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<div class="headertitle"><div class="title">dsu_path_compression.cpp</div></div>
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<div class="contents">
<a href="../../d3/dae/dsu__path__compression_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span> </div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="preprocessor">#include &lt;cassert&gt;</span> </div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="preprocessor">#include &lt;cstdint&gt;</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="preprocessor">#include &lt;iostream&gt;</span> </div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="preprocessor">#include &lt;vector&gt;</span> </div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="keyword">using </span>std::cout;</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="keyword">using </span>std::endl;</div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keyword">using </span>std::vector;</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="foldopen" id="foldopen00034" data-start="{" data-end="};">
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html"> 34</a></span><span class="keyword">class </span><a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> {</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keyword">private</span>:</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb"> 36</a></span> vector&lt;uint64_t&gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>; </div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429"> 37</a></span> vector&lt;uint64_t&gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>; </div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55"> 38</a></span> vector&lt;uint64_t&gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>; </div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53"> 39</a></span> vector&lt;uint64_t&gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>; </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63"> 40</a></span> vector&lt;uint64_t&gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>; </div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> <span class="keyword">public</span>:</div>
<div class="foldopen" id="foldopen00046" data-start="{" data-end="}">
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72"> 46</a></span> <span class="keyword">explicit</span> <a class="code hl_function" href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72">dsu</a>(uint64_t n) {</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>.assign(n, 0);</div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] = i;</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> }</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>.assign(n, 0);</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>.assign(n, 0);</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>.assign(n, 0);</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[i] = 0;</div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>[i] = i;</div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>[i] = i;</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> }</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>.assign(n, 0);</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; n; i++) {</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[i] = 1;</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> }</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> }</div>
</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="foldopen" id="foldopen00074" data-start="{" data-end="}">
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c"> 74</a></span> uint64_t <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(uint64_t i) {</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] == i) {</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">return</span> i;</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordflow">return</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i] = <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[i]));</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> }</div>
</div>
<div class="foldopen" id="foldopen00088" data-start="{" data-end="}">
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559"> 88</a></span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559">UnionSet</a>(uint64_t i, uint64_t j) {</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">isSame</a>(i, j)) {</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordflow">return</span>;</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> }</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="comment">// we find the representative of the i and j</span></div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> uint64_t x = <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i);</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> uint64_t y = <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(j);</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[x] &gt; <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[y]) {</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> std::swap(x, y);</div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> }</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">p</a>[x] = y;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[x] == <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[y]) {</div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">depth</a>[y]++;</div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> }</div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[y] += <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[x];</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>[y] = std::max(<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>[x], <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>[y]);</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>[y] = std::min(<a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>[x], <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>[y]);</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> }</div>
</div>
<div class="foldopen" id="foldopen00124" data-start="{" data-end="}">
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303"> 124</a></span> <span class="keywordtype">bool</span> <a class="code hl_function" href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">isSame</a>(uint64_t i, uint64_t j) {</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keywordflow">if</span> (<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i) == <a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(j)) {</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> }</div>
</div>
<div class="foldopen" id="foldopen00136" data-start="{" data-end="}">
