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10.2 &nbsp; 二分查找插入点
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10.3 &nbsp; 二分查找边界
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第 12 章 &nbsp; 分治
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12.1 &nbsp; 分治算法
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12.2 &nbsp; 分治搜索策略
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12.3 &nbsp; 构建树问题
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12.4 &nbsp; 汉诺塔问题
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12.5 &nbsp; 小结
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第 14 章 &nbsp; 动态规划
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14.1 &nbsp; 初探动态规划
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14.2 &nbsp; DP 问题特性
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14.3 &nbsp; DP 解题思路
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14.4 &nbsp; 0-1 背包问题
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14.5 &nbsp; 完全背包问题
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14.6 &nbsp; 编辑距离问题
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14.7 &nbsp; 小结
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第 15 章 &nbsp; 贪心
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15.1 &nbsp; 贪心算法
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15.2 &nbsp; 分数背包问题
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15.3 &nbsp; 最大容量问题
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15.4 &nbsp; 最大切分乘积问题
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15.5 &nbsp; 小结
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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><img alt="遍历寻找最大的 k 个元素" src="../top_k.assets/top_k_traversal.png" /></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 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><img alt="排序寻找最大的 k 个元素" src="../top_k.assets/top_k_sorting.png" /></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 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><img alt="基于堆寻找最大的 k 个元素" src="../top_k.assets/top_k_heap_step1.png" /></p>
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