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<div class="headertitle"><div class="title">boruvkas_minimum_spanning_tree.cpp</div></div>
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<div class="contents">
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<a href="../../d4/d6c/boruvkas__minimum__spanning__tree_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>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> </div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="preprocessor">#include <climits></span> </div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="preprocessor">#include <iostream></span> </div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="preprocessor">#include <vector></span> </div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d2/d90/namespacegreedy__algorithms.html">greedy_algorithms</a> {</div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../d8/d64/namespaceboruvkas__minimum__spanning__tree.html">boruvkas_minimum_spanning_tree</a> {</div>
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<div class="foldopen" id="foldopen00047" data-start="{" data-end="}">
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"><a class="line" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a95de0f5e70e83164dbd1b4c515565e84"> 47</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a95de0f5e70e83164dbd1b4c515565e84">findParent</a>(std::vector<std::pair<int, int>> parent, <span class="keyword">const</span> <span class="keywordtype">int</span> v) {</div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> <span class="keywordflow">if</span> (parent[v].first != v) {</div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> parent[v].first = <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a95de0f5e70e83164dbd1b4c515565e84">findParent</a>(parent, parent[v].first);</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keywordflow">return</span> parent[v].first;</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span>}</div>
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</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span></div>
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<div class="foldopen" id="foldopen00060" data-start="{" data-end="}">
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"><a class="line" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a94c615fc66b72e0adbcbcb99aabb1a59"> 60</a></span>std::vector<std::vector<int>> <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a94c615fc66b72e0adbcbcb99aabb1a59">boruvkas</a>(std::vector<std::vector<int>> adj) {</div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keywordtype">size_t</span> size = adj.size();</div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordtype">size_t</span> total_groups = size;</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> </div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> <span class="keywordflow">if</span> (size <= 1) {</div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="keywordflow">return</span> adj;</div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> }</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> </div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> <span class="comment">// Stores the current Minimum Spanning Tree. As groups are combined, they</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="comment">// are added to the MST</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> std::vector<std::vector<int>> MST(size, std::vector<int>(size, INT_MAX));</div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < size; i++) {</div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> MST[i][i] = 0;</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> }</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// Step 1: Create a group for each vertex</span></div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> </div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// Stores the parent of the vertex and its current depth, both initialized</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// to 0</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> std::vector<std::pair<int, int>> parent(size, std::make_pair(0, 0));</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < size; i++) {</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> parent[i].first =</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> i; <span class="comment">// Sets parent of each vertex to itself, depth remains 0</span></div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> }</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> <span class="comment">// Repeat until all are in a single group</span></div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="keywordflow">while</span> (total_groups > 1) {</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> std::vector<std::pair<int, int>> smallest_edge(</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> size, std::make_pair(-1, -1)); <span class="comment">// Pairing: start node, end node</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="comment">// Step 2: Look throught each vertex for its smallest edge, only using</span></div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="comment">// the right half of the adj matrix</span></div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < size; i++) {</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < size; j++) {</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keywordflow">if</span> (adj[i][j] == INT_MAX || adj[i][j] == 0) { <span class="comment">// No connection</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> }</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> </div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> <span class="comment">// Finds the parents of the start and end points to make sure</span></div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="comment">// they arent in the same group</span></div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> <span class="keywordtype">int</span> parentA = <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a95de0f5e70e83164dbd1b4c515565e84">findParent</a>(parent, i);</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> <span class="keywordtype">int</span> parentB = <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a95de0f5e70e83164dbd1b4c515565e84">findParent</a>(parent, j);</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> </div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordflow">if</span> (parentA != parentB) {</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> <span class="comment">// Grabs the start and end points for the first groups</span></div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="comment">// current smallest edge</span></div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> <span class="keywordtype">int</span> start = smallest_edge[parentA].first;</div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keywordtype">int</span> end = smallest_edge[parentA].second;</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> </div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// If there is no current smallest edge, or the new edge is</span></div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> <span class="comment">// smaller, records