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<p><a href="https://en.wikipedia.org/wiki/Disjoint_union">Disjoint union</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;set&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for connected_components_with_dsu.cpp:</div>
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<tr class="memdesc:df/dce/namespacegraph"><td class="mdescLeft">&#160;</td><td class="mdescRight"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms. <br /></td></tr>
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<tr class="memitem:de/db4/namespacedisjoint__union"><td class="memItemLeft" align="right" valign="top"> &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/db4/namespacedisjoint__union.html">disjoint_union</a></td></tr>
<tr class="memdesc:de/db4/namespacedisjoint__union"><td class="mdescLeft">&#160;</td><td class="mdescRight">Functions for <a href="https://en.wikipedia.org/wiki/Disjoint_union">Disjoint union</a> implementation. <br /></td></tr>
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Functions</h2></td></tr>
<tr class="memitem:ae91ed94113c56191b75fe45f688d6e62"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d99/connected__components__with__dsu_8cpp.html#ae91ed94113c56191b75fe45f688d6e62">graph::disjoint_union::make_set</a> ()</td></tr>
<tr class="memdesc:ae91ed94113c56191b75fe45f688d6e62"><td class="mdescLeft">&#160;</td><td class="mdescRight">function the initialize every node as it's own parent <a href="../../d8/d99/connected__components__with__dsu_8cpp.html#ae91ed94113c56191b75fe45f688d6e62">More...</a><br /></td></tr>
<tr class="separator:ae91ed94113c56191b75fe45f688d6e62"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a469384d8a4197a9b24482ce7c321a85e"><td class="memItemLeft" align="right" valign="top">int64_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">graph::disjoint_union::find_set</a> (int64_t val)</td></tr>
<tr class="memdesc:a469384d8a4197a9b24482ce7c321a85e"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find the component where following node belongs to. <a href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">More...</a><br /></td></tr>
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<tr class="memitem:a67cb7472f310a798f555fe45cdf50145"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d99/connected__components__with__dsu_8cpp.html#a67cb7472f310a798f555fe45cdf50145">graph::disjoint_union::union_sets</a> (int64_t node1, int64_t node2)</td></tr>
<tr class="memdesc:a67cb7472f310a798f555fe45cdf50145"><td class="mdescLeft">&#160;</td><td class="mdescRight">Merge 2 components to become one. <a href="../../d8/d99/connected__components__with__dsu_8cpp.html#a67cb7472f310a798f555fe45cdf50145">More...</a><br /></td></tr>
<tr class="separator:a67cb7472f310a798f555fe45cdf50145"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ac2d6698b71384a352ec4b81b31b13141"><td class="memItemLeft" align="right" valign="top">uint32_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d99/connected__components__with__dsu_8cpp.html#ac2d6698b71384a352ec4b81b31b13141">graph::disjoint_union::no_of_connected_components</a> ()</td></tr>
<tr class="memdesc:ac2d6698b71384a352ec4b81b31b13141"><td class="mdescLeft">&#160;</td><td class="mdescRight">Find total no. of connected components. <a href="../../d8/d99/connected__components__with__dsu_8cpp.html#ac2d6698b71384a352ec4b81b31b13141">More...</a><br /></td></tr>
<tr class="separator:ac2d6698b71384a352ec4b81b31b13141"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d99/connected__components__with__dsu_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Test Implementations. <a href="../../d8/d99/connected__components__with__dsu_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">More...</a><br /></td></tr>
<tr class="separator:aa8dca7b867074164d5f45b0f3851269d"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d99/connected__components__with__dsu_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <a href="../../d8/d99/connected__components__with__dsu_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">More...</a><br /></td></tr>
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Variables</h2></td></tr>
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uint32_t&#160;</td><td class="memItemRight" valign="bottom"><b>graph::disjoint_union::number_of_nodes</b> = 0</td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; int64_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>graph::disjoint_union::parent</b> {}</td></tr>
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<tr class="memitem:af675d8149b6a82cb7fa07f39210b8a2b"><td class="memItemLeft" align="right" valign="top"><a id="af675d8149b6a82cb7fa07f39210b8a2b"></a>
<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>&lt; uint32_t &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>graph::disjoint_union::connected_set_size</b> {}</td></tr>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
<div class="textblock"><p><a href="https://en.wikipedia.org/wiki/Disjoint_union">Disjoint union</a> </p>
<p>The Disjoint union is the technique to find connected component in graph efficiently.</p>
<h3><a class="anchor" id="autotoc_md57"></a>
Algorithm</h3>
<p>In <a class="el" href="../../da/d9a/class_graph.html">Graph</a>, if you have to find out the number of connected components, there are 2 options</p><ol type="1">
<li>Depth first search</li>
<li>Disjoint union 1st option is inefficient, Disjoint union is the most optimal way to find this.</li>
</ol>
<dl class="section author"><dt>Author</dt><dd>Unknown author </dd>
<dd>
<a href="https://github.com/sagarpandyansit">Sagar Pandya</a> </dd></dl>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a469384d8a4197a9b24482ce7c321a85e"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a469384d8a4197a9b24482ce7c321a85e">&#9670;&nbsp;</a></span>find_set()</h2>
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<td class="memname">int64_t graph::disjoint_union::find_set </td>
<td>(</td>
<td class="paramtype">int64_t&#160;</td>
<td class="paramname"><em>val</em></td><td>)</td>
<td></td>
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<p>Find the component where following node belongs to. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">val</td><td>parent of val should be found </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>parent of val </dd></dl>
<div class="fragment"><div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160; <span class="keywordflow">while</span> (parent[val] != val) {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; parent[val] = parent[parent[val]];</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160; val = parent[val];</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; }</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; <span class="keywordflow">return</span> val;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&nbsp;</a></span>main()</h2>
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<td class="memname">int main </td>
<td>(</td>
<td class="paramtype">void&#160;</td>
<td class="paramname"></td><td>)</td>
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<p>Main function. </p>
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
<div class="fragment"><div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; {</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; <a class="code" href="../../d8/d99/connected__components__with__dsu_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Execute the tests</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160;}</div>
