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<h1 id="112">11.2 选择排序<a class="headerlink" href="#112" title="Permanent link">¶</a></h1>
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<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>
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<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>
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<p>设数组的长度为 <span class="arithmatex">\(n\)</span> ,选择排序的算法流程如图 11-2 所示。</p>
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<ol>
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<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>
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<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>
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</div>
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</div>
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</div>
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<p align="center"> 图:选择排序步骤 </p>
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<p align="center"> 图 11-2 选择排序步骤 </p>
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<p>在代码中,我们用 <span class="arithmatex">\(k\)</span> 来记录未排序区间内的最小元素。</p>
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<div class="tabbed-set tabbed-alternate" data-tabs="2:12"><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" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" 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">JS</label><label for="__tabbed_2_6">TS</label><label for="__tabbed_2_7">C</label><label for="__tabbed_2_8">C#</label><label for="__tabbed_2_9">Swift</label><label for="__tabbed_2_10">Zig</label><label for="__tabbed_2_11">Dart</label><label for="__tabbed_2_12">Rust</label></div>
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<ul>
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<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>
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<li><strong>空间复杂度 <span class="arithmatex">\(O(1)\)</span> 、原地排序</strong>:指针 <span class="arithmatex">\(i\)</span> , <span class="arithmatex">\(j\)</span> 使用常数大小的额外空间。</li>
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<li><strong>非稳定排序</strong>:如下图所示,元素 <code>nums[i]</code> 有可能被交换至与其相等的元素的右边,导致两者相对顺序发生改变。</li>
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<li><strong>非稳定排序</strong>:如图 11-3 所示,元素 <code>nums[i]</code> 有可能被交换至与其相等的元素的右边,导致两者相对顺序发生改变。</li>
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</ul>
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<p><img alt="选择排序非稳定示例" src="../selection_sort.assets/selection_sort_instability.png" /></p>
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<p align="center"> 图:选择排序非稳定示例 </p>
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<p align="center"> 图 11-3 选择排序非稳定示例 </p>
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