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pageFillDescription: '小知识, 如何判断一个排序算法是否稳定, 速记, 排序方式, 算法策略, 算法详解, 总结小知识如何判断一个排序算法是否稳定稳定如果原本在前面而排序之后仍然在的前面不稳定如果原本在的前面而排序之后可能会出现在的后面速记不稳定算法快选堆希排序方式原地算法指算法执行过程中不需要额外的辅助空间而是在原始数据上进行操作非原地算法指算法执行过程中需要额外的辅助空间来存储数据而不会在原始数据上进行直接操作所以非原地算法通常具有较高的空间复杂度算法策略分治法快速排序归并排序算法详解冒泡排序选择排序插入排序希尔排序归并排序快速排序堆排序计数排序桶排序基数排序冒泡排序也是一种简单直观的排序算法它重复地走访过要排序的数列一次比较两个元素如果他们的顺序错误就把他们交换过来走访数列的工作是重复地进行直到没有再需要交换也就是说该数列已经排序完成基本步骤比较相邻的两个元素如果前一个比后一个大升序排序或者小降序排序则交换它们的位置对每一对相邻元素重复步骤直到列表末尾这样一次遍历完成后最大或最小的元素将移动到列表末尾针对剩下的未排序元素重复以上步骤直到列表中的所有元素都排好序选择排序是一种简单直观的排序算法无论什么数据进去都是的时间复杂度所以用到它的时候数据规模越小越好唯一的好处可能就是不占用额外的内存空间基本步骤遍历数组从未排序部分找到最小或最大的元素交换位置将找到的最小或最大元素与未排序部分的第一个元素交换位置缩小范围将未排序部分的范围缩小一个元素即将排序范围向右移动一个位置重复步骤至步骤直到所有元素都被排序完成插入排序的代码实现虽然没有冒泡排序和选择排序那么简单粗暴但它的原理应该是最容易理解的了因为只要打过扑克牌的人都应该能够秒懂插入排序是一种最简单直观的排序算法它的工作原理是通过构建有序序列对于未排序数据在已排序序列中从后向前扫描找到相应位置并插入基本步骤初始状态将第一个元素视为已排序部分其余元素视为未排序部分遍历未排序部分依次取出未排序部分的元素插入已排序部分将取出的元素与已排序部分的元素依次比较找到合适的位置插入重复步骤至步骤直到所有元素都被插入到已排序部分希尔排序也称递减增量排序算法是插入排序的一种更高效的改进版本但希尔排序是非稳定排序算法基本步骤确定间隔序列选择一个增量序列也称为间隔序列该序列的最后一个元素必须为常用的增量序列有希尔建议的序列例如或者序列分组排序根据增量序列将原始列表分割成若干个子列表对每个子列表分别进行插入排序逐步缩小间隔逐渐缩小增量重复步骤直到增量为最后的插入排序当增量为时进行最后一次插入排序此时列表已经被预排序插入排序的效率较高归并排序是建立在归并操作上的一种有效的排序算法该算法是采用分治法的一个非常典型的应用基本步骤分割将待排序的列表分成两个子列表直到每个子列表的长度为即列表无法再分割排序对每个子列表进行递归排序递归的过程就是不断地将列表分割并排序合并将两个已排序的子列表合并成一个有序列表合并过程中比较两个子列表的头部元素将较小或较大的元素放入合并后的列表中直到其中一个子列表为空然后将另一个子列表的剩余部分直接放入合并后的列表中快速排序是由东尼霍尔所发展的一种排序算法在平均状况下排序个项目要次比较在最坏状况下则需要次比较但这种状况并不常见事实上快速排序通常明显比其他算法更快因为它的内部循环可以在大部分的架构上很有效率地被实现出来基本步骤选择基准从列表中选择一个元素作为基准元素一般情况下是选择数组的第一个或最后一个分区将列表中小于基准元素的元素放在基准元素的左边大于基准元素的元素放在右边基准元素放在中间这个过程称为分区操作递归排序对左右两个子列表分别进行递归排序直到列表为空或只包含一个元素合并由于快速排序是原地排序算法不需要显式的合并步骤再详细一点原数组选择基准元素分成左半部分和右半部分对左半部分递归调用快速排序算法得到有序数组对右半部分选择基准元素分成左半部分和右半部分对左半部分递归调用快速排序算法得到有序数组对右半部分选择基准元素分成左半部分和右半部分对左半部分选择基准元素分成左半部分和右半部分对左半部分递归调用快速排序算法得到有序数组对右半部分递归调用快速排序算法得到有序数组将左半部分基准元素和右半部分拼接起来得到有序数组将左半部分基准元素和右半部分拼接起来得到有序数组将左半部分基准元素和右半部分拼接起来得到有序数组堆排序是指利用堆这种数据结构所设计的一种排序算法堆积是一个近似完全二叉树的结构并同时满足堆积的性质即子结点的键值或索引总是小于或者大于它的父节点堆排序可以说是一种利用堆的概念来排序的选择排序分为两种方法大顶堆每个节点的值都大于或等于其子节点的值在堆排序算法中用于升序排列小顶堆每个节点的值都小于或等于其子节点的值在堆排序算法中用于降序排列基本步骤建立堆将待排序的列表构建成一个最大堆这一步通常是从列表的中间位置开始自底向上地调整每个节点使得整个列表满足堆的性质排序将最大堆中的根节点即最大值与堆中的最后一个元素交换位置并将堆的大小减交换后可能会破坏堆的性质因此需要进行堆调整操作使得堆重新满足堆的性质重复步骤直到堆的大小为此时整个列表已经排序完成计数排序的核心在于将输入的数据值转化为键存储在额外开辟的数组空间中作为一种线性时间复杂度的排序计数排序要求输入的数据必须是有确定范围的整数基本步骤统计元素出现次数遍历待排序的列表统计每个元素出现的次数并将统计结果存储在一个额外的计数数组中计数数组的索引对应于待排序元素的值而数组中的值对应于该元素出现的次数累加计数对计数数组进行累加操作使得每个索引位置的值等于其前面所有索引位置的值之和这一步可以使得计数数组中的值表示小于等于该索引值的元素个数输出排序结果根据计数数组中的统计结果将待排序列表中的元素放置到正确的位置上最终得到排序结果桶排序是计数排序的升级版它利用了函数的映射关系高效与否的关键就在于这个映射函数的确定