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krahets
2023-02-24 11:43:41 +08:00
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</div>
<div class="admonition question">
<p class="admonition-title">广度优先遍历的序列是否唯一？</p>
<p>不唯一。广度优先遍历只要求“由近及远”，而相同距离的多个顶点的遍历顺序允许任意被打乱。以上图为例，顶点 <span class="arithmatex">\(1\)</span> , <span class="arithmatex">\(3\)</span> 的访问顺序可以交换、顶点 <span class="arithmatex">\(2\)</span> , <span class="arithmatex">\(4\)</span> , <span class="arithmatex">\(6\)</span> 的访问顺序也可以任意交换、以此类推……</p>
<p>不唯一。广度优先遍历只要求“由近及远”，<strong>而多个相同距离的顶点的遍历顺序允许被任意打乱</strong>。以上图为例，顶点 <span class="arithmatex">\(1\)</span> , <span class="arithmatex">\(3\)</span> 的访问顺序可以交换、顶点 <span class="arithmatex">\(2\)</span> , <span class="arithmatex">\(4\)</span> , <span class="arithmatex">\(6\)</span> 的访问顺序也可以任意交换、以此类推……</p>
</div>
<h3 id="_2">复杂度分析<a class="headerlink" href="#_2" title="Permanent link">&para;</a></h3>
<p><strong>时间复杂度：</strong> 所有顶点都会入队、出队一次，使用 <span class="arithmatex">\(O(|V|)\)</span> 时间；在遍历邻接顶点的过程中，由于是无向图，因此所有边都会被访问 <span class="arithmatex">\(2\)</span> 次，使用 <span class="arithmatex">\(O(2|E|)\)</span> 时间；总体使用 <span class="arithmatex">\(O(|V| + |E|)\)</span> 时间。</p>