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graph-searching-algorithms.html
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<div id="content">
<h1 class="title">Graph Searching Algorithms</h1>
<div id="outline-container-org07a4115" class="outline-2">
<h2 id="org07a4115">Depth-First</h2>
<div class="outline-text-2" id="text-org07a4115">
<p class="verse">
<b>ALGORITHM</b> <i>DFS(G)</i><br />
<i>//</i> Implements a depth-first search traversal of a given graph<br />
<i>//</i> Input: Graph <i>G = <V,E></i><br />
<i>//</i> Output: Graph <i>G</i> with its vertices marked with consecutive integers<br />
<i>//</i> in the order they are first encountered by the DFS traversal<br />
mark each vertex in <i>V</i> with 0 as a mark of being "unvisited"<br />
<i>count ← 0</i><br />
<b>for</b> each vertex <i>v</i> in <i>V</i> <b>do</b><br />
    <b>if</b> <i>v</i> is marked with 0<br />
        <i>dfs(v)</i><br />
</p>
<p class="verse">
<i>dfs(v)</i><br />
<i>//</i> visits recursively all the unvisited vertices connected to vertex <i>v</i><br />
<i>//</i> by a path and numbers them in the order they are encountered<br />
<i>count ← count + 1</i>; mark <i>v</i> with <i>count</i><br />
<b>for</b> each vertex <i>w</i> in <i>V</i> adjacent to <i>v</i> <b>do</b><br />
    <b>if</b> <i>w</i> is marked with 0<br />
        <i>dfs(w)</i><br />
</p>
</div>
</div>
<div id="outline-container-org6f10792" class="outline-2">
<h2 id="org6f10792">Breadth-First</h2>
<div class="outline-text-2" id="text-org6f10792">
<p class="verse">
<b>ALGORITHM</b> <i>BFS(G)</i><br />
<i>//</i> Implements a breadth-first search traversal of a given graph<br />
<i>//</i> Input: Graph <i>G = <V,E></i><br />
<i>//</i> Output: Graph <i>G</i> with its vertices marked with consecutive integers<br />
<i>//</i> in the order they are visited by the BFS traversal.<br />
mark each vertex in <i>V</i> with 0 as a mark of being "unvisited"<br />
<i>count ← 0</i><br />
<b>for</b> each vertex <i>v</i> in <i>V</i> <b>do</b><br />
    <b>if</b> <i>v</i> is marked with 0<br />
        <i>bfs(v)</i><br />
</p>
<p class="verse">
<i>bfs(v)</i><br />
<i>//</i> visits all the unvisited vertices connected to vertex <i>v</i><br />
<i>//</i> by a path and numbers them in the order they are visited<br />
<i>count ← count + 1</i>; mark <i>v</i> with <i>count</i> and initialize a queue with <i>v</i><br />
<b>while</b> the queue is not empty <b>do</b><br />
    <b>for</b> each vertex <i>w</i> in <i>V</i> adjacent to the front vertex <b>do</b><br />
        <b>if</b> <i>w</i> is marked with 0<br />
            <i>count ← count + 1</i>; mark <i>v</i> with <i>count</i><br />
            add <i>w</i> to the queue<br />
    remove the front vertex from the queue<br />
</p>
</div>
</div>
<div id="outline-container-orgf60751c" class="outline-2">
<h2 id="orgf60751c">Practice</h2>
<div class="outline-text-2" id="text-orgf60751c">
<p>
<a href="https://firstthreeodds.org/img/eleven-node-seventeen-edge-graph.png">Eleven Node Seventeen Edge Graph</a>
</p>
</div>
</div>
</div>
<div id="postamble" class="status">
<p class="author">Author: Rick Neff</p>
<p class="date">Created: 2017-11-07 Tue 12:29</p>
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
</div>
</body>
</html>