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<div class="headertitle"><div class="title">boruvkas_minimum_spanning_tree.cpp File Reference</div></div>
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<p>[Borůvkas Algorithm](<a href="https://en.wikipedia.org/wiki/Borůvka's_algorithm">https://en.wikipedia.org/wiki/Borůvka's_algorithm</a>) to find the <a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> Spanning Tree
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <cassert></code><br />
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<code>#include <climits></code><br />
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<code>#include <iostream></code><br />
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<code>#include <vector></code><br />
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</div><div class="textblock"><div class="dynheader">
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Include dependency graph for boruvkas_minimum_spanning_tree.cpp:</div>
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<div class="dyncontent">
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<div class="center"><iframe scrolling="no" frameborder="0" src="../../dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.svg" width="335" height="126"><p><b>This browser is not able to show SVG: try Firefox, Chrome, Safari, or Opera instead.</b></p></iframe></div>
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</div><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="namespaces" name="namespaces"></a>
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Namespaces</h2></td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d2/d90/namespacegreedy__algorithms.html">greedy_algorithms</a></td></tr>
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<tr class="memdesc:d2/d90/namespacegreedy__algorithms"><td class="mdescLeft"> </td><td class="mdescRight">for string class <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../d8/d64/namespaceboruvkas__minimum__spanning__tree.html">boruvkas_minimum_spanning_tree</a></td></tr>
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<tr class="memdesc:d8/d64/namespaceboruvkas__minimum__spanning__tree"><td class="mdescLeft"> </td><td class="mdescRight">Functions for the [Borůvkas Algorithm](<a href="https://en.wikipedia.org/wiki/Borůvka's_algorithm">https://en.wikipedia.org/wiki/Borůvka's_algorithm</a>) implementation. <br /></td></tr>
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<tr class="separator:"><td class="memSeparator" colspan="2"> </td></tr>
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</table><table class="memberdecls">
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<tr class="heading"><td colspan="2"><h2 class="groupheader"><a id="func-members" name="func-members"></a>
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Functions</h2></td></tr>
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<tr class="memitem:a95de0f5e70e83164dbd1b4c515565e84" id="r_a95de0f5e70e83164dbd1b4c515565e84"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#a95de0f5e70e83164dbd1b4c515565e84">greedy_algorithms::boruvkas_minimum_spanning_tree::findParent</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>< int, int > > parent, const int v)</td></tr>
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<tr class="memdesc:a95de0f5e70e83164dbd1b4c515565e84"><td class="mdescLeft"> </td><td class="mdescRight">Recursively returns the vertex's parent at the root of the tree. <br /></td></tr>
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<tr class="separator:a95de0f5e70e83164dbd1b4c515565e84"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a94c615fc66b72e0adbcbcb99aabb1a59" id="r_a94c615fc66b72e0adbcbcb99aabb1a59"><td class="memItemLeft" align="right" valign="top"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< int > > </td><td class="memItemRight" valign="bottom"><a class="el" href="#a94c615fc66b72e0adbcbcb99aabb1a59">greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< int > > adj)</td></tr>
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<tr class="memdesc:a94c615fc66b72e0adbcbcb99aabb1a59"><td class="mdescLeft"> </td><td class="mdescRight">the implementation of boruvka's algorithm <br /></td></tr>
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<tr class="separator:a94c615fc66b72e0adbcbcb99aabb1a59"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a2311b22324cf09926726e4ce1309af8b" id="r_a2311b22324cf09926726e4ce1309af8b"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#a2311b22324cf09926726e4ce1309af8b">greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum</a> (<a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< int > > adj)</td></tr>
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<tr class="memdesc:a2311b22324cf09926726e4ce1309af8b"><td class="mdescLeft"> </td><td class="mdescRight">counts the sum of edges in the given tree <br /></td></tr>
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<tr class="separator:a2311b22324cf09926726e4ce1309af8b"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:a483bb8ccf42aaf7375a83e91490eda1e" id="r_a483bb8ccf42aaf7375a83e91490eda1e"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a> ()</td></tr>
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<tr class="memdesc:a483bb8ccf42aaf7375a83e91490eda1e"><td class="mdescLeft"> </td><td class="mdescRight">Self-test implementations. <br /></td></tr>
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<tr class="separator:a483bb8ccf42aaf7375a83e91490eda1e"><td class="memSeparator" colspan="2"> </td></tr>
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<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
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<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft"> </td><td class="mdescRight">Main function. <br /></td></tr>
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<tr class="separator:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memSeparator" colspan="2"> </td></tr>
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</table>
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<a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
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<div class="textblock"><p>[Borůvkas Algorithm](<a href="https://en.wikipedia.org/wiki/Borůvka's_algorithm">https://en.wikipedia.org/wiki/Borůvka's_algorithm</a>) to find the <a class="el" href="../../d4/d12/namespace_minimum.html" title="Implementation of Minimum Edit Distance algorithm.">Minimum</a> Spanning Tree </p>
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<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/JNardoni" target="_blank">Jason Nardoni</a></dd></dl>
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<p>Boruvka's algorithm is a greepy algorithm to find the MST by starting with small trees, and combining them to build bigger ones.</p><ol type="1">
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<li>Creates a group for every vertex.</li>
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<li>looks through each edge of every vertex for the smallest weight. Keeps track of the smallest edge for each of the current groups.</li>
