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krahets
2023-02-13 16:26:34 +08:00
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<h3 id="_5">输入数据并建堆 *<a class="headerlink" href="#_5" title="Permanent link">&para;</a></h3>
<p>如果我们想要直接输入一个列表并将其建堆,那么该怎么做呢?最直接地,考虑使用「元素入堆」方法,将列表元素依次入堆。元素入堆的时间复杂度为 <span class="arithmatex">\(O(n)\)</span> ,而平均长度为 <span class="arithmatex">\(\frac{n}{2}\)</span> ,因此该方法的总体时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span></p>
<p>如果我们想要直接输入一个列表并将其建堆,那么该怎么做呢?最直接地,考虑使用「元素入堆」方法,将列表元素依次入堆。元素入堆的时间复杂度为 <span class="arithmatex">\(O(\log n)\)</span> ,而平均长度为 <span class="arithmatex">\(\frac{n}{2}\)</span> ,因此该方法的总体时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span></p>
<p>然而,存在一种更加优雅的建堆方法。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>
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