为了使桶排序更加高效我们需要做到这两点在额外空间充足的情况下尽量增大桶的数量使用的映射函数能够将输入的个数据均匀的分配到个桶中基本步骤划分桶根据待排序元素的范围确定一定数量的桶并将待排序元素分配到相应的桶中桶内排序对每个桶中的元素进行排序可以使用任何适合的排序算法如插入排序快速排序等合并结果按照桶的顺序依次取出各个桶中的元素即可得到有序的结果基数排序是一种非比较型整数排序算法其原理是将整数按位数切割成不同的数字然后按每个位数分别比较由于整数也可以表达字符串比如名字或日期和特定格式的浮点数所以基数排序也不是只能使用于整数基本步骤按位排序从最低位开始对待排序的元素按照当前位数进行排序可以使用稳定的排序算法如计数排序或桶排序重复排序重复第一步的过程对每一位进行排序直到对最高位进行排序合并结果完成所有位的排序后即可得到有序的结果总结排序算法平均时间复杂度最好情况最坏情况空间复杂度排序方式稳定性冒泡排序稳定选择排序不稳定插入排序稳定希尔排序不稳定归并排序稳定快速排序不稳定堆排序不稳定计数排序稳定桶排序稳定基数排序稳定',
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headline">排序算法详解</h1><span itemprop="author" itemscope itemtype="http://schema.org/Person">伴随</span><time itemprop="dateCreated datePublished" datetime="2024-04-06T10:07:20.000Z" title="发表于 2024-04-06 18:07:20">2024-04-06</time><time itemprop="dateCreated datePublished" datetime="2024-04-20T10:07:20.000Z" title="更新于 2024-04-20 18:07:20">2024-04-20</time></header><h1>小知识</h1>
<h3 id="如何判断一个排序算法是否稳定">如何判断一个排序算法是否稳定</h3>
<ul>
<li><strong>稳定</strong>：如果a原本在b前面，而a=b，排序之后a仍然在b的前面；</li>
<li><strong>不稳定</strong>：如果a原本在b的前面，而a=b，排序之后a可能会出现在b的后面；</li>
</ul>
<h3 id="速记">速记</h3>
<ul>
<li><strong>不稳定算法</strong>：<wavy>快选堆希</wavy></li>
</ul>
<h3 id="排序方式">排序方式</h3>
<ul>
<li><strong>In-place（原地算法）</strong>：指算法执行过程中不需要额外的辅助空间，而是在原始数据上进行操作。</li>
<li><strong>Out-of-place（非原地算法）</strong>：指算法执行过程中需要额外的辅助空间来存储数据，而不会在原始数据上进行直接操作。</li>
</ul>
<mark class="hl-label purple">所以非原地算法通常具有较高的空间复杂度</mark>
<h3 id="算法策略">算法策略</h3>
<ul>
<li><strong>分治法</strong>：快速排序，归并排序</li>
</ul>
<h1>算法详解</h1>
<div class="tabs" id="test1"><ul class="nav-tabs"><button type="button" class="tab active" data-href="test1-1">冒泡排序</button><button type="button" class="tab " data-href="test1-2">选择排序</button><button type="button" class="tab " data-href="test1-3">插入排序</button><button type="button" class="tab " data-href="test1-4">希尔排序</button><button type="button" class="tab " data-href="test1-5">归并排序</button><button type="button" class="tab " data-href="test1-6">快速排序</button><button type="button" class="tab " data-href="test1-7">堆排序</button><button type="button" class="tab " data-href="test1-8">计数排序</button><button type="button" class="tab " data-href="test1-9">桶排序</button><button type="button" class="tab " data-href="test1-10">基数排序</button></ul><div class="tab-contents"><div class="tab-item-content active" id="test1-1"><div class="note info no-icon flat"><p> 冒泡排序（Bubble Sort）也是一种简单直观的排序算法。它重复地走访过要排序的数列，一次比较两个元素，如果他们的顺序错误就把他们交换过来。走访数列的工作是重复地进行直到没有再需要交换，也就是说该数列已经排序完成。</p>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li>