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a0ce2672c570f4235eafddb0c9a58115a"> 136</a></span> vector&lt;uint64_t&gt; <a class="code hl_function" href="../../dd/d1f/classdsu.html#a0ce2672c570f4235eafddb0c9a58115a">get</a>(uint64_t i) {</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> vector&lt;uint64_t&gt; ans;</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> ans.push_back(<a class="code hl_function" href="../../dd/d1f/classdsu.html#ac713a5b496d0405c82e2808a85e58415">get_min</a>(i));</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> ans.push_back(<a class="code hl_function" href="../../dd/d1f/classdsu.html#a696141b8b092466767f4bfe1c5e46cde">get_max</a>(i));</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> ans.push_back(<a class="code hl_function" href="../../dd/d1f/classdsu.html#a1c24228b0f2f49220133fb8c3566a55c">size</a>(i));</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordflow">return</span> ans;</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> }</div>
</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a1c24228b0f2f49220133fb8c3566a55c"> 149</a></span> uint64_t <a class="code hl_function" href="../../dd/d1f/classdsu.html#a1c24228b0f2f49220133fb8c3566a55c">size</a>(uint64_t i) { <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">setSize</a>[<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i)]; }</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#a696141b8b092466767f4bfe1c5e46cde"> 156</a></span> uint64_t <a class="code hl_function" href="../../dd/d1f/classdsu.html#a696141b8b092466767f4bfe1c5e46cde">get_max</a>(uint64_t i) { <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">maxElement</a>[<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i)]; }</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"><a class="line" href="../../dd/d1f/classdsu.html#ac713a5b496d0405c82e2808a85e58415"> 163</a></span> uint64_t <a class="code hl_function" href="../../dd/d1f/classdsu.html#ac713a5b496d0405c82e2808a85e58415">get_min</a>(uint64_t i) { <span class="keywordflow">return</span> <a class="code hl_variable" href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">minElement</a>[<a class="code hl_function" href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">findSet</a>(i)]; }</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span>};</div>
</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> </div>
<div class="foldopen" id="foldopen00170" data-start="{" data-end="}">
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"><a class="line" href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243"> 170</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>() {</div>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="comment">// the minimum, maximum, and size of the set</span></div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> uint64_t n = 10; </div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); </div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="comment">// set 1</span></div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559">UnionSet</a>(1, 2); <span class="comment">// performs union operation on 1 and 2</span></div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559">UnionSet</a>(1, 4); <span class="comment">// performs union operation on 1 and 4</span></div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> vector&lt;uint64_t&gt; ans = {1, 4, 3};</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; ans.size(); i++) {</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> assert(d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a0ce2672c570f4235eafddb0c9a58115a">get</a>(4).at(i) == ans[i]); <span class="comment">// makes sure algorithm works fine</span></div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> }</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> cout &lt;&lt; <span class="stringliteral">&quot;1st test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span>}</div>
</div>
<div class="foldopen" id="foldopen00187" data-start="{" data-end="}">
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"><a class="line" href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae"> 187</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>() {</div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <span class="comment">// the minimum, maximum, and size of the set</span></div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> uint64_t n = 10; </div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); </div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="comment">// set 1</span></div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559">UnionSet</a>(3, 5);</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559">UnionSet</a>(5, 6);</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559">UnionSet</a>(5, 7);</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> vector&lt;uint64_t&gt; ans = {3, 7, 4};</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> <span class="keywordflow">for</span> (uint64_t i = 0; i &lt; ans.size(); i++) {</div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> assert(d.<a class="code hl_function" href="../../dd/d1f/classdsu.html#a0ce2672c570f4235eafddb0c9a58115a">get</a>(3).at(i) == ans[i]); <span class="comment">// makes sure algorithm works fine</span></div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> }</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> cout &lt;&lt; <span class="stringliteral">&quot;2nd test passed!&quot;</span> &lt;&lt; <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span>}</div>
</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> </div>
<div class="foldopen" id="foldopen00206" data-start="{" data-end="}">
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"><a class="line" href="../../d3/dae/dsu__path__compression_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 206</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> uint64_t n = 10; </div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <a class="code hl_class" href="../../dd/d1f/classdsu.html">dsu</a> d(n + 1); </div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> </div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a>(); <span class="comment">// run 1st test case</span></div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> <a class="code hl_function" href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a>(); <span class="comment">// run 2nd test case</span></div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> </div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span>}</div>
</div>
<div class="ttc" id="aclassdsu_html"><div class="ttname"><a href="../../dd/d1f/classdsu.html">dsu</a></div><div class="ttdoc">Disjoint sets union data structure, class based representation.</div><div class="ttdef"><b>Definition</b> <a href="#l00034">dsu_path_compression.cpp:34</a></div></div>
