This commit is contained in:
krahets
2023-08-21 19:32:49 +08:00
parent c0f960b443
commit c359c07fe0
67 changed files with 443 additions and 442 deletions
+2 -2
View File
@@ -3399,7 +3399,7 @@
<h1 id="112">11.2 &nbsp; 选择排序<a class="headerlink" href="#112" title="Permanent link">&para;</a></h1>
<p>「选择排序 selection sort」的工作原理非常直接:开启一个循环,每轮从未排序区间选择最小的元素,将其放到已排序区间的末尾。</p>
<p>设数组的长度为 <span class="arithmatex">\(n\)</span> ,选择排序的算法流程如下</p>
<p>设数组的长度为 <span class="arithmatex">\(n\)</span> ,选择排序的算法流程如下图所示。</p>
<ol>
<li>初始状态下,所有元素未排序,即未排序(索引)区间为 <span class="arithmatex">\([0, n-1]\)</span></li>
<li>选取区间 <span class="arithmatex">\([0, n-1]\)</span> 中的最小元素,将其与索引 <span class="arithmatex">\(0\)</span> 处元素交换。完成后,数组前 1 个元素已排序。</li>
@@ -3664,7 +3664,7 @@
<ul>
<li><strong>时间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> 、非自适应排序</strong>:外循环共 <span class="arithmatex">\(n - 1\)</span> 轮,第一轮的未排序区间长度为 <span class="arithmatex">\(n\)</span> ,最后一轮的未排序区间长度为 <span class="arithmatex">\(2\)</span> ,即各轮外循环分别包含 <span class="arithmatex">\(n\)</span> , <span class="arithmatex">\(n - 1\)</span> , <span class="arithmatex">\(\dots\)</span> , <span class="arithmatex">\(2\)</span> 轮内循环,求和为 <span class="arithmatex">\(\frac{(n - 1)(n + 2)}{2}\)</span></li>
<li><strong>空间复杂度 <span class="arithmatex">\(O(1)\)</span> 、原地排序</strong>:指针 <span class="arithmatex">\(i\)</span> , <span class="arithmatex">\(j\)</span> 使用常数大小的额外空间。</li>
<li><strong>非稳定排序</strong>在交换元素时,有可能将 <code>nums[i]</code> 交换至其相等元素的右边,导致两者相对顺序发生改变。</li>
<li><strong>非稳定排序</strong>如下图所示,元素 <code>nums[i]</code> 有可能被交换至其相等元素的右边,导致两者相对顺序发生改变。</li>
</ul>
<p><img alt="选择排序非稳定示例" src="../selection_sort.assets/selection_sort_instability.png" /></p>
<p align="center"> 图:选择排序非稳定示例 </p>