<p>比较相邻的两个元素，如果前一个比后一个大（升序排序）或者小（降序排序），则交换它们的位置。</p>
</li>
<li>
<p>对每一对相邻元素重复步骤1，直到列表末尾。这样一次遍历完成后，最大（或最小）的元素将移动到列表末尾。</p>
</li>
<li>
<p>针对剩下的未排序元素重复以上步骤，直到列表中的所有元素都排好序。</p>
</li>
</ol>
<img src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="https://www.runoob.com/wp-content/uploads/2019/03/bubbleSort.gif"/></div><div class="tab-item-content" id="test1-2"><div class="note info no-icon flat"><p> 选择排序是一种简单直观的排序算法，无论什么数据进去都是 O(n²) 的时间复杂度。所以用到它的时候，数据规模越小越好。唯一的好处可能就是不占用额外的内存空间</p>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li><strong>遍历数组</strong>：从未排序部分找到最小（或最大）的元素。</li>
<li><strong>交换位置</strong>：将找到的最小（或最大）元素与未排序部分的第一个元素交换位置。</li>
<li><strong>缩小范围</strong>：将未排序部分的范围缩小一个元素，即将排序范围向右移动一个位置。</li>
<li><strong>重复步骤1至步骤3</strong>，直到所有元素都被排序完成。</li>
</ol>
<img src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="//www.runoob.com/wp-content/uploads/2019/03/selectionSort.gif"></div><div class="tab-item-content" id="test1-3"><div class="note info no-icon flat"><p> 插入排序的代码实现虽然没有冒泡排序和选择排序那么简单粗暴，但它的原理应该是最容易理解的了，因为只要打过扑克牌的人都应该能够秒懂。插入排序是一种最简单直观的排序算法，它的工作原理是通过构建有序序列，对于未排序数据，在已排序序列中从后向前扫描，找到相应位置并插入。</p>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li><strong>初始状态</strong>：将第一个元素视为已排序部分，其余元素视为未排序部分。</li>
<li><strong>遍历未排序部分</strong>：依次取出未排序部分的元素。</li>
<li><strong>插入已排序部分</strong>：将取出的元素与已排序部分的元素依次比较，找到合适的位置插入。</li>
<li><strong>重复步骤2至步骤3</strong>，直到所有元素都被插入到已排序部分。</li>
</ol>
<img src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="//www.runoob.com/wp-content/uploads/2019/03/insertionSort.gif"></div><div class="tab-item-content" id="test1-4"><div class="note info no-icon flat"><p> 希尔排序，也称递减增量排序算法，是插入排序的一种更高效的改进版本。但希尔排序是非稳定排序算法。</p>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li><strong>确定间隔序列</strong>：选择一个增量序列（也称为间隔序列），该序列的最后一个元素必须为1。常用的增量序列有希尔建议的序列（例如：{n/2, n/4, …, 1}）或者Sedgewick序列。</li>
<li><strong>分组排序</strong>：根据增量序列，将原始列表分割成若干个子列表，对每个子列表分别进行插入排序。</li>
<li><strong>逐步缩小间隔</strong>：逐渐缩小增量，重复步骤2，直到增量为1。</li>
<li><strong>最后的插入排序</strong>：当增量为1时，进行最后一次插入排序，此时列表已经被“预排序”，插入排序的效率较高。</li>
</ol>
<img decoding="async" src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="//www.runoob.com/wp-content/uploads/2019/03/Sorting_shellsort_anim.gif" alt=""></div><div class="tab-item-content" id="test1-5"><div class="note info no-icon flat"><p> 归并排序（Merge sort）是建立在归并操作上的一种有效的排序算法。该算法是采用分治法（Divide and Conquer）的一个非常典型的应用。</p>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li><strong>分割</strong>：将待排序的列表分成两个子列表，直到每个子列表的长度为1（即列表无法再分割）。</li>
