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</div><!--header-->
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<div class="contents">
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<p>Algorithm to count paths between two nodes in a directed graph using DFS.
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<a href="#details">More...</a></p>
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<div class="textblock"><code>#include <vector></code><br />
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<code>#include <iostream></code><br />
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<code>#include <cassert></code><br />
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<code>#include <cstdint></code><br />
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Include dependency graph for number_of_paths.cpp:</div>
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Namespaces</h2></td></tr>
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<tr class="memitem:graph" id="r_graph"><td class="memItemLeft" align="right" valign="top">namespace  </td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html">graph</a></td></tr>
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<tr class="memdesc:df/dce/namespacegraph"><td class="mdescLeft"> </td><td class="mdescRight"><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms. <br /></td></tr>
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<tr class="heading"><td colspan="2"><h2 id="header-func-members" 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:af99fccdd19e8f223e8749561589a762b" id="r_af99fccdd19e8f223e8749561589a762b"><td class="memItemLeft" align="right" valign="top">std::uint32_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#af99fccdd19e8f223e8749561589a762b">graph::count_paths_dfs</a> (const std::vector< std::vector< std::uint32_t > > &A, std::uint32_t u, std::uint32_t v, std::uint32_t n, std::vector< bool > &visited)</td></tr>
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||||
<tr class="memdesc:af99fccdd19e8f223e8749561589a762b"><td class="mdescLeft"> </td><td class="mdescRight">Helper function to perform DFS and count the number of paths from node <span class="tt">u</span> to node <span class="tt">v</span> <br /></td></tr>
|
||||
<tr class="memitem:a7c3adb1551bc527a7aa93f331b1c0987" id="r_a7c3adb1551bc527a7aa93f331b1c0987"><td class="memItemLeft" align="right" valign="top">std::uint32_t </td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a> (const std::vector< std::vector< std::uint32_t > > &A, std::uint32_t u, std::uint32_t v, std::uint32_t n)</td></tr>
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||||
<tr class="memdesc:a7c3adb1551bc527a7aa93f331b1c0987"><td class="mdescLeft"> </td><td class="mdescRight">Counts the number of paths from node <span class="tt">u</span> to node <span class="tt">v</span> in a directed graph using Depth First Search (DFS) <br /></td></tr>
|
||||
<tr class="memitem:aa8dca7b867074164d5f45b0f3851269d" id="r_aa8dca7b867074164d5f45b0f3851269d"><td class="memItemLeft" align="right" valign="top">static void </td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
|
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<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft"> </td><td class="mdescRight">Self-test implementations. <br /></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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||||
</table>
|
||||
<a name="details" id="details"></a><h2 id="header-details" class="groupheader">Detailed Description</h2>
|
||||
<div class="textblock"><p>Algorithm to count paths between two nodes in a directed graph using DFS. </p>
|
||||
<p>This algorithm implements Depth First Search (DFS) to count the number of possible paths between two nodes in a directed graph. It is represented using an adjacency matrix. The algorithm recursively traverses the graph to find all paths from the source node <span class="tt">u</span> to the destination node <span class="tt">v</span>.</p>
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||||
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/adi776borate" target="_blank">Aditya Borate</a> </dd></dl>
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||||
<dl class="section see"><dt>See also</dt><dd><a href="https://en.wikipedia.org/wiki/Path_(graph_theory)">https://en.wikipedia.org/wiki/Path_(graph_theory)</a> </dd></dl>
|
||||
|
||||
<p class="definition">Definition in file <a class="el" href="../../d2/d32/number__of__paths_8cpp_source.html">number_of_paths.cpp</a>.</p>
|
||||
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
|
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<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
|
||||
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">◆ </a></span>main()</h2>
|
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|
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<div class="memitem">
|
||||
<div class="memproto">
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||||
<table class="memname">
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||||
<tr>
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<td class="memname">int main </td>
|
||||
<td>(</td>
|
||||
<td class="paramtype">void</td> <td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
|
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<td></td>
|
||||
</tr>
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||||
</table>
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||||
</div><div class="memdoc">
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||||
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||||
<p>Main function. </p>
|
||||
<dl class="section return"><dt>Returns</dt><dd>0 on exit </dd></dl>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../d2/d32/number__of__paths_8cpp_source.html#l00148">148</a> of file <a class="el" href="../../d2/d32/number__of__paths_8cpp_source.html">number_of_paths.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 148</span> {</div>