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</ol>
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<p>Combine each group with the group it shares its smallest edge, adding the smallest edge to the MST.</p><ol type="1">
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<li>Repeat step 2-3 until all vertices are combined into a single group.</li>
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</ol>
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<p>It assumes that the graph is connected. Non-connected edges can be represented using 0 or INT_MAX </p>
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</div><h2 class="groupheader">Function Documentation</h2>
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<a id="a94c615fc66b72e0adbcbcb99aabb1a59" name="a94c615fc66b72e0adbcbcb99aabb1a59"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a94c615fc66b72e0adbcbcb99aabb1a59">◆ </a></span>boruvkas()</h2>
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<div class="memitem">
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<div class="memproto">
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<table class="memname">
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<tr>
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<td class="memname"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< int > > greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< int > ></td> <td class="paramname"><span class="paramname"><em>adj</em></span></td><td>)</td>
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<td></td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>the implementation of boruvka's algorithm </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">adj</td><td>a graph adjancency matrix stored as 2d vectors. </td></tr>
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</table>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>the MST as 2d vectors </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 60</span> {</div>
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<div class="line"><span class="lineno"> 61</span> <span class="keywordtype">size_t</span> size = adj.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
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<div class="line"><span class="lineno"> 62</span> <span class="keywordtype">size_t</span> total_groups = size;</div>
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<div class="line"><span class="lineno"> 63</span> </div>
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<div class="line"><span class="lineno"> 64</span> <span class="keywordflow">if</span> (size <= 1) {</div>
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<div class="line"><span class="lineno"> 65</span> <span class="keywordflow">return</span> adj;</div>
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<div class="line"><span class="lineno"> 66</span> }</div>
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<div class="line"><span class="lineno"> 67</span> </div>
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<div class="line"><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"><span class="lineno"> 69</span> <span class="comment">// are added to the MST</span></div>
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<div class="line"><span class="lineno"> 70</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<std::vector<int></a>> MST(size, <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<int></a>(size, INT_MAX));</div>
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<div class="line"><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"><span class="lineno"> 72</span> MST[i][i] = 0;</div>
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<div class="line"><span class="lineno"> 73</span> }</div>
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<div class="line"><span class="lineno"> 74</span> </div>
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<div class="line"><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"><span class="lineno"> 76</span> </div>
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<div class="line"><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"><span class="lineno"> 78</span> <span class="comment">// to 0</span></div>
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<div class="line"><span class="lineno"> 79</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<std::pair<int, int></a>> parent(size, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(0, 0));</div>
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<div class="line"><span class="lineno"> 80</span> </div>
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<div class="line"><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"><span class="lineno"> 82</span> parent[i].first =</div>
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<div class="line"><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"><span class="lineno"> 84</span> }</div>
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<div class="line"><span class="lineno"> 85</span> </div>
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<div class="line"><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"><span class="lineno"> 87</span> <span class="keywordflow">while</span> (total_groups > 1) {</div>
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<div class="line"><span class="lineno"> 88</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<std::pair<int, int></a>> smallest_edge(</div>
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<div class="line"><span class="lineno"> 89</span> size, <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a>(-1, -1)); <span class="comment">// Pairing: start node, end node</span></div>
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<div class="line"><span class="lineno"> 90</span> </div>
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<div class="line"><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"><span class="lineno"> 92</span> <span class="comment">// the right half of the adj matrix</span></div>
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<div class="line"><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"><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"><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"><span class="lineno"> 96</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><span class="lineno"> 97</span> }</div>
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<div class="line"><span class="lineno"> 98</span> </div>
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<div class="line"><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"><span class="lineno"> 100</span> <span class="comment">// they arent in the same group</span></div>
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<div class="line"><span class="lineno"> 101</span> <span class="keywordtype">int</span> parentA = <a class="code hl_function" href="#a95de0f5e70e83164dbd1b4c515565e84">findParent</a>(parent, i);</div>