<li><strong>排序</strong>：对每个子列表进行递归排序。递归的过程就是不断地将列表分割并排序。</li>
<li><strong>合并</strong>：将两个已排序的子列表合并成一个有序列表。合并过程中，比较两个子列表的头部元素，将较小（或较大）的元素放入合并后的列表中，直到其中一个子列表为空，然后将另一个子列表的剩余部分直接放入合并后的列表中。</li>
</ol>
<img decoding="async" src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="//www.runoob.com/wp-content/uploads/2019/03/mergeSort.gif"></div><div class="tab-item-content" id="test1-6"><div class="note info no-icon flat"><p> 快速排序是由东尼·霍尔所发展的一种排序算法。在平均状况下，排序 n 个项目要 Ο(nlogn) 次比较。在最坏状况下则需要 Ο(n2) 次比较，但这种状况并不常见。事实上，快速排序通常明显比其他 Ο(nlogn) 算法更快，因为它的内部循环（inner loop）可以在大部分的架构上很有效率地被实现出来。</p>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li><strong>选择基准</strong>：从列表中选择一个元素作为基准元素（一般情况下是选择数组的第一个或最后一个）。</li>
<li><strong>分区</strong>：将列表中小于基准元素的元素放在基准元素的左边，大于基准元素的元素放在右边，基准元素放在中间。这个过程称为分区操作。</li>
<li><strong>递归排序</strong>：对左右两个子列表分别进行递归排序，直到列表为空或只包含一个元素。</li>
<li><strong>合并</strong>：由于快速排序是原地排序算法，不需要显式的合并步骤。</li>
</ol>
<p><strong>再详细一点：</strong></p>
<ol>
<li>原数组：[3, 5, 1, 9, 7, 2, 8, 4, 6]</li>
<li>选择基准元素 3，分成左半部分 [1, 2] 和右半部分 [5, 9, 7, 8, 4, 6]</li>
<li>对左半部分 [1, 2] 递归调用快速排序算法，得到有序数组 [1, 2]</li>
<li>对右半部分 [5, 9, 7, 8, 4, 6] 选择基准元素 5，分成左半部分 [4] 和右半部分 [9, 7, 8, 6]</li>
<li>对左半部分 [4] 递归调用快速排序算法，得到有序数组 [4]</li>
<li>对右半部分 [9, 7, 8, 6] 选择基准元素 9，分成左半部分 [7, 8, 6] 和右半部分 []</li>
<li>对左半部分 [7, 8, 6] 选择基准元素 7，分成左半部分 [6] 和右半部分 [8]</li>
<li>对左半部分 [6] 递归调用快速排序算法，得到有序数组 [6]</li>
<li>对右半部分 [8] 递归调用快速排序算法，得到有序数组 [8]</li>
<li>将左半部分 [6]、基准元素 7 和右半部分 [8] 拼接起来，得到有序数组 [6, 7, 8]</li>
<li>将左半部分 [4]、基准元素 5 和右半部分 [6, 7, 8, 9] 拼接起来，得到有序数组 [4, 5, 6, 7, 8, 9]</li>
<li>将左半部分 [1, 2]、基准元素 3 和右半部分 [4, 5, 6, 7, 8, 9] 拼接起来，得到有序数组 [1, 2, 3, 4, 5, 6, 7, 8, 9]</li>
</ol>
<img decoding="async" src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="//www.runoob.com/wp-content/uploads/2019/03/quickSort.gif" alt=""></div><div class="tab-item-content" id="test1-7"><div class="note info no-icon flat"><p> 堆排序（Heapsort）是指利用堆这种数据结构所设计的一种排序算法。堆积是一个近似完全二叉树的结构，并同时满足堆积的性质：即子结点的键值或索引总是小于（或者大于）它的父节点。堆排序可以说是一种利用堆的概念来排序的选择排序。分为两种方法：</p>
<ul>
<li>大顶堆：每个节点的值都大于或等于其子节点的值，在堆排序算法中用于升序排列；</li>
<li>小顶堆：每个节点的值都小于或等于其子节点的值，在堆排序算法中用于降序排列；</li>
</ul>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li><strong>建立堆</strong>：将待排序的列表构建成一个最大堆。这一步通常是从列表的中间位置开始，自底向上地调整每个节点，使得整个列表满足堆的性质。</li>
<li><strong>排序</strong>：将最大堆中的根节点（即最大值）与堆中的最后一个元素交换位置，并将堆的大小减1。交换后可能会破坏堆的性质，因此需要进行堆调整操作，使得堆重新满足堆的性质。</li>
<li><strong>重复步骤2</strong>，直到堆的大小为1，此时整个列表已经排序完成。</li>
</ol>
<ul>
<li>
<img decoding="async" src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="//www.runoob.com/wp-content/uploads/2019/03/heapSort.gif">