|
||||
<div class="line"><span class="lineno"> 149</span> <a class="code hl_function" href="#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Run self-test implementations</span></div>
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<div class="line"><span class="lineno"> 150</span> <span class="keywordflow">return</span> 0;</div>
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||||
<div class="line"><span class="lineno"> 151</span>}</div>
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||||
<div class="ttc" id="anumber__of__paths_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="../../d2/d32/number__of__paths_8cpp_source.html#l00086">number_of_paths.cpp:86</a></div></div>
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||||
</div><!-- fragment -->
|
||||
</div>
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||||
</div>
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||||
<a id="aa8dca7b867074164d5f45b0f3851269d" name="aa8dca7b867074164d5f45b0f3851269d"></a>
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||||
<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">◆ </a></span>test()</h2>
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||||
|
||||
<div class="memitem">
|
||||
<div class="memproto">
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||||
<table class="mlabels">
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||||
<tr>
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||||
<td class="mlabels-left">
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||||
<table class="memname">
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<tr>
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||||
<td class="memname">void test </td>
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||||
<td>(</td>
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||||
<td class="paramname"><span class="paramname"><em></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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</td>
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<td class="mlabels-right">
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<span class="mlabels"><span class="mlabel static">static</span></span> </td>
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</tr>
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</table>
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</div><div class="memdoc">
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<p>Self-test implementations. </p>
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<dl class="section return"><dt>Returns</dt><dd>void </dd></dl>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../d2/d32/number__of__paths_8cpp_source.html#l00086">86</a> of file <a class="el" href="../../d2/d32/number__of__paths_8cpp_source.html">number_of_paths.cpp</a>.</p>
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||||
<div class="fragment"><div class="line"><span class="lineno"> 86</span> {</div>
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<div class="line"><span class="lineno"> 87</span> <span class="comment">// Test case 1: Simple directed graph with multiple paths</span></div>
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<div class="line"><span class="lineno"> 88</span> std::vector<std::vector<std::uint32_t>> graph1 = {</div>
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<div class="line"><span class="lineno"> 89</span> {0, 1, 0, 1, 0}, </div>
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<div class="line"><span class="lineno"> 90</span> {0, 0, 1, 0, 1}, </div>
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<div class="line"><span class="lineno"> 91</span> {0, 0, 0, 0, 1}, </div>
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<div class="line"><span class="lineno"> 92</span> {0, 0, 1, 0, 0}, </div>
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||||
<div class="line"><span class="lineno"> 93</span> {0, 0, 0, 0, 0} </div>
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<div class="line"><span class="lineno"> 94</span> };</div>
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<div class="line"><span class="lineno"> 95</span> std::uint32_t n1 = 5, u1 = 0, v1 = 4;</div>
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<div class="line"><span class="lineno"> 96</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph1, u1, v1, n1) == 3); <span class="comment">// There are 3 paths from node 0 to 4</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> <span class="comment">// Test case 2: No possible path (disconnected graph)</span></div>
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<div class="line"><span class="lineno"> 99</span> std::vector<std::vector<std::uint32_t>> graph2 = {</div>
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<div class="line"><span class="lineno"> 100</span> {0, 1, 0, 0, 0}, </div>
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<div class="line"><span class="lineno"> 101</span> {0, 0, 0, 0, 0}, </div>
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<div class="line"><span class="lineno"> 102</span> {0, 0, 0, 0, 1}, </div>
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<div class="line"><span class="lineno"> 103</span> {0, 0, 1, 0, 0}, </div>
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<div class="line"><span class="lineno"> 104</span> {0, 0, 0, 0, 0} </div>
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<div class="line"><span class="lineno"> 105</span> };</div>
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<div class="line"><span class="lineno"> 106</span> std::uint32_t n2 = 5, u2 = 0, v2 = 4;</div>
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<div class="line"><span class="lineno"> 107</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph2, u2, v2, n2) == 0); <span class="comment">// No path from node 0 to 4</span></div>