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<div class="line"><span class="lineno"> 102</span> <span class="keywordtype">int</span> parentB = <a class="code hl_function" href="#a95de0f5e70e83164dbd1b4c515565e84">findParent</a>(parent, j);</div>
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<div class="line"><span class="lineno"> 103</span> </div>
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<div class="line"><span class="lineno"> 104</span> <span class="keywordflow">if</span> (parentA != parentB) {</div>
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<div class="line"><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"><span class="lineno"> 106</span> <span class="comment">// current smallest edge</span></div>
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<div class="line"><span class="lineno"> 107</span> <span class="keywordtype">int</span> start = smallest_edge[parentA].first;</div>
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<div class="line"><span class="lineno"> 108</span> <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = smallest_edge[parentA].second;</div>
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<div class="line"><span class="lineno"> 109</span> </div>
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<div class="line"><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"><span class="lineno"> 111</span> <span class="comment">// smaller, records the new smallest</span></div>
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<div class="line"><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"><span class="lineno"> 113</span> smallest_edge[parentA].first = i;</div>
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<div class="line"><span class="lineno"> 114</span> smallest_edge[parentA].second = j;</div>
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<div class="line"><span class="lineno"> 115</span> }</div>
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<div class="line"><span class="lineno"> 116</span> </div>
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<div class="line"><span class="lineno"> 117</span> <span class="comment">// Does the same for the second group</span></div>
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<div class="line"><span class="lineno"> 118</span> start = smallest_edge[parentB].first;</div>
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<div class="line"><span class="lineno"> 119</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = smallest_edge[parentB].second;</div>
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<div class="line"><span class="lineno"> 120</span> </div>
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<div class="line"><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"><span class="lineno"> 122</span> smallest_edge[parentB].first = j;</div>
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<div class="line"><span class="lineno"> 123</span> smallest_edge[parentB].second = i;</div>
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<div class="line"><span class="lineno"> 124</span> }</div>
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<div class="line"><span class="lineno"> 125</span> }</div>
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<div class="line"><span class="lineno"> 126</span> }</div>
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<div class="line"><span class="lineno"> 127</span> }</div>
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<div class="line"><span class="lineno"> 128</span> </div>
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<div class="line"><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"><span class="lineno"> 130</span> </div>
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<div class="line"><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"><span class="lineno"> 132</span> <span class="comment">// Makes sure the smallest edge exists</span></div>
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<div class="line"><span class="lineno"> 133</span> <span class="keywordflow">if</span> (smallest_edge[i].first != -1) {</div>
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<div class="line"><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"><span class="lineno"> 135</span> <span class="keywordtype">int</span> start = smallest_edge[i].first;</div>
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<div class="line"><span class="lineno"> 136</span> <span class="keywordtype">int</span> <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a> = smallest_edge[i].second;</div>
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<div class="line"><span class="lineno"> 137</span> </div>
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<div class="line"><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"><span class="lineno"> 139</span> <span class="keywordtype">int</span> parentA = i;</div>
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<div class="line"><span class="lineno"> 140</span> <span class="keywordtype">int</span> parentB = <a class="code hl_function" href="#a95de0f5e70e83164dbd1b4c515565e84">findParent</a>(parent, end);</div>
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<div class="line"><span class="lineno"> 141</span> </div>
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<div class="line"><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"><span class="lineno"> 143</span> <span class="comment">// happen if the two groups have been</span></div>
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<div class="line"><span class="lineno"> 144</span> <span class="comment">// merged previously through a common shortest edge</span></div>
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<div class="line"><span class="lineno"> 145</span> <span class="keywordflow">if</span> (parentA == parentB) {</div>
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<div class="line"><span class="lineno"> 146</span> <span class="keywordflow">continue</span>;</div>
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<div class="line"><span class="lineno"> 147</span> }</div>
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<div class="line"><span class="lineno"> 148</span> </div>
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<div class="line"><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"><span class="lineno"> 150</span> <span class="comment">// merged. The parent of the shallower</span></div>
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<div class="line"><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"><span class="lineno"> 152</span> <span class="keywordflow">if</span> (parent[parentA].second < parent[parentB].second) {</div>
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<div class="line"><span class="lineno"> 153</span> parent[parentB].first = parentA; <span class="comment">// New parent</span></div>
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<div class="line"><span class="lineno"> 154</span> parent[parentB].second++; <span class="comment">// Increase depth</span></div>
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<div class="line"><span class="lineno"> 155</span> } <span class="keywordflow">else</span> {</div>