the new smallest</span></div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> <span class="keywordflow">if</span> (start == -1 || adj[i][j] < adj[start][end]) {</div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> smallest_edge[parentA].first = i;</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> smallest_edge[parentA].second = j;</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> }</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> <span class="comment">// Does the same for the second group</span></div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> start = smallest_edge[parentB].first;</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> end = smallest_edge[parentB].second;</div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> </div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordflow">if</span> (start == -1 || adj[j][i] < adj[start][end]) {</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> smallest_edge[parentB].first = j;</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> smallest_edge[parentB].second = i;</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> }</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> }</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> }</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> }</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> </div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="comment">// Step 3: Combine the groups based off their smallest edge</span></div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> </div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < size; i++) {</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// Makes sure the smallest edge exists</span></div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> <span class="keywordflow">if</span> (smallest_edge[i].first != -1) {</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <span class="comment">// Start and end points for the groups smallest edge</span></div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <span class="keywordtype">int</span> start = smallest_edge[i].first;</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> <span class="keywordtype">int</span> end = smallest_edge[i].second;</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> </div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="comment">// Parents of the two groups - A is always itself</span></div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordtype">int</span> parentA = i;</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> <span class="keywordtype">int</span> parentB = <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a95de0f5e70e83164dbd1b4c515565e84">findParent</a>(parent, end);</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> </div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="comment">// Makes sure the two nodes dont share the same parent. Would</span></div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="comment">// happen if the two groups have been</span></div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="comment">// merged previously through a common shortest edge</span></div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> <span class="keywordflow">if</span> (parentA == parentB) {</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> }</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> </div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="comment">// Tries to balance the trees as much as possible as they are</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="comment">// merged. The parent of the shallower</span></div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> <span class="comment">// tree will be pointed to the parent of the deeper tree.</span></div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="keywordflow">if</span> (parent[parentA].second < parent[parentB].second) {</div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> parent[parentB].first = parentA; <span class="comment">// New parent</span></div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> parent[parentB].second++; <span class="comment">// Increase depth</span></div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> parent[parentA].first = parentB;</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> parent[parentA].second++;</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> }</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="comment">// Add the connection to the MST, using both halves of the adj</span></div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> <span class="comment">// matrix</span></div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> MST[start][end] = adj[start][end];</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> MST[end][start] = adj[end][start];</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> total_groups--; <span class="comment">// one fewer group</span></div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> }</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> }</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> }</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keywordflow">return</span> MST;</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span>}</div>
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</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span></div>
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<div class="foldopen" id="foldopen00175" data-start="{" data-end="}">
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"><a class="line" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a2311b22324cf09926726e4ce1309af8b"> 175</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a2311b22324cf09926726e4ce1309af8b">test_findGraphSum</a>(std::vector<std::vector<int>> adj) {</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <span class="keywordtype">size_t</span> size = adj.size();</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> <span class="keywordtype">int</span> sum = 0;</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> </div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> <span class="comment">// Moves through one side of the adj matrix, counting the sums of each edge</span></div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < size; i++) {</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = i + 1; j < size; j++) {</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordflow">if</span> (adj[i][j] < INT_MAX) {</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> sum += adj[i][j];</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> }</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> }</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> }</div>
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<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> <span class="keywordflow">return</span> sum;</div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span>}</div>
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</div>
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<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span>} <span class="comment">// namespace boruvkas_minimum_spanning_tree</span></div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span>} <span class="comment">// namespace greedy_algorithms</span></div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span></div>