<img decoding="async" src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="//www.runoob.com/wp-content/uploads/2019/03/Sorting_heapsort_anim.gif">
</li>
</ul></div><div class="tab-item-content" id="test1-8"><div class="note info no-icon flat"><p> 计数排序的核心在于将输入的数据值转化为键存储在额外开辟的数组空间中。作为一种线性时间复杂度的排序，计数排序要求输入的数据必须是有确定范围的整数。</p>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li><strong>统计元素出现次数</strong>：遍历待排序的列表，统计每个元素出现的次数，并将统计结果存储在一个额外的计数数组中。计数数组的索引对应于待排序元素的值，而数组中的值对应于该元素出现的次数。</li>
<li><strong>累加计数</strong>：对计数数组进行累加操作，使得每个索引位置的值等于其前面所有索引位置的值之和。这一步可以使得计数数组中的值表示小于等于该索引值的元素个数。</li>
<li><strong>输出排序结果</strong>：根据计数数组中的统计结果，将待排序列表中的元素放置到正确的位置上，最终得到排序结果。</li>
</ol>
<img decoding="async" src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="//www.runoob.com/wp-content/uploads/2019/03/countingSort.gif"></div><div class="tab-item-content" id="test1-9"><div class="note info no-icon flat"><p> 桶排序是计数排序的升级版。它利用了函数的映射关系，高效与否的关键就在于这个映射函数的确定。为了使桶排序更加高效，我们需要做到这两点：</p>
<p>在额外空间充足的情况下，尽量增大桶的数量<br>
使用的映射函数能够将输入的 N 个数据均匀的分配到 K 个桶中</p>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li><strong>划分桶</strong>：根据待排序元素的范围，确定一定数量的桶，并将待排序元素分配到相应的桶中。</li>
<li><strong>桶内排序</strong>：对每个桶中的元素进行排序。可以使用任何适合的排序算法，如插入排序、快速排序等。</li>
<li><strong>合并结果</strong>：按照桶的顺序依次取出各个桶中的元素，即可得到有序的结果。</li>
</ol></div><div class="tab-item-content" id="test1-10"><div class="note info no-icon flat"><p> 基数排序是一种非比较型整数排序算法，其原理是将整数按位数切割成不同的数字，然后按每个位数分别比较。由于整数也可以表达字符串（比如名字或日期）和特定格式的浮点数，所以基数排序也不是只能使用于整数。</p>
</div>
<p><strong>基本步骤：</strong></p>
<ol>
<li><strong>按位排序</strong>：从最低位开始，对待排序的元素按照当前位数进行排序。可以使用稳定的排序算法，如计数排序或桶排序。</li>
<li><strong>重复排序</strong>：重复第一步的过程，对每一位进行排序，直到对最高位进行排序。</li>
<li><strong>合并结果</strong>：完成所有位的排序后，即可得到有序的结果。</li>
</ol>
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<h1>总结</h1>
<table>
<thead>
<tr>
<th style="text-align:center">排序算法</th>
<th style="text-align:center">平均时间复杂度</th>
<th style="text-align:center">最好情况</th>
<th style="text-align:center">最坏情况</th>
<th style="text-align:center">空间复杂度</th>
<th style="text-align:center">排序方式</th>
<th style="text-align:center">稳定性</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:center">冒泡排序</td>
<td style="text-align:center">O(n^2)</td>
<td style="text-align:center">O(n)</td>
<td style="text-align:center">O(n)</td>
<td style="text-align:center">O(1)</td>
<td style="text-align:center">In-place</td>
<td style="text-align:center">稳定</td>
</tr>
<tr>
<td style="text-align:center">选择排序</td>
