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<title>8.3.   Top-K 问题 - Hello 算法</title>
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<h2 id="831">8.3.1. &nbsp; 方法一:遍历选择<a class="headerlink" href="#831" title="Permanent link">&para;</a></h2>
<p>我们可以进行 <span class="arithmatex">\(k\)</span> 轮遍历,分别在每轮中提取第 <span class="arithmatex">\(1\)</span> , <span class="arithmatex">\(2\)</span> , <span class="arithmatex">\(\cdots\)</span> , <span class="arithmatex">\(k\)</span> 大的元素,时间复杂度为 <span class="arithmatex">\(O(nk)\)</span></p>
<p>该方法只适用于 <span class="arithmatex">\(k \ll n\)</span> 的情况,因为当 <span class="arithmatex">\(k\)</span><span class="arithmatex">\(n\)</span> 比较接近时,其时间复杂度趋向于 <span class="arithmatex">\(O(n^2)\)</span> ,非常耗时。</p>
<p><img alt="遍历寻找最大的 \(k\) 个元素" src="../top_k.assets/top_k_traversal.png" /></p>
<p align="center"> Fig. 遍历寻找最大的 $k$ 个元素 </p>
<p><img alt="遍历寻找最大的 k 个元素" src="../top_k.assets/top_k_traversal.png" /></p>
<p align="center"> Fig. 遍历寻找最大的 k 个元素 </p>
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<h2 id="832">8.3.2. &nbsp; 方法二:排序<a class="headerlink" href="#832" title="Permanent link">&para;</a></h2>
<p>我们可以对数组 <code>nums</code> 进行排序,并返回最右边的 <span class="arithmatex">\(k\)</span> 个元素,时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span></p>
<p>显然,该方法“超额”完成任务了,因为我们只需要找出最大的 <span class="arithmatex">\(k\)</span> 个元素即可,而不需要排序其他元素。</p>
<p><img alt="排序寻找最大的 \(k\) 个元素" src="../top_k.assets/top_k_sorting.png" /></p>
<p align="center"> Fig. 排序寻找最大的 $k$ 个元素 </p>
<p><img alt="排序寻找最大的 k 个元素" src="../top_k.assets/top_k_sorting.png" /></p>
<p align="center"> Fig. 排序寻找最大的 k 个元素 </p>
<h2 id="833">8.3.3. &nbsp; 方法三:堆<a class="headerlink" href="#833" title="Permanent link">&para;</a></h2>
<p>我们可以基于堆更加高效地解决 Top-K 问题,流程如下:</p>
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