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<a href="connected__components_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">// Copyright 2010-2018 Google LLC</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment">// Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment">// you may not use this file except in compliance with the License.</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment">// You may obtain a copy of the License at</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160;<span class="comment">// distributed under the License is distributed on an &quot;AS IS&quot; BASIS,</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>&#160;<span class="comment">// See the License for the specific language governing permissions and</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160;<span class="comment">// limitations under the License.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;<span class="comment">// Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;<span class="comment">// you may not use this file except in compliance with the License.</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;<span class="comment">// You may obtain a copy of the License at</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160;<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160;<span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160;<span class="comment">// distributed under the License is distributed on an &quot;AS IS&quot; BASIS,</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160;<span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160;<span class="comment">// See the License for the specific language governing permissions and</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160;<span class="comment">// limitations under the License.</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160; </div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;<span class="comment">// The following uses disjoint-sets algorithms, see:</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160;<span class="comment">// https://en.wikipedia.org/wiki/Disjoint-set_data_structure#Disjoint-set_forests</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="connected__components_8h.html">ortools/graph/connected_components.h</a>&quot;</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160; </div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160;<span class="preprocessor">#include &lt;numeric&gt;</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160; </div>
<div class="line"><a name="l00034"></a><span class="lineno"><a class="line" href="classDenseConnectedComponentsFinder.html#ad8e718920ab9683d39af650d714cffe1"> 34</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classDenseConnectedComponentsFinder.html#ad8e718920ab9683d39af650d714cffe1">DenseConnectedComponentsFinder::SetNumberOfNodes</a>(<span class="keywordtype">int</span> num_nodes) {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> old_num_nodes = <a class="code" href="classDenseConnectedComponentsFinder.html#aeeb8b88902830cab41c69ef944b5694f">GetNumberOfNodes</a>();</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>&#160; <span class="keywordflow">if</span> (num_nodes == old_num_nodes) {</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>&#160; <span class="keywordflow">return</span>;</div>
<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; CHECK_GT(num_nodes, old_num_nodes);</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>&#160; <span class="comment">// Each new node starts as an isolated component:</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>&#160; <span class="comment">// It has itself as root.</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>&#160; parent_.resize(num_nodes);</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; std::iota(parent_.begin() + old_num_nodes, parent_.end(), old_num_nodes);</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="comment">// It&#39;s in an isolated component of size 1.</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; component_size_.resize(num_nodes, 1);</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160; <span class="comment">// Its rank is 0.</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160; rank_.resize(num_nodes);</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160; <span class="comment">// This introduces one extra component per added node.</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160; num_components_ += num_nodes - old_num_nodes;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160;}</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160; </div>
<div class="line"><a name="l00052"></a><span class="lineno"><a class="line" href="classDenseConnectedComponentsFinder.html#a5484947d25c2901c60d02ea14d0e1a06"> 52</a></span>&#160;<span class="keywordtype">int</span> <a class="code" href="classDenseConnectedComponentsFinder.html#a5484947d25c2901c60d02ea14d0e1a06">DenseConnectedComponentsFinder::FindRoot</a>(<span class="keywordtype">int</span> node) {</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160; DCHECK_GE(node, 0);</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160; DCHECK_LT(node, <a class="code" href="classDenseConnectedComponentsFinder.html#aeeb8b88902830cab41c69ef944b5694f">GetNumberOfNodes</a>());</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160; </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160; <span class="comment">// Search the root.</span></div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; <span class="keywordtype">int</span> root = parent_[node];</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160; <span class="keywordflow">while</span> (parent_[root] != root) {</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160; root = parent_[root];</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; }</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160; </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160; <span class="comment">// Apply path compression.</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keywordflow">while</span> (node != root) {</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> prev_parent = parent_[node];</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; parent_[node] = root;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; node = prev_parent;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keywordflow">return</span> root;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160;}</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"><a class="line" href="classDenseConnectedComponentsFinder.html#a3bd75ea47488e500083fd8401d833f5d"> 71</a></span>&#160;<span class="keywordtype">void</span> <a class="code" href="classDenseConnectedComponentsFinder.html#a3bd75ea47488e500083fd8401d833f5d">DenseConnectedComponentsFinder::AddEdge</a>(<span class="keywordtype">int</span> node1, <span class="keywordtype">int</span> node2) {</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="comment">// Grow if needed.