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<div class="admonition question">
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<p class="admonition-title">广度优先遍历的序列是否唯一?</p>
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<p>不唯一。广度优先遍历只要求按“由近及远”的顺序遍历,<strong>而多个相同距离的顶点的遍历顺序是允许被任意打乱的</strong>。以图 9-10 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。</p>
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<p>不唯一。广度优先遍历只要求按“由近及远”的顺序遍历,<strong>而多个相同距离的顶点的遍历顺序是允许被任意打乱的</strong>。以图 9-10 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。</p>
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</div>
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<h3 id="2">2. 复杂度分析<a class="headerlink" href="#2" title="Permanent link">¶</a></h3>
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<p><strong>时间复杂度:</strong> 所有顶点都会入队并出队一次,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>
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</div>
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</div>
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</div>
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<p>深度优先遍历的算法流程如图 9-12 所示,其中:</p>
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<p>深度优先遍历的算法流程如图 9-12 所示。</p>
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<ul>
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<li><strong>直虚线代表向下递推</strong>,表示开启了一个新的递归方法来访问新顶点。</li>
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<li><strong>曲虚线代表向上回溯</strong>,表示此递归方法已经返回,回溯到了开启此递归方法的位置。</li>
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