<td style="text-align:center">O(n^2)</td>
<td style="text-align:center">O(n^2)</td>
<td style="text-align:center">O(n^2)</td>
<td style="text-align:center">O(1)</td>
<td style="text-align:center">In-place</td>
<td style="text-align:center">不稳定</td>
</tr>
<tr>
<td style="text-align:center">插入排序</td>
<td style="text-align:center">O(n^2)</td>
<td style="text-align:center">O(n)</td>
<td style="text-align:center">O(n^2)</td>
<td style="text-align:center">O(1)</td>
<td style="text-align:center">In-place</td>
<td style="text-align:center">稳定</td>
</tr>
<tr>
<td style="text-align:center">希尔排序</td>
<td style="text-align:center">O(n log n)</td>
<td style="text-align:center">O(n log^2 n)</td>
<td style="text-align:center">O(n log^2 n)</td>
<td style="text-align:center">O(1)</td>
<td style="text-align:center">In-place</td>
<td style="text-align:center">不稳定</td>
</tr>
<tr>
<td style="text-align:center">归并排序</td>
<td style="text-align:center">O(n log n)</td>
<td style="text-align:center">O(n log n)</td>
<td style="text-align:center">O(n logn)</td>
<td style="text-align:center">O(n)</td>
<td style="text-align:center">Out-place</td>
<td style="text-align:center">稳定</td>
</tr>
<tr>
<td style="text-align:center">快速排序</td>
<td style="text-align:center">O(n log n)</td>
<td style="text-align:center">O(n log n)</td>
<td style="text-align:center">O(n^2)</td>
<td style="text-align:center">O(log n)</td>
<td style="text-align:center">In-place</td>
<td style="text-align:center">不稳定</td>
</tr>
<tr>
<td style="text-align:center">堆排序</td>
<td style="text-align:center">O(n log n)</td>
<td style="text-align:center">O(n log n)</td>
<td style="text-align:center">O(n log n)</td>
<td style="text-align:center">O(1)</td>
<td style="text-align:center">In-place</td>
<td style="text-align:center">不稳定</td>
</tr>
<tr>
<td style="text-align:center">计数排序</td>
<td style="text-align:center">O(n+k)</td>
<td style="text-align:center">O(n+k)</td>
<td style="text-align:center">O(n+k)</td>
<td style="text-align:center">O(k)</td>
<td style="text-align:center">Out-place</td>
<td style="text-align:center">稳定</td>
</tr>
<tr>
<td style="text-align:center">桶排序</td>
<td style="text-align:center">O(n+k)</td>
<td style="text-align:center">O(n+k)</td>
<td style="text-align:center">O(n^2)</td>
<td style="text-align:center">O(n+k)</td>
<td style="text-align:center">Out-place</td>
<td style="text-align:center">稳定</td>
</tr>
<tr>
<td style="text-align:center">基数排序</td>
<td style="text-align:center">O(n×k)</td>