<div class="ttc" id="aconnected__components__with__dsu_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d8/d99/connected__components__with__dsu_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Test Implementations.</div><div class="ttdef"><b>Definition:</b> connected_components_with_dsu.cpp:92</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae91ed94113c56191b75fe45f688d6e62">&#9670;&nbsp;</a></span>make_set()</h2>
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<td class="memname">void graph::disjoint_union::make_set </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
<td></td>
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<p>function the initialize every node as it's own parent </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; {</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; <span class="keywordflow">for</span> (uint32_t i = 1; i &lt;= number_of_nodes; i++) {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; parent[i] = i;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; connected_set_size[i] = 1;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; }</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ac2d6698b71384a352ec4b81b31b13141">&#9670;&nbsp;</a></span>no_of_connected_components()</h2>
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<td class="memname">uint32_t graph::disjoint_union::no_of_connected_components </td>
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<td class="paramname"></td><td>)</td>
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<p>Find total no. of connected components. </p>
<dl class="section return"><dt>Returns</dt><dd>Number of connected components </dd></dl>
<div class="fragment"><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; {</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/set.html">std::set&lt;int64_t&gt;</a> temp; <span class="comment">// temp set to count number of connected components</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="keywordflow">for</span> (uint32_t i = 1; i &lt;= number_of_nodes; i++) temp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/set/insert.html">insert</a>(<a class="code" href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">find_set</a>(i));</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keywordflow">return</span> temp.<a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/set/size.html">size</a>(); <span class="comment">// return the size of temp set</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160;}</div>
<div class="ttc" id="aconnected__components__with__dsu_8cpp_html_a469384d8a4197a9b24482ce7c321a85e"><div class="ttname"><a href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">graph::disjoint_union::find_set</a></div><div class="ttdeci">int64_t find_set(int64_t val)</div><div class="ttdoc">Find the component where following node belongs to.</div><div class="ttdef"><b>Definition:</b> connected_components_with_dsu.cpp:49</div></div>
<div class="ttc" id="ainsert_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/set/insert.html">std::set::insert</a></div><div class="ttdeci">T insert(T... args)</div></div>
<div class="ttc" id="aset_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/set.html">std::set</a></div></div>
<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/set/size.html">std::set::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&nbsp;</a></span>test()</h2>
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<td class="memname">static void test </td>
<td>(</td>
<td class="paramname"></td><td>)</td>
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<p>Test Implementations. </p>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; {</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="keyword">namespace </span>dsu = graph::disjoint_union;</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; dsu::number_of_nodes;</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; dsu::parent.resize(dsu::number_of_nodes + 1);</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; dsu::connected_set_size.resize(dsu::number_of_nodes + 1);</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; dsu::make_set();</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; uint32_t edges = 0;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; edges; <span class="comment">// no of edges in the graph</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="keywordflow">while</span> (edges--) {</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; int64_t node_a = 0, node_b = 0;</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a> &gt;&gt; node_a &gt;&gt; node_b;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; dsu::union_sets(node_a, node_b);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; }</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> &lt;&lt; dsu::no_of_connected_components() &lt;&lt; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;}</div>
<div class="ttc" id="abasic_istream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_istream.html">std::cin</a></div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a67cb7472f310a798f555fe45cdf50145">&#9670;&nbsp;</a></span>union_sets()</h2>
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<td class="memname">void graph::disjoint_union::union_sets </td>
<td>(</td>
<td class="paramtype">int64_t&#160;</td>
<td class="paramname"><em>node1</em>, </td>
</tr>
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<td class="paramkey"></td>
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<td class="paramtype">int64_t&#160;</td>
<td class="paramname"><em>node2</em>&#160;</td>
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<td></td>
<td>)</td>
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<p>Merge 2 components to become one. </p>
<dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">node1</td><td>1st component </td></tr>
<tr><td class="paramname">node2</td><td>2nd component </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
<div class="fragment"><div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; node1 = <a class="code" href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">find_set</a>(node1); <span class="comment">// find the parent of node1</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; node2 = <a class="code" href="../../d8/d99/connected__components__with__dsu_8cpp.html#a469384d8a4197a9b24482ce7c321a85e">find_set</a>(node2); <span class="comment">// find the parent of node2</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="comment">// If parents of both nodes are not same, combine them</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordflow">if</span> (node1 != node2) {</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">if</span> (connected_set_size[node1] &lt; connected_set_size[node2]) {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/algorithm/swap.html">std::swap</a>(node1, node2); <span class="comment">// swap both components</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; }</div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; parent[node2] = node1; <span class="comment">// make node1 as parent of node2.</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; connected_set_size[node1] +=</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; connected_set_size[node2]; <span class="comment">// sum the size of both as they combined</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; }</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160;}</div>
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