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<div class="line"><span class="lineno"> 156</span> parent[parentA].first = parentB;</div>
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<div class="line"><span class="lineno"> 157</span> parent[parentA].second++;</div>
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<div class="line"><span class="lineno"> 158</span> }</div>
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<div class="line"><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"><span class="lineno"> 160</span> <span class="comment">// matrix</span></div>
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<div class="line"><span class="lineno"> 161</span> MST[start][<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>] = adj[start][<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>];</div>
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<div class="line"><span class="lineno"> 162</span> MST[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>][start] = adj[<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/iterator/end.html">end</a>][start];</div>
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<div class="line"><span class="lineno"> 163</span> total_groups--; <span class="comment">// one fewer group</span></div>
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<div class="line"><span class="lineno"> 164</span> }</div>
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<div class="line"><span class="lineno"> 165</span> }</div>
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<div class="line"><span class="lineno"> 166</span> }</div>
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<div class="line"><span class="lineno"> 167</span> <span class="keywordflow">return</span> MST;</div>
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<div class="line"><span class="lineno"> 168</span>}</div>
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<div class="ttc" id="aboruvkas__minimum__spanning__tree_8cpp_html_a95de0f5e70e83164dbd1b4c515565e84"><div class="ttname"><a href="#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> boruvkas_minimum_spanning_tree.cpp:47</div></div>
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<div class="ttc" id="aend_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/iterator/end.html">std::end</a></div><div class="ttdeci">T end(T... args)</div></div>
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<div class="ttc" id="amake_pair_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/utility/pair/make_pair.html">std::make_pair</a></div><div class="ttdeci">T make_pair(T... args)</div></div>
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<div class="ttc" id="asize_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/container/vector/size.html">std::vector::size</a></div><div class="ttdeci">T size(T... args)</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a95de0f5e70e83164dbd1b4c515565e84">◆ </a></span>findParent()</h2>
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<td class="memname">int greedy_algorithms::boruvkas_minimum_spanning_tree::findParent </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/utility/pair.html">std::pair</a>< int, int > ></td> <td class="paramname"><span class="paramname"><em>parent</em></span>, </td>
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<td class="paramtype">const int</td> <td class="paramname"><span class="paramname"><em>v</em></span> )</td>
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<p>Recursively returns the vertex's parent at the root of the tree. </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">parent</td><td>the array that will be checked </td></tr>
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<tr><td class="paramname">v</td><td>vertex to find parent of </td></tr>
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</dd>
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</dl>
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<dl class="section return"><dt>Returns</dt><dd>the parent of the vertex </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 47</span> {</div>
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<div class="line"><span class="lineno"> 48</span> <span class="keywordflow">if</span> (parent[v].first != v) {</div>
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<div class="line"><span class="lineno"> 49</span> parent[v].first = <a class="code hl_function" href="#a95de0f5e70e83164dbd1b4c515565e84">findParent</a>(parent, parent[v].first);</div>
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<div class="line"><span class="lineno"> 50</span> }</div>
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<div class="line"><span class="lineno"> 51</span> </div>
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<div class="line"><span class="lineno"> 52</span> <span class="keywordflow">return</span> parent[v].first;</div>
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<div class="line"><span class="lineno"> 53</span>}</div>
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<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
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<td class="memname">int main </td>
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<td>(</td>
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<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Main function. </p>
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<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 224</span> {</div>
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<div class="line"><span class="lineno"> 225</span> <a class="code hl_function" href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a>(); <span class="comment">// run self-test implementations</span></div>
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<div class="line"><span class="lineno"> 226</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><span class="lineno"> 227</span>}</div>
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<div class="ttc" id="aboruvkas__minimum__spanning__tree_8cpp_html_a483bb8ccf42aaf7375a83e91490eda1e"><div class="ttname"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">tests</a></div><div class="ttdeci">static void tests()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> boruvkas_minimum_spanning_tree.cpp:196</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a2311b22324cf09926726e4ce1309af8b">◆ </a></span>test_findGraphSum()</h2>
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<td class="memname">int greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum </td>
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<td>(</td>
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<td class="paramtype"><a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< <a class="elRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector</a>< int > ></td> <td class="paramname"><span class="paramname"><em>adj</em></span></td><td>)</td>
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<p>counts the sum of edges in the given tree </p>