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<div class="foldopen" id="foldopen00196" data-start="{" data-end="}">
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"><a class="line" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e"> 196</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>() {</div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> std::cout << <span class="stringliteral">"Starting tests...\n\n"</span>;</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> std::vector<std::vector<int>> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a> = {</div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> {0, 5, INT_MAX, 3, INT_MAX}, {5, 0, 2, INT_MAX, 5},</div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> {INT_MAX, 2, 0, INT_MAX, 3}, {3, INT_MAX, INT_MAX, 0, INT_MAX},</div>
|
|
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> {INT_MAX, 5, 3, INT_MAX, 0},</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> };</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> std::vector<std::vector<int>> MST =</div>
|
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a94c615fc66b72e0adbcbcb99aabb1a59">greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas</a>(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>);</div>
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|
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> assert(<a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a2311b22324cf09926726e4ce1309af8b">greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum</a>(</div>
|
|
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> MST) == 13);</div>
|
|
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> std::cout << <span class="stringliteral">"1st test passed!"</span> << std::endl;</div>
|
|
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> </div>
|
|
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a> = {{0, 2, 0, 6, 0},</div>
|
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> {2, 0, 3, 8, 5},</div>
|
|
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> {0, 3, 0, 0, 7},</div>
|
|
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> {6, 8, 0, 0, 9},</div>
|
|
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> {0, 5, 7, 9, 0}};</div>
|
|
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> MST = <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a94c615fc66b72e0adbcbcb99aabb1a59">greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas</a>(<a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>);</div>
|
|
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> assert(<a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a2311b22324cf09926726e4ce1309af8b">greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum</a>(</div>
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|
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> MST) == 16);</div>
|
|
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> std::cout << <span class="stringliteral">"2nd test passed!"</span> << std::endl;</div>
|
|
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span>}</div>
|
|
</div>
|
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span></div>
|
|
<div class="foldopen" id="foldopen00224" data-start="{" data-end="}">
|
|
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"><a class="line" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 224</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
|
|
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <a class="code hl_function" href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// run self-test implementations</span></div>
|
|
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> <span class="keywordflow">return</span> 0;</div>
|
|
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span>}</div>
|
|
</div>
|
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<div class="ttc" id="aboruvkas__minimum__spanning__tree_8cpp_html_a2311b22324cf09926726e4ce1309af8b"><div class="ttname"><a href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a2311b22324cf09926726e4ce1309af8b">greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum</a></div><div class="ttdeci">int test_findGraphSum(std::vector< std::vector< int > > adj)</div><div class="ttdoc">counts the sum of edges in the given tree</div><div class="ttdef"><b>Definition</b> <a href="#l00175">boruvkas_minimum_spanning_tree.cpp:175</a></div></div>
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|
<div class="ttc" id="aboruvkas__minimum__spanning__tree_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="#l00196">boruvkas_minimum_spanning_tree.cpp:196</a></div></div>
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<div class="ttc" id="aboruvkas__minimum__spanning__tree_8cpp_html_a94c615fc66b72e0adbcbcb99aabb1a59"><div class="ttname"><a href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a94c615fc66b72e0adbcbcb99aabb1a59">greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas</a></div><div class="ttdeci">std::vector< std::vector< int > > boruvkas(std::vector< std::vector< int > > adj)</div><div class="ttdoc">the implementation of boruvka's algorithm</div><div class="ttdef"><b>Definition</b> <a href="#l00060">boruvkas_minimum_spanning_tree.cpp:60</a></div></div>
|
|
<div class="ttc" id="aboruvkas__minimum__spanning__tree_8cpp_html_a95de0f5e70e83164dbd1b4c515565e84"><div class="ttname"><a href="../../d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a95de0f5e70e83164dbd1b4c515565e84">greedy_algorithms::boruvkas_minimum_spanning_tree::findParent</a></div><div class="ttdeci">int findParent(std::vector< std::pair< int, int > > parent, const int v)</div><div class="ttdoc">Recursively returns the vertex's parent at the root of the tree.</div><div class="ttdef"><b>Definition</b> <a href="#l00047">boruvkas_minimum_spanning_tree.cpp:47</a></div></div>
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<div class="ttc" id="aboruvkas__minimum__spanning__tree_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d4/d6c/boruvkas__minimum__spanning__tree_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="#l00224">boruvkas_minimum_spanning_tree.cpp:224</a></div></div>
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<div class="ttc" id="anamespaceboruvkas__minimum__spanning__tree_html"><div class="ttname"><a href="../../d8/d64/namespaceboruvkas__minimum__spanning__tree.html">boruvkas_minimum_spanning_tree</a></div><div class="ttdoc">Functions for the [Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) implementat...</div></div>
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<div class="ttc" id="anamespacegraph_html"><div class="ttname"><a href="../../df/dce/namespacegraph.html">graph</a></div><div class="ttdoc">Graph Algorithms.</div></div>
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|
<div class="ttc" id="anamespacegreedy__algorithms_html"><div class="ttname"><a href="../../d2/d90/namespacegreedy__algorithms.html">greedy_algorithms</a></div><div class="ttdoc">for string class</div><div class="ttdef"><b>Definition</b> <a href="../../d9/d1f/binary__addition_8cpp_source.html#l00027">binary_addition.cpp:27</a></div></div>
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