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1.3. &nbsp; 小结
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9.4. &nbsp; 小结
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<h3 id="_1">借助入堆方法实现<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h3>
<p>最直接地，考虑借助「元素入堆」方法，先建立一个空堆，<strong>再将列表元素依次入堆即可</strong>。</p>
<h3 id="_2">基于堆化操作实现<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h3>
<p>然而，<strong>存在一种更加高效的建堆方法</strong>。设结点数量为 <span class="arithmatex">\(n\)</span> ，我们先将列表所有元素原封不动添加进堆，<strong>然后迭代地对各个结点执行「从顶至底堆化」</strong>。当然，<strong>无需对叶结点执行堆化</strong>，因为其没有子结点。</p>
<p>然而，<strong>存在一种更加高效的建堆方法</strong>。设元素数量为 <span class="arithmatex">\(n\)</span> ，我们先将列表所有元素原封不动添加进堆，<strong>然后迭代地对各个结点执行「从顶至底堆化」</strong>。当然，<strong>无需对叶结点执行堆化</strong>，因为其没有子结点。</p>
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<div class="arithmatex">\[
T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \cdots + 2^{(h-1)}\times1
\]</div>
<p><img alt="完美二叉树的各层结点数量" src="../heap.assets/heapify_operations_count.png" /></p>
<p><img alt="完美二叉树的各层结点数量" src="../build_heap.assets/heapify_operations_count.png" /></p>
<p align="center"> Fig. 完美二叉树的各层结点数量 </p>
<p>化简上式需要借助中学的数列知识，先对 <span class="arithmatex">\(T(h)\)</span> 乘以 <span class="arithmatex">\(2\)</span> ，易得</p>
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