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<dl class="params"><dt>Parameters</dt><dd>
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<table class="params">
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<tr><td class="paramname">adj</td><td>2D vector adjacency matrix </td></tr>
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<dl class="section return"><dt>Returns</dt><dd>the int size of the tree </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 175</span> {</div>
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<div class="line"><span class="lineno"> 176</span> <span class="keywordtype">size_t</span> size = adj.<a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector/size.html">size</a>();</div>
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<div class="line"><span class="lineno"> 177</span> <span class="keywordtype">int</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> = 0;</div>
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<div class="line"><span class="lineno"> 178</span> </div>
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<div class="line"><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"><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"><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"><span class="lineno"> 182</span> <span class="keywordflow">if</span> (adj[i][j] < INT_MAX) {</div>
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<div class="line"><span class="lineno"> 183</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a> += adj[i][j];</div>
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<div class="line"><span class="lineno"> 184</span> }</div>
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<div class="line"><span class="lineno"> 185</span> }</div>
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<div class="line"><span class="lineno"> 186</span> }</div>
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<div class="line"><span class="lineno"> 187</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">sum</a>;</div>
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<div class="line"><span class="lineno"> 188</span>}</div>
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<div class="ttc" id="anamespacemachine__learning_html_a6f1c98c016ad34ff3d9f39372161bd35"><div class="ttname"><a href="../../d8/d77/namespacemachine__learning.html#a6f1c98c016ad34ff3d9f39372161bd35">machine_learning::sum</a></div><div class="ttdeci">T sum(const std::vector< std::valarray< T > > &A)</div><div class="ttdef"><b>Definition</b> vector_ops.hpp:232</div></div>
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<h2 class="memtitle"><span class="permalink"><a href="#a483bb8ccf42aaf7375a83e91490eda1e">◆ </a></span>tests()</h2>
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<td>(</td>
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<p>Self-test implementations. </p>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
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<div class="fragment"><div class="line"><span class="lineno"> 196</span> {</div>
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<div class="line"><span class="lineno"> 197</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"Starting tests...\n\n"</span>;</div>
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<div class="line"><span class="lineno"> 198</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<std::vector<int></a>> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a> = {</div>
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<div class="line"><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"><span class="lineno"> 200</span> {INT_MAX, 2, 0, INT_MAX, 3}, {3, INT_MAX, INT_MAX, 0, INT_MAX},</div>
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<div class="line"><span class="lineno"> 201</span> {INT_MAX, 5, 3, INT_MAX, 0},</div>
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<div class="line"><span class="lineno"> 202</span> };</div>
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<div class="line"><span class="lineno"> 203</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/container/vector.html">std::vector<std::vector<int></a>> MST =</div>
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<div class="line"><span class="lineno"> 204</span> <a class="code hl_function" href="#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"><span class="lineno"> 205</span> assert(greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum(</div>
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<div class="line"><span class="lineno"> 206</span> MST) == 13);</div>
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<div class="line"><span class="lineno"> 207</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"1st test passed!"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 208</span> </div>
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<div class="line"><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"><span class="lineno"> 210</span> {2, 0, 3, 8, 5},</div>
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<div class="line"><span class="lineno"> 211</span> {0, 3, 0, 0, 7},</div>
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<div class="line"><span class="lineno"> 212</span> {6, 8, 0, 0, 9},</div>
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<div class="line"><span class="lineno"> 213</span> {0, 5, 7, 9, 0}};</div>
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<div class="line"><span class="lineno"> 214</span> MST = <a class="code hl_function" href="#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"><span class="lineno"> 215</span> assert(greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum(</div>
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<div class="line"><span class="lineno"> 216</span> MST) == 16);</div>
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<div class="line"><span class="lineno"> 217</span> <a class="code hl_classRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a> << <span class="stringliteral">"2nd test passed!"</span> << <a class="code hl_functionRef" target="_blank" href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a>;</div>
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<div class="line"><span class="lineno"> 218</span>}</div>
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<div class="ttc" id="abasic_ostream_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/basic_ostream.html">std::cout</a></div></div>
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<div class="ttc" id="aboruvkas__minimum__spanning__tree_8cpp_html_a94c615fc66b72e0adbcbcb99aabb1a59"><div class="ttname"><a href="#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> boruvkas_minimum_spanning_tree.cpp:60</div></div>
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<div class="ttc" id="aendl_html"><div class="ttname"><a href="http://en.cppreference.com/w/cpp/io/manip/endl.html">std::endl</a></div><div class="ttdeci">T endl(T... args)</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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