<td style="text-align:center">O(n×k)</td>
<td style="text-align:center">O(n×k)</td>
<td style="text-align:center">O(n+k)</td>
<td style="text-align:center">Out-place</td>
<td style="text-align:center">稳定</td>
</tr>
</tbody>
</table>
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class="anzhiyufont anzhiyu-icon-bars"></i><span>文章目录</span><span class="toc-percentage"></span></div><div class="toc-content"><ol class="toc"><li class="toc-item toc-level-1"><a class="toc-link"><span class="toc-number">1.</span> <span class="toc-text">小知识</span></a><ol class="toc-child"><li class="toc-item toc-level-3"><a class="toc-link" href="#%E5%A6%82%E4%BD%95%E5%88%A4%E6%96%AD%E4%B8%80%E4%B8%AA%E6%8E%92%E5%BA%8F%E7%AE%97%E6%B3%95%E6%98%AF%E5%90%A6%E7%A8%B3%E5%AE%9A"><span class="toc-number">1.0.1.</span> <span class="toc-text">如何判断一个排序算法是否稳定</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E9%80%9F%E8%AE%B0"><span class="toc-number">1.0.2.</span> <span class="toc-text">速记</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E6%8E%92%E5%BA%8F%E6%96%B9%E5%BC%8F"><span class="toc-number">1.0.3.</span> <span class="toc-text">排序方式</span></a></li><li class="toc-item toc-level-3"><a class="toc-link" href="#%E7%AE%97%E6%B3%95%E7%AD%96%E7%95%A5"><span class="toc-number">1.0.4.</span> <span class="toc-text">算法策略</span></a></li></ol></li></ol></li><li class="toc-item toc-level-1"><a class="toc-link"><span class="toc-number">2.</span> <span class="toc-text">算法详解</span></a></li><li class="toc-item toc-level-1"><a class="toc-link"><span class="toc-number">3.</span> <span class="toc-text">总结</span></a></li></ol></div></div><div class="card-widget card-recent-post"><div class="item-headline"><i class="anzhiyufont anzhiyu-icon-history"></i><span>最近发布</span></div><div class="aside-list"><div class="aside-list-item"><a class="thumbnail" href="/8a0c.html" title="JAVA表达式解析器———EvalEx"><img src= "data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" onerror="this.onerror=null,this.src="https://up.ctext.top/default_bg.png"" data-lazy-src="https://up.ctext.top/article/2024/11/tools3.png" onerror="this.onerror=null;this.src='https://up.ctext.top/default_bg.png'" 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nick: '你的专属昵称',
nickError: '昵称太短啦！至少得有3个字符才能算数哦！',
mail: '你的电子小信箱',
mailError: '哎呀，这不是一个合格的邮箱地址哦，请再检查一遍！',
link: '你有个酷酷的网址吗？',
optional: '这个嘛，想填就填，不填也行！',
placeholder: '吐槽一下？',
sofa: '来，坐沙发上，发表你的评论吧！',
submit: '一键发送，让世界听到你的声音！',
like: '点个赞，让TA知道你的心意！',
cancelLike: '哎呀，不小心点错了，取消赞！',
