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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>我们可以进行图 8-6 所示的 <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">\(\dots\)</span>、<span class="arithmatex">\(k\)</span> 大的元素，时间复杂度为 <span class="arithmatex">\(O(nk)\)</span> 。</p>
<p>此方法只适用于 <span class="arithmatex">\(k \ll n\)</span> 的情况，因为当 <span class="arithmatex">\(k\)</span> 与 <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><a class="glightbox" href="../top_k.assets/top_k_traversal.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="遍历寻找最大的 k 个元素" src="../top_k.assets/top_k_traversal.png" /></a></p>
<p><a class="glightbox" href="../top_k.assets/top_k_traversal.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="遍历寻找最大的 k 个元素" class="animation-figure" src="../top_k.assets/top_k_traversal.png" /></a></p>
<p align="center"> 图 8-6 &nbsp; 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>如图 8-7 所示，我们可以先对数组 <code>nums</code> 进行排序，再返回最右边的 <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><a class="glightbox" href="../top_k.assets/top_k_sorting.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="排序寻找最大的 k 个元素" src="../top_k.assets/top_k_sorting.png" /></a></p>
<p><a class="glightbox" href="../top_k.assets/top_k_sorting.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="排序寻找最大的 k 个元素" class="animation-figure" src="../top_k.assets/top_k_sorting.png" /></a></p>
<p align="center"> 图 8-7 &nbsp; 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>
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<p><a class="glightbox" href="../top_k.assets/top_k_heap_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="基于堆寻找最大的 k 个元素" class="animation-figure" src="../top_k.assets/top_k_heap_step1.png" /></a></p>
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