<div class="ttc" id="aclassdsu_html_a0ce2672c570f4235eafddb0c9a58115a"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a0ce2672c570f4235eafddb0c9a58115a">dsu::get</a></div><div class="ttdeci">vector&lt; uint64_t &gt; get(uint64_t i)</div><div class="ttdoc">prints the minimum, maximum and size of the set to which i belongs to</div><div class="ttdef"><b>Definition</b> <a href="#l00136">dsu_path_compression.cpp:136</a></div></div>
<div class="ttc" id="aclassdsu_html_a126e3002a464e53cd54b07ba56482a72"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a126e3002a464e53cd54b07ba56482a72">dsu::dsu</a></div><div class="ttdeci">dsu(uint64_t n)</div><div class="ttdoc">contructor for initialising all data members.</div><div class="ttdef"><b>Definition</b> <a href="#l00046">dsu_path_compression.cpp:46</a></div></div>
<div class="ttc" id="aclassdsu_html_a16851f78fe390fc1430905c83d6a2f1c"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a16851f78fe390fc1430905c83d6a2f1c">dsu::findSet</a></div><div class="ttdeci">uint64_t findSet(uint64_t i)</div><div class="ttdoc">Method to find the representative of the set to which i belongs to, T(n) = O(1)</div><div class="ttdef"><b>Definition</b> <a href="#l00074">dsu_path_compression.cpp:74</a></div></div>
<div class="ttc" id="aclassdsu_html_a1c24228b0f2f49220133fb8c3566a55c"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a1c24228b0f2f49220133fb8c3566a55c">dsu::size</a></div><div class="ttdeci">uint64_t size(uint64_t i)</div><div class="ttdoc">A utility function that returns the size of the set to which i belongs to.</div><div class="ttdef"><b>Definition</b> <a href="#l00149">dsu_path_compression.cpp:149</a></div></div>
<div class="ttc" id="aclassdsu_html_a1d77aad7fc39fe7140d834cd347e5c63"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a1d77aad7fc39fe7140d834cd347e5c63">dsu::minElement</a></div><div class="ttdeci">vector&lt; uint64_t &gt; minElement</div><div class="ttdoc">minimum of each set to which i belongs to</div><div class="ttdef"><b>Definition</b> <a href="#l00040">dsu_path_compression.cpp:40</a></div></div>
<div class="ttc" id="aclassdsu_html_a1ef0b0462a0dda63514f641cbb7dd8cb"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a1ef0b0462a0dda63514f641cbb7dd8cb">dsu::p</a></div><div class="ttdeci">vector&lt; uint64_t &gt; p</div><div class="ttdoc">keeps track of the parent of ith element</div><div class="ttdef"><b>Definition</b> <a href="#l00036">dsu_path_compression.cpp:36</a></div></div>
<div class="ttc" id="aclassdsu_html_a4ade6f16c418fc98b54452f7b0252a53"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a4ade6f16c418fc98b54452f7b0252a53">dsu::maxElement</a></div><div class="ttdeci">vector&lt; uint64_t &gt; maxElement</div><div class="ttdoc">maximum of each set to which i belongs to</div><div class="ttdef"><b>Definition</b> <a href="#l00039">dsu_path_compression.cpp:39</a></div></div>
<div class="ttc" id="aclassdsu_html_a4bf54d33fba178998dbbe4c57f2e9429"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a4bf54d33fba178998dbbe4c57f2e9429">dsu::depth</a></div><div class="ttdeci">vector&lt; uint64_t &gt; depth</div><div class="ttdoc">tracks the depth(rank) of i in the tree</div><div class="ttdef"><b>Definition</b> <a href="#l00037">dsu_path_compression.cpp:37</a></div></div>
<div class="ttc" id="aclassdsu_html_a64d25c5986742f7c234ed449b2ff7303"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a64d25c5986742f7c234ed449b2ff7303">dsu::isSame</a></div><div class="ttdeci">bool isSame(uint64_t i, uint64_t j)</div><div class="ttdoc">A utility function which check whether i and j belongs to same set or not.</div><div class="ttdef"><b>Definition</b> <a href="#l00124">dsu_path_compression.cpp:124</a></div></div>
<div class="ttc" id="aclassdsu_html_a696141b8b092466767f4bfe1c5e46cde"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a696141b8b092466767f4bfe1c5e46cde">dsu::get_max</a></div><div class="ttdeci">uint64_t get_max(uint64_t i)</div><div class="ttdoc">A utility function that returns the max element of the set to which i belongs to.</div><div class="ttdef"><b>Definition</b> <a href="#l00156">dsu_path_compression.cpp:156</a></div></div>
<div class="ttc" id="aclassdsu_html_a6ac30c07abca2aaa3b291504c25c3559"><div class="ttname"><a href="../../dd/d1f/classdsu.html#a6ac30c07abca2aaa3b291504c25c3559">dsu::UnionSet</a></div><div class="ttdeci">void UnionSet(uint64_t i, uint64_t j)</div><div class="ttdoc">Method that combines two disjoint sets to which i and j belongs to and make a single set having a com...</div><div class="ttdef"><b>Definition</b> <a href="#l00088">dsu_path_compression.cpp:88</a></div></div>
<div class="ttc" id="aclassdsu_html_ac0dc3e17e49fe19b159b4ea4096d7b55"><div class="ttname"><a href="../../dd/d1f/classdsu.html#ac0dc3e17e49fe19b159b4ea4096d7b55">dsu::setSize</a></div><div class="ttdeci">vector&lt; uint64_t &gt; setSize</div><div class="ttdoc">size of each chunk(set)</div><div class="ttdef"><b>Definition</b> <a href="#l00038">dsu_path_compression.cpp:38</a></div></div>
<div class="ttc" id="aclassdsu_html_ac713a5b496d0405c82e2808a85e58415"><div class="ttname"><a href="../../dd/d1f/classdsu.html#ac713a5b496d0405c82e2808a85e58415">dsu::get_min</a></div><div class="ttdeci">uint64_t get_min(uint64_t i)</div><div class="ttdoc">A utility function that returns the min element of the set to which i belongs to.</div><div class="ttdef"><b>Definition</b> <a href="#l00163">dsu_path_compression.cpp:163</a></div></div>
<div class="ttc" id="adsu__path__compression_8cpp_html_a45d94ead4cf4e1ff9f87c38bc99f59ae"><div class="ttname"><a href="../../d3/dae/dsu__path__compression_8cpp.html#a45d94ead4cf4e1ff9f87c38bc99f59ae">test2</a></div><div class="ttdeci">static void test2()</div><div class="ttdoc">Self-implementations, 2nd test.</div><div class="ttdef"><b>Definition</b> <a href="#l00187">dsu_path_compression.cpp:187</a></div></div>
<div class="ttc" id="adsu__path__compression_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d3/dae/dsu__path__compression_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="#l00206">dsu_path_compression.cpp:206</a></div></div>
<div class="ttc" id="adsu__path__compression_8cpp_html_ae7880ce913f3058a35ff106d5be9e243"><div class="ttname"><a href="../../d3/dae/dsu__path__compression_8cpp.html#ae7880ce913f3058a35ff106d5be9e243">test1</a></div><div class="ttdeci">static void test1()</div><div class="ttdoc">Self-test implementations, 1st test.</div><div class="ttdef"><b>Definition</b> <a href="#l00170">dsu_path_compression.cpp:170</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> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00036">matrix_exponentiation.cpp:36</a></div></div>
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