergeSort</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 递归右子数组</span><span class="w"></span>
|
||
<a id="__codelineno-5-38" name="__codelineno-5-38" href="#__codelineno-5-38"></a><span class="w"> </span><span class="c1">// 合并阶段</span><span class="w"></span>
|
||
<a id="__codelineno-5-39" name="__codelineno-5-39" href="#__codelineno-5-39"></a><span class="w"> </span><span class="nx">merge</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">mid</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">);</span><span class="w"></span>
|
||
<a id="__codelineno-5-40" name="__codelineno-5-40" href="#__codelineno-5-40"></a><span class="p">}</span><span class="w"></span>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">merge_sort.c</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
<div class="tabbed-block">
|
||
<div class="highlight"><span class="filename">merge_sort.cs</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a>
|
||
</code></pre></div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<p>下面重点解释一下合并方法 <code>merge()</code> 的流程：</p>
|
||
<ol>
|
||
<li>初始化一个辅助数组 <code>tmp</code> 暂存待合并区间 <code>[left, right]</code> 内的元素，后续通过覆盖原数组 <code>nums</code> 的元素来实现合并；</li>
|
||
<li>初始化指针 <code>i</code> , <code>j</code> , <code>k</code> 分别指向左子数组、右子数组、原数组的首元素；</li>
|
||
<li>循环判断 <code>tmp[i]</code> 和 <code>tmp[j]</code> 的大小，将较小的先覆盖至 <code>nums[k]</code> ，指针 <code>i</code> , <code>j</code> 根据判断结果交替前进（指针 <code>k</code> 也前进），直至两个子数组都遍历完，即可完成合并。</li>
|
||
</ol>
|
||
<p>合并方法 <code>merge()</code> 代码中的主要难点：</p>
|
||
<ul>
|
||
<li><code>nums</code> 的待合并区间为 <code>[left, right]</code> ，而因为 <code>tmp</code> 只复制了 <code>nums</code> 该区间元素，所以 <code>tmp</code> 对应区间为 <code>[0, right - left]</code> ，<strong>需要特别注意代码中各个变量的含义</strong>。</li>
|
||
<li>判断 <code>tmp[i]</code> 和 <code>tmp[j]</code> 的大小的操作中，还 <strong>需考虑当子数组遍历完成后的索引越界问题</strong>，即 <code>i > leftEnd</code> 和 <code>j > rightEnd</code> 的情况，索引越界的优先级是最高的，例如如果左子数组已经被合并完了，那么不用继续判断，直接合并右子数组元素即可。</li>
|
||
</ul>
|
||
<h2 id="_3">算法特性<a class="headerlink" href="#_3" title="Permanent link">¶</a></h2>
|
||
<ul>
|
||
<li><strong>时间复杂度 <span class="arithmatex">\(O(n \log n)\)</span> ：</strong> 划分形成高度为 <span class="arithmatex">\(\log n\)</span> 的递归树，每层合并的总操作数量为 <span class="arithmatex">\(n\)</span> ，总体使用 <span class="arithmatex">\(O(n \log n)\)</span> 时间。</li>
|
||
<li><strong>空间复杂度 <span class="arithmatex">\(O(n)\)</span> ：</strong> 需借助辅助数组实现合并，使用 <span class="arithmatex">\(O(n)\)</span> 大小的额外空间；递归深度为 <span class="arithmatex">\(\log n\)</span> ，使用 <span class="arithmatex">\(O(\log n)\)</span> 大小的栈帧空间。</li>
|
||
<li><strong>非原地排序：</strong> 辅助数组需要使用 <span class="arithmatex">\(O(n)\)</span> 额外空间。</li>
|
||
<li><strong>稳定排序：</strong> 在合并时可保证相等元素的相对位置不变。</li>
|
||
<li><strong>非自适应排序：</strong> 对于任意输入数据，归并排序的时间复杂度皆相同。</li>
|
||
</ul>
|
||
<h2 id="_4">链表排序 *<a class="headerlink" href="#_4" title="Permanent link">¶</a></h2>
|
||
<p>归并排序有一个很特别的优势，用于排序链表时有很好的性能表现，<strong>空间复杂度可被优化至 <span class="arithmatex">\(O(1)\)</span></strong> ，这是因为：</p>
|
||
<ul>
|
||
<li>由于链表可仅通过改变指针来实现结点增删，因此 “将两个短有序链表合并为一个长有序链表” 无需使用额外空间，即回溯合并阶段不用像排序数组一样建立辅助数组 <code>tmp</code> ；</li>
|
||
<li>通过使用「迭代」代替「递归划分」，可省去递归使用的栈帧空间；</li>
|
||
</ul>
|
||
<blockquote>
|
||
<p>详情参考：<a href="https://leetcode-cn.com/problems/sort-list/solution/sort-list-gui-bing-pai-xu-lian-biao-by-jyd/">148. 排序链表</a></p>
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