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<div class="line"><span class="lineno"> 108</span> </div>
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<div class="line"><span class="lineno"> 109</span> <span class="comment">// Test case 3: Cyclic graph with multiple paths</span></div>
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<div class="line"><span class="lineno"> 110</span> std::vector<std::vector<std::uint32_t>> graph3 = {</div>
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<div class="line"><span class="lineno"> 111</span> {0, 1, 0, 0, 0}, </div>
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<div class="line"><span class="lineno"> 112</span> {0, 0, 1, 1, 0}, </div>
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<div class="line"><span class="lineno"> 113</span> {1, 0, 0, 0, 1}, </div>
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<div class="line"><span class="lineno"> 114</span> {0, 0, 1, 0, 1}, </div>
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<div class="line"><span class="lineno"> 115</span> {0, 0, 0, 0, 0} </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> std::uint32_t n3 = 5, u3 = 0, v3 = 4;</div>
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<div class="line"><span class="lineno"> 118</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph3, u3, v3, n3) == 3); <span class="comment">// There are 3 paths from node 0 to 4</span></div>
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<div class="line"><span class="lineno"> 119</span> </div>
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<div class="line"><span class="lineno"> 120</span> <span class="comment">// Test case 4: Single node graph (self-loop)</span></div>
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<div class="line"><span class="lineno"> 121</span> std::vector<std::vector<std::uint32_t>> graph4 = {</div>
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<div class="line"><span class="lineno"> 122</span> {0}</div>
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<div class="line"><span class="lineno"> 123</span> };</div>
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<div class="line"><span class="lineno"> 124</span> std::uint32_t n4 = 1, u4 = 0, v4 = 0;</div>
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<div class="line"><span class="lineno"> 125</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph4, u4, v4, n4) == 1); <span class="comment">// There is self-loop, so 1 path from node 0 to 0</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> <span class="comment">// Test case 5: Empty graph (no nodes, no paths)</span></div>
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<div class="line"><span class="lineno"> 128</span> std::vector<std::vector<std::uint32_t>> graph5 = {{}};</div>
|
||||
<div class="line"><span class="lineno"> 129</span> <span class="keywordtype">int</span> n5 = 0, u5 = 0, v5 = 0;</div>
|
||||
<div class="line"><span class="lineno"> 130</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph5, u5, v5, n5) == 0); <span class="comment">// There are no paths in an empty graph</span></div>
|
||||
<div class="line"><span class="lineno"> 131</span> </div>
|
||||
<div class="line"><span class="lineno"> 132</span> <span class="comment">// Test case 6: Invalid nodes (out of bounds)</span></div>
|
||||
<div class="line"><span class="lineno"> 133</span> std::vector<std::vector<std::uint32_t>> graph6 = {</div>
|
||||
<div class="line"><span class="lineno"> 134</span> {0, 1, 0}, </div>
|
||||
<div class="line"><span class="lineno"> 135</span> {0, 0, 1}, </div>
|
||||
<div class="line"><span class="lineno"> 136</span> {0, 0, 0}</div>
|
||||
<div class="line"><span class="lineno"> 137</span> };</div>
|
||||
<div class="line"><span class="lineno"> 138</span> <span class="keywordtype">int</span> n6 = 3, u6 = 0, v6 = 5; <span class="comment">// Node `v` is out of bounds (n = 3, so valid indices are 0, 1, 2)</span></div>
|
||||
<div class="line"><span class="lineno"> 139</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph6, u6, v6, n6) == 0); <span class="comment">// Should return 0 because `v = 5` is invalid</span></div>
|
||||
<div class="line"><span class="lineno"> 140</span> </div>
|
||||
<div class="line"><span class="lineno"> 141</span> std::cout << <span class="stringliteral">"All tests have successfully passed!\n"</span>;</div>
|
||||
<div class="line"><span class="lineno"> 142</span>}</div>
|
||||
<div class="ttc" id="anamespacegraph_html_a7c3adb1551bc527a7aa93f331b1c0987"><div class="ttname"><a href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a></div><div class="ttdeci">std::uint32_t count_paths(const std::vector< std::vector< std::uint32_t > > &A, std::uint32_t u, std::uint32_t v, std::uint32_t n)</div><div class="ttdoc">Counts the number of paths from node u to node v in a directed graph using Depth First Search (DFS)</div><div class="ttdef"><b>Definition</b> <a href="../../d2/d32/number__of__paths_8cpp_source.html#l00067">number_of_paths.cpp:67</a></div></div>
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<a href="../../d2/d32/number__of__paths_8cpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span></div>
|
||||
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
|
||||
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include <vector></span> </div>
|
||||
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include <iostream></span> </div>
|
||||
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <cassert></span> </div>
|
||||
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <cstdint></span> </div>
|
||||
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span></div>
|
||||
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="keyword">namespace </span><a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a> {</div>
|
||||
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span></div>
|
||||
