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 <li>In each iteration of the loop, pop the vertex at the front of the queue and record it as visited, then add all adjacent vertices of that vertex to the back of the queue.</li>
 <li>Repeat step <code>2.</code> until all vertices have been visited.</li>
 </ol>
-<p>To prevent revisiting vertices, we use a hash table <code>visited</code> to record which nodes have been visited.</p>
+<p>To prevent revisiting vertices, we use a hash set <code>visited</code> to record which nodes have been visited.</p>
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 <h3 id="2-complexity-analysis">2. &nbsp; Complexity analysis<a class="headerlink" href="#2-complexity-analysis" title="Permanent link">&para;</a></h3>
 <p><strong>Time complexity</strong>: All vertices will be enqueued and dequeued once, using <span class="arithmatex">\(O(|V|)\)</span> time; in the process of traversing adjacent vertices, since it is an undirected graph, all edges will be visited <span class="arithmatex">\(2\)</span> times, using <span class="arithmatex">\(O(2|E|)\)</span> time; overall using <span class="arithmatex">\(O(|V| + |E|)\)</span> time.</p>
-<p><strong>Space complexity</strong>: The maximum number of vertices in list <code>res</code>, hash table <code>visited</code>, and queue <code>que</code> is <span class="arithmatex">\(|V|\)</span>, using <span class="arithmatex">\(O(|V|)\)</span> space.</p>
+<p><strong>Space complexity</strong>: The maximum number of vertices in list <code>res</code>, hash set <code>visited</code>, and queue <code>que</code> is <span class="arithmatex">\(|V|\)</span>, using <span class="arithmatex">\(O(|V|)\)</span> space.</p>
 <h2 id="932-depth-first-search">9.3.2 &nbsp; Depth-first search<a class="headerlink" href="#932-depth-first-search" title="Permanent link">&para;</a></h2>
 <p><strong>Depth-first search is a traversal method that prioritizes going as far as possible and then backtracks when no further paths are available</strong>. As shown in Figure 9-11, starting from the top left vertex, visit some adjacent vertex of the current vertex until no further path is available, then return and continue until all vertices are traversed.</p>
 <p><a class="glightbox" href="../graph_traversal.assets/graph_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Depth-first traversal of a graph" class="animation-figure" src="../graph_traversal.assets/graph_dfs.png" /></a></p>
 <p align="center"> Figure 9-11 &nbsp; Depth-first traversal of a graph </p>
 
 <h3 id="1-algorithm-implementation_1">1. &nbsp; Algorithm implementation<a class="headerlink" href="#1-algorithm-implementation_1" title="Permanent link">&para;</a></h3>
-<p>This "go as far as possible and then return" algorithm paradigm is usually implemented based on recursion. Similar to breadth-first search, in depth-first search, we also need the help of a hash table <code>visited</code> to record the visited vertices to avoid revisiting.</p>
+<p>This "go as far as possible and then return" algorithm paradigm is usually implemented based on recursion. Similar to breadth-first search, in depth-first search, we also need the help of a hash set <code>visited</code> to record the visited vertices to avoid revisiting.</p>
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 <h3 id="2-complexity-analysis_1">2. &nbsp; Complexity analysis<a class="headerlink" href="#2-complexity-analysis_1" title="Permanent link">&para;</a></h3>
 <p><strong>Time complexity</strong>: All vertices will be visited once, using <span class="arithmatex">\(O(|V|)\)</span> time; all edges will be visited twice, using <span class="arithmatex">\(O(2|E|)\)</span> time; overall using <span class="arithmatex">\(O(|V| + |E|)\)</span> time.</p>
-<p><strong>Space complexity</strong>: The maximum number of vertices in list <code>res</code>, hash table <code>visited</code> is <span class="arithmatex">\(|V|\)</span>, and the maximum recursion depth is <span class="arithmatex">\(|V|\)</span>, therefore using <span class="arithmatex">\(O(|V|)\)</span> space.</p>
+<p><strong>Space complexity</strong>: The maximum number of vertices in list <code>res</code>, hash set <code>visited</code> is <span class="arithmatex">\(|V|\)</span>, and the maximum recursion depth is <span class="arithmatex">\(|V|\)</span>, therefore using <span class="arithmatex">\(O(|V|)\)</span> space.</p>
 
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