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<p><a href="https://en.wikipedia.org/wiki/Disjoint-set_data_structure">Disjoint Sets Data Structure (Disjoint Sets)</a>
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;vector&gt;</code><br />
</div><div class="textblock"><div class="dynheader">
Include dependency graph for disjoint_set.cpp:</div>
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Functions</h2></td></tr>
<tr class="memitem:a010965fc5f16cca5a62506afab24e4ec"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d23/disjoint__set_8cpp.html#a010965fc5f16cca5a62506afab24e4ec">CreateSet</a> (int n)</td></tr>
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<tr class="memitem:a34b9ead0608e676d9ae5188672427cc8"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a> (int x)</td></tr>
<tr class="separator:a34b9ead0608e676d9ae5188672427cc8"><td class="memSeparator" colspan="2">&#160;</td></tr>
<tr class="memitem:a2fb0a7cd26a477e2d48ba7e0118bc985"><td class="memItemLeft" align="right" valign="top">bool&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d23/disjoint__set_8cpp.html#a2fb0a7cd26a477e2d48ba7e0118bc985">InSameUnion</a> (int x, int y)</td></tr>
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<tr class="memitem:a44481bb75386fbb0f958a388d4b9f757"><td class="memItemLeft" align="right" valign="top">void&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d23/disjoint__set_8cpp.html#a44481bb75386fbb0f958a388d4b9f757">Union</a> (int x, int y)</td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../de/d23/disjoint__set_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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Variables</h2></td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>root</b></td></tr>
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<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector</a>&lt; int &gt;&#160;</td><td class="memItemRight" valign="bottom"><b>rank</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-set_data_structure">Disjoint Sets Data Structure (Disjoint Sets)</a> </p>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/leoyang429">leoyang429</a></dd></dl>
<p>A disjoint set data structure (also called union find or merge find set) is a data structure that tracks a set of elements partitioned into a number of disjoint (non-overlapping) subsets. Some situations where disjoint sets can be used are- to find connected components of a graph, kruskal's algorithm for finding Minimum Spanning Tree etc. There are two operation which we perform on disjoint sets - 1) Union 2) Find </p>
</div><h2 class="groupheader">Function Documentation</h2>
<a id="a010965fc5f16cca5a62506afab24e4ec"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a010965fc5f16cca5a62506afab24e4ec">&#9670;&nbsp;</a></span>CreateSet()</h2>
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<td class="memname">void CreateSet </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>n</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Function to create a set </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">n</td><td>number of element </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>&#160; root = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;int&gt;</a>(n + 1);</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>&#160; rank = <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">vector&lt;int&gt;</a>(n + 1, 1);</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= n; ++i) {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; root[i] = i;</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>
</div><!-- fragment -->
</div>
</div>
<a id="a34b9ead0608e676d9ae5188672427cc8"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a34b9ead0608e676d9ae5188672427cc8">&#9670;&nbsp;</a></span>Find()</h2>
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<td class="memname">int Find </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>x</em></td><td>)</td>
<td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Find operation takes a number x and returns the set to which this number belongs to. </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>element of some set </td></tr>
</table>
</dd>
</dl>
<dl class="section return"><dt>Returns</dt><dd>set to which x belongs to </dd></dl>
<div class="fragment"><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">if</span> (root[x] == x) {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; <span class="keywordflow">return</span> x;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; }</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordflow">return</span> root[x] = <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(root[x]);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;}</div>
</div><!-- fragment -->
</div>
</div>
<a id="a2fb0a7cd26a477e2d48ba7e0118bc985"></a>
<h2 class="memtitle"><span class="permalink"><a href="#a2fb0a7cd26a477e2d48ba7e0118bc985">&#9670;&nbsp;</a></span>InSameUnion()</h2>
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<td class="memname">bool InSameUnion </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>y</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>A utility function to check if x and y are from same set or not </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>element of some set </td></tr>
<tr><td class="paramname">y</td><td>element of some set </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;{ <span class="keywordflow">return</span> <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(x) == <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(y); }</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>
<td></td>
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</div><div class="memdoc">
<p>Main function </p>