</span></div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> min_num_nodes = <a class="code" href="alldiff__cst_8cc.html#a9d0c202d5fdd62f4fa2c613339ff168a">std::max</a>(node1, node2) + 1;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; <span class="keywordflow">if</span> (min_num_nodes &gt; <a class="code" href="classDenseConnectedComponentsFinder.html#aeeb8b88902830cab41c69ef944b5694f">GetNumberOfNodes</a>()) {</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; <a class="code" href="classDenseConnectedComponentsFinder.html#ad8e718920ab9683d39af650d714cffe1">SetNumberOfNodes</a>(min_num_nodes);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; }</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; </div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="comment">// Just union the sets for node1 and node2.</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; <span class="keywordtype">int</span> root1 = <a class="code" href="classDenseConnectedComponentsFinder.html#a5484947d25c2901c60d02ea14d0e1a06">FindRoot</a>(node1);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; <span class="keywordtype">int</span> root2 = <a class="code" href="classDenseConnectedComponentsFinder.html#a5484947d25c2901c60d02ea14d0e1a06">FindRoot</a>(node2);</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; </div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; <span class="comment">// Already the same set.</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keywordflow">if</span> (root1 == root2) {</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; }</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; DCHECK_GE(num_components_, 2);</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; --num_components_;</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; <span class="keyword">const</span> <span class="keywordtype">int</span> component_size = component_size_[root1] + component_size_[root2];</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; <span class="comment">// Attach the shallowest tree to root of the deepest one. Note that this</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160; <span class="comment">// operation grows the rank of the new common root by at most one (if the two</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="comment">// trees originally have the same rank).</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; <span class="keywordflow">if</span> (rank_[root1] &gt; rank_[root2]) {</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; parent_[root2] = root1;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; component_size_[root1] = component_size;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; parent_[root1] = root2;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; component_size_[root2] = component_size;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; <span class="comment">// If the ranks were the same then attaching just grew the rank by one.</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; <span class="keywordflow">if</span> (rank_[root1] == rank_[root2]) {</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; ++rank_[root2];</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; }</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;}</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"><a class="line" href="classDenseConnectedComponentsFinder.html#a962b54327591b21cc0a9273f78906a8b"> 108</a></span>&#160;<span class="keywordtype">bool</span> <a class="code" href="classDenseConnectedComponentsFinder.html#a962b54327591b21cc0a9273f78906a8b">DenseConnectedComponentsFinder::Connected</a>(<span class="keywordtype">int</span> node1, <span class="keywordtype">int</span> node2) {</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; <span class="keywordflow">if</span> (node1 &lt; 0 || node1 &gt;= <a class="code" href="classDenseConnectedComponentsFinder.html#aeeb8b88902830cab41c69ef944b5694f">GetNumberOfNodes</a>() || node2 &lt; 0 ||</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; node2 &gt;= <a class="code" href="classDenseConnectedComponentsFinder.html#aeeb8b88902830cab41c69ef944b5694f">GetNumberOfNodes</a>()) {</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; <span class="keywordflow">return</span> <span class="keyword">false</span>;</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> <a class="code" href="classDenseConnectedComponentsFinder.html#a5484947d25c2901c60d02ea14d0e1a06">FindRoot</a>(node1) == <a class="code" href="classDenseConnectedComponentsFinder.html#a5484947d25c2901c60d02ea14d0e1a06">FindRoot</a>(node2);</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160;}</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; </div>
<div class="line"><a name="l00116"></a><span class="lineno"><a class="line" href="classDenseConnectedComponentsFinder.html#af783278e17675394e30c3de598b11169"> 116</a></span>&#160;<span class="keywordtype">int</span> <a class="code" href="classDenseConnectedComponentsFinder.html#af783278e17675394e30c3de598b11169">DenseConnectedComponentsFinder::GetSize</a>(<span class="keywordtype">int</span> node) {</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="keywordflow">if</span> (node &lt; 0 || node &gt;= <a class="code" href="classDenseConnectedComponentsFinder.html#aeeb8b88902830cab41c69ef944b5694f">GetNumberOfNodes</a>()) {</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; }</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; <span class="keywordflow">return</span> component_size_[<a class="code" href="classDenseConnectedComponentsFinder.html#a5484947d25c2901c60d02ea14d0e1a06">FindRoot</a>(node)];</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160;}</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; </div>
<div class="line"><a name="l00123"></a><span class="lineno"><a class="line" href="classDenseConnectedComponentsFinder.html#a74aadb96adc6f37110393d5fbd2279c5"> 123</a></span>&#160;std::vector&lt;int&gt; <a class="code" href="classDenseConnectedComponentsFinder.html#a74aadb96adc6f37110393d5fbd2279c5">DenseConnectedComponentsFinder::GetComponentIds</a>() {</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; std::vector&lt;int&gt; component_ids(<a class="code" href="classDenseConnectedComponentsFinder.html#aeeb8b88902830cab41c69ef944b5694f">GetNumberOfNodes</a>(), -1);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; <span class="keywordtype">int</span> current_component = 0;</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> node = 0; node &lt; <a class="code" href="classDenseConnectedComponentsFinder.html#aeeb8b88902830cab41c69ef944b5694f">GetNumberOfNodes</a>(); ++node) {</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; <span class="keywordtype">int</span>&amp; root_component = component_ids[<a class="code" href="classDenseConnectedComponentsFinder.html#a5484947d25c2901c60d02ea14d0e1a06">FindRoot</a>(node)];</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keywordflow">if</span> (root_component &lt; 0) {</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="comment">// This is the first node in a yet unseen component.</span></div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; root_component = current_component;</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; ++current_component;</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; }</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; component_ids[node] = root_component;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; }</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; <span class="keywordflow">return</span> component_ids;</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160;}</div>
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