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<div><h1 class="main-title">dfs backedge detection</h1></div>
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<p>When performing a DFS traversal, it can be useful finding backedges, i.e edges to nodes we would have visited, had we not done so already. A simple way of doing this, is to mutate your undirected graph to a directed graph during the DFS traversal.</p>
<div class="highlight"><pre><span></span><span class="linenos"> 1</span><span class="k">class</span> <span class="nc">Graph</span><span class="p">:</span>
<span class="linenos"> 2</span> <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">adjlist</span><span class="p">):</span>
<span class="linenos"> 3</span> <span class="bp">self</span><span class="o">.</span><span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
<span class="linenos"> 4</span> <span class="bp">self</span><span class="o">.</span><span class="n">adjlist</span> <span class="o">=</span> <span class="n">adjlist</span>
<span class="linenos"> 5</span>
<span class="linenos"> 6</span> <span class="k">def</span> <span class="nf">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">parent</span><span class="p">,</span> <span class="n">node</span><span class="p">):</span>
<span class="linenos"> 7</span> <span class="k">if</span> <span class="n">node</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">visited</span><span class="p">:</span>
<span class="linenos"> 8</span> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"backedge: </span><span class="si">{</span><span class="n">parent</span><span class="si">}</span><span class="s2"> -> </span><span class="si">{</span><span class="n">node</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="linenos"> 9</span> <span class="k">return</span>
<span class="linenos">10</span> <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">node</span><span class="si">}</span><span class="s2">"</span><span class="p">)</span>
<span class="linenos">11</span> <span class="bp">self</span><span class="o">.</span><span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<span class="linenos">12</span> <span class="k">for</span> <span class="n">neighbour</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adjlist</span><span class="p">[</span><span class="n">node</span><span class="p">]:</span>
<span class="linenos">13</span> <span class="bp">self</span><span class="o">.</span><span class="n">adjlist</span><span class="p">[</span><span class="n">neighbour</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
<span class="linenos">14</span> <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="n">node</span><span class="p">,</span> <span class="n">neighbour</span><span class="p">)</span>
<span class="linenos">15</span>
<span class="linenos">16</span>
<span class="linenos">17</span><span class="n">g</span> <span class="o">=</span> <span class="p">{}</span>
<span class="linenos">18</span><span class="n">g</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
<span class="linenos">19</span><span class="n">g</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
<span class="linenos">20</span><span class="n">g</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
<span class="linenos">21</span><span class="n">g</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
<span class="linenos">22</span><span class="n">g</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">]</span>
<span class="linenos">23</span><span class="n">g</span><span class="p">[</span><span class="mi">6</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">5</span><span class="p">,</span> <span class="mi">3</span><span class="p">]</span>
<span class="linenos">24</span>
<span class="linenos">25</span>
<span class="linenos">26</span><span class="n">g1</span> <span class="o">=</span> <span class="n">Graph</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
<span class="linenos">27</span><span class="n">g1</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
</pre></div>
<p>At which point, the only nodes that get visited twice during the DFS are via backedges.</p>
<div class="highlight"><pre><span></span><span class="linenos">1</span><span class="mi">1</span>
<span class="linenos">2</span><span class="mi">4</span>
<span class="linenos">3</span><span class="mi">3</span>
<span class="linenos">4</span><span class="mi">5</span>
<span class="linenos">5</span><span class="mi">6</span>
<span class="linenos">6</span><span class="n">backedge</span><span class="p">:</span> <span class="mi">6</span> <span class="o">-></span> <span class="mi">3</span>
<span class="linenos">7</span><span class="mi">2</span>
<span class="linenos">8</span><span class="n">backedge</span><span class="p">:</span> <span class="mi">2</span> <span class="o">-></span> <span class="mi">1</span>
</pre></div>
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