reply: '回复TA，开启一场对话吧！',
cancelReply: '等等，我话还没说完，取消回复！',
comment: '来，说说你的看法，让评论区热闹起来！',
refresh: '刷新一下，看看有啥新动态！',
more: '哇塞，还有更多精彩内容等你来加载！',
preview: '先睹为快，预览一下你的大作吧！',
emoji: '来，加点表情，让你的评论更生动！',
uploadImage: '上传你的美照，让大家一起欣赏！',
seconds: '刚刚才发的，新鲜出炉！',
minutes: '几分钟前，还热乎着呢！',
hours: '几小时前，热度还在哦！',
days: '几天前，但依旧值得一看！',
now: '哇塞，刚刚发的，快抢沙发！',
uploading: '稍等片刻，你的图片正在飞奔而来！',
login: '登录一下，解锁更多功能！',
logout: '拜拜了您嘞，下次再见！',
admin: '博主大人在此，谁敢造次！',
sticky: '置顶一下，让更多人看到你的精彩内容！',
word: '字',
wordHint: '评论字数要在0到1字之间哦！\n现在你已经写了$2个字了，加油！',
anonymous: '神秘人出没，猜猜是谁？',
level0: '潜水员，深藏不露！',
level1: '冒泡小能手，偶尔露个头！',
level2: '吐槽大师，一针见血！',
level3: '活跃分子，无处不在！',
level4: '话痨达人，说个不停！',
level5: '传说级大神，膜拜一下！',
gif: '动态表情包，让你的评论更有趣！',
gifSearchPlaceholder: '快来搜索你喜欢的表情包，让评论更生动！',
profile: '看看我的个人资料，了解一下我吧！',
approved: '审核通过，可以展示啦！',
waiting: '正在等待审核，别急哦！',
spam: '垃圾内容，走开走开！',
unsticky: '换个位置看看！',
oldest: '看看最早的评论！',
latest: '看看最新的动态！',
hottest: '看看哪条评论最火！',
reactionTitle: '快来对这篇文章发表你的看法吧，让博主知道你的想法！😜'
};
const initWaline = () => {
const waline = Waline.init(Object.assign({
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serverURL: 'https://bc.ctext.top/',
pageview: false,
dark: 'html[data-theme="dark"]',
path: window.location.pathname,
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initWaline()
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$dom && ($dom.innerHTML= result)
window.lazyLoadInstance && window.lazyLoadInstance.update()
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}
const getComment = async () => {
try {
const res = await fetch('https://bc.ctext.top/api/comment?type=recent&count=6', { method: 'GET' })
const result = await res.json()
const walineArray = result.data.map(e => {
return {
'content': changeContent(e.comment),
'avatar': e.avatar,
'nick': e.nick,
'url': e.url + '#' + e.objectId,
'date': e.time || e.insertedAt
}
})
saveToLocal.set('waline-newest-comments', JSON.stringify(walineArray), 10/(60*24))
generateHtml(walineArray)
} catch (err) {
console.error(err)
const $dom = document.querySelector('#card-newest-comments .aside-list')
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}
}
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const data = saveToLocal.get('waline-newest-comments')
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} else {
getComment()
}
}
}
newestCommentInit()
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newScript.appendChild(document.createTextNode(content))
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