<div class="fragment"><div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; {</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="comment">// tests CreateSet &amp; Find</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keywordtype">int</span> n = 100;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a010965fc5f16cca5a62506afab24e4ec">CreateSet</a>(n);</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i &lt;= 100; ++i) {</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; <span class="keywordflow">if</span> (root[i] != i) {</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_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Fail&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; }</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; }</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="comment">// tests InSameUnion &amp; Union</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1 and 2 are initially not in the same subset&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="keywordflow">if</span> (<a class="code" href="../../de/d23/disjoint__set_8cpp.html#a2fb0a7cd26a477e2d48ba7e0118bc985">InSameUnion</a>(1, 2)) {</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Fail&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; }</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a44481bb75386fbb0f958a388d4b9f757">Union</a>(1, 2);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;1 and 2 are now in the same subset&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; <span class="keywordflow">if</span> (!<a class="code" href="../../de/d23/disjoint__set_8cpp.html#a2fb0a7cd26a477e2d48ba7e0118bc985">InSameUnion</a>(1, 2)) {</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <a class="codeRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">cout</a> &lt;&lt; <span class="stringliteral">&quot;Fail&quot;</span> &lt;&lt; <a class="code" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<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; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#a44481bb75386fbb0f958a388d4b9f757">&#9670;&nbsp;</a></span>Union()</h2>
<div class="memitem">
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<td class="memname">void Union </td>
<td>(</td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>x</em>, </td>
</tr>
<tr>
<td class="paramkey"></td>
<td></td>
<td class="paramtype">int&#160;</td>
<td class="paramname"><em>y</em>&#160;</td>
</tr>
<tr>
<td></td>
<td>)</td>
<td></td><td></td>
</tr>
</table>
</div><div class="memdoc">
<p>Union operation combines two disjoint sets to make a single set in this union function we pass two elements and check if they are from different sets then combine those sets </p><dl class="params"><dt>Parameters</dt><dd>
<table class="params">
<tr><td class="paramname">x</td><td>element of some set </td></tr>
<tr><td class="paramname">y</td><td>element of some set </td></tr>
</table>
</dd>
</dl>
<div class="fragment"><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; {</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="keywordtype">int</span> a = <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(x), b = <a class="code" href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a>(y);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordflow">if</span> (a != b) {</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="keywordflow">if</span> (rank[a] &lt; rank[b]) {</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; root[a] = b;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (rank[a] &gt; rank[b]) {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; root[b] = a;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; root[a] = b;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; ++rank[b];</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; }</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; }</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160;}</div>
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<div class="ttc" id="adisjoint__set_8cpp_html_a010965fc5f16cca5a62506afab24e4ec"><div class="ttname"><a href="../../de/d23/disjoint__set_8cpp.html#a010965fc5f16cca5a62506afab24e4ec">CreateSet</a></div><div class="ttdeci">void CreateSet(int n)</div><div class="ttdef"><b>Definition:</b> disjoint_set.cpp:37</div></div>
<div class="ttc" id="avector_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a></div><div class="ttdoc">STL class.</div></div>
<div class="ttc" id="adisjoint__set_8cpp_html_a34b9ead0608e676d9ae5188672427cc8"><div class="ttname"><a href="../../de/d23/disjoint__set_8cpp.html#a34b9ead0608e676d9ae5188672427cc8">Find</a></div><div class="ttdeci">int Find(int x)</div><div class="ttdef"><b>Definition:</b> disjoint_set.cpp:53</div></div>
<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
<div class="ttc" id="amatrix__exponentiation_8cpp_html_a600eaf353befc174637855795f12d258"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a></div><div class="ttdeci">#define endl</div><div class="ttdef"><b>Definition:</b> matrix_exponentiation.cpp:36</div></div>
<div class="ttc" id="adisjoint__set_8cpp_html_a2fb0a7cd26a477e2d48ba7e0118bc985"><div class="ttname"><a href="../../de/d23/disjoint__set_8cpp.html#a2fb0a7cd26a477e2d48ba7e0118bc985">InSameUnion</a></div><div class="ttdeci">bool InSameUnion(int x, int y)</div><div class="ttdef"><b>Definition:</b> disjoint_set.cpp:67</div></div>
<div class="ttc" id="adisjoint__set_8cpp_html_a44481bb75386fbb0f958a388d4b9f757"><div class="ttname"><a href="../../de/d23/disjoint__set_8cpp.html#a44481bb75386fbb0f958a388d4b9f757">Union</a></div><div class="ttdeci">void Union(int x, int y)</div><div class="ttdef"><b>Definition:</b> disjoint_set.cpp:78</div></div>
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