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chapter_sorting/bubble_sort/index.html
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<span class="md-ellipsis">
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</span>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
<label class="md-nav__title" for="__nav_3">
<span class="md-nav__icon md-icon"></span>
第 2 章 &nbsp; 复杂度
第 2 章 &nbsp; 时空复杂度
</label>
<ul class="md-nav__list" data-md-scrollfix>
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<span class="md-ellipsis">
第 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</span>
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<label class="md-nav__title" for="__nav_7">
<span class="md-nav__icon md-icon"></span>
第 6 章 &nbsp; 散列表
第 6 章 &nbsp; 哈希表
</label>
<ul class="md-nav__list" data-md-scrollfix>
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</div>
<h2 id="1133">11.3.3 &nbsp; 算法特性<a class="headerlink" href="#1133" title="Permanent link">&para;</a></h2>
<ul>
<li><strong>时间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> 、自适应排序</strong> ：各轮“冒泡”遍历的数组长度依次为 <span class="arithmatex">\(n - 1\)</span> , <span class="arithmatex">\(n - 2\)</span> , <span class="arithmatex">\(\cdots\)</span> , <span class="arithmatex">\(2\)</span> , <span class="arithmatex">\(1\)</span> ，总和为 <span class="arithmatex">\(\frac{(n - 1) n}{2}\)</span> 。在引入 <code>flag</code> 优化后，最佳时间复杂度可达到 <span class="arithmatex">\(O(n)\)</span> 。</li>
<li><strong>时间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> 、自适应排序</strong> ：各轮“冒泡”遍历的数组长度依次为 <span class="arithmatex">\(n - 1\)</span> , <span class="arithmatex">\(n - 2\)</span> , <span class="arithmatex">\(\dots\)</span> , <span class="arithmatex">\(2\)</span> , <span class="arithmatex">\(1\)</span> ，总和为 <span class="arithmatex">\((n - 1) n / 2\)</span> 。在引入 <code>flag</code> 优化后，最佳时间复杂度可达到 <span class="arithmatex">\(O(n)\)</span> 。</li>
<li><strong>空间复杂度为 <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>稳定排序</strong>：由于在“冒泡”中遇到相等元素不交换。</li>
</ul>