<div class="foldopen" id="foldopen00034" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"><a class="line" href="../../df/dce/namespacegraph.html#af99fccdd19e8f223e8749561589a762b"> 34</a></span> std::uint32_t <a class="code hl_function" href="../../df/dce/namespacegraph.html#af99fccdd19e8f223e8749561589a762b">count_paths_dfs</a>(<span class="keyword">const</span> std::vector<std::vector<std::uint32_t>>& A, </div>
|
||||
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> std::uint32_t u, </div>
|
||||
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> std::uint32_t v, </div>
|
||||
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> std::uint32_t n, </div>
|
||||
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> std::vector<bool>& visited) {</div>
|
||||
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">if</span> (u == v) {</div>
|
||||
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span> <span class="keywordflow">return</span> 1; <span class="comment">// Base case: Reached the destination node</span></div>
|
||||
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> }</div>
|
||||
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
|
||||
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> visited[u] = <span class="keyword">true</span>; <span class="comment">// Mark the current node as visited</span></div>
|
||||
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> std::uint32_t path_count = 0; <span class="comment">// Count of all paths from `u` to `v`</span></div>
|
||||
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
|
||||
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> <span class="keywordflow">for</span> (std::uint32_t i = 0; i < n; i++) {</div>
|
||||
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordflow">if</span> (A[u][i] == 1 && !visited[i]) { <span class="comment">// Check if there is an edge and the node is not visited</span></div>
|
||||
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> path_count += <a class="code hl_function" href="../../df/dce/namespacegraph.html#af99fccdd19e8f223e8749561589a762b">count_paths_dfs</a>(A, i, v, n, visited); <span class="comment">// Recursively explore paths from `i` to `v`</span></div>
|
||||
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
|
||||
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
|
||||
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
|
||||
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> visited[u] = <span class="keyword">false</span>; <span class="comment">// Unmark the current node as visited (backtracking)</span></div>
|
||||
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">return</span> path_count;</div>
|
||||
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
|
||||
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span></div>
|
||||
<div class="foldopen" id="foldopen00067" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"><a class="line" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987"> 67</a></span> std::uint32_t <a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">count_paths</a>(<span class="keyword">const</span> std::vector<std::vector<std::uint32_t>>& A, </div>
|
||||
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> std::uint32_t u, </div>
|
||||
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> std::uint32_t v, </div>
|
||||
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> std::uint32_t n) {</div>
|
||||
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="comment">// Check for invalid nodes or empty graph</span></div>
|
||||
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">if</span> (u >= n || v >= n || A.empty() || A[0].empty()) {</div>
|
||||
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="keywordflow">return</span> 0; <span class="comment">// No valid paths if graph is empty or nodes are out of bounds</span></div>
|
||||
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> }</div>
|
||||
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
|
||||
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> std::vector<bool> visited(n, <span class="keyword">false</span>); <span class="comment">// Initialize a visited vector for tracking nodes</span></div>
|
||||
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="keywordflow">return</span> <a class="code hl_function" href="../../df/dce/namespacegraph.html#af99fccdd19e8f223e8749561589a762b">count_paths_dfs</a>(A, u, v, n, visited); <span class="comment">// Start DFS</span></div>
|
||||
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
|
||||
</div>
|
||||
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
|
||||
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span>} <span class="comment">// namespace graph</span></div>
|
||||
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span></div>
|
||||
<div class="foldopen" id="foldopen00086" data-start="{" data-end="}">
|
||||
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"><a class="line" href="../../d2/d32/number__of__paths_8cpp.html#aa8dca7b867074164d5f45b0f3851269d"> 86</a></span><span class="keyword">static</span> <span class="keywordtype">void</span> <a class="code hl_function" href="../../d2/d32/number__of__paths_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>() {</div>
|
||||
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// Test case 1: Simple directed graph with multiple paths</span></div>
|
||||
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> std::vector<std::vector<std::uint32_t>> graph1 = {</div>
|
||||
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> {0, 1, 0, 1, 0}, </div>
|
||||
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> {0, 0, 1, 0, 1}, </div>
|
||||
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> {0, 0, 0, 0, 1}, </div>
|
||||
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> {0, 0, 1, 0, 0}, </div>
|
||||
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> {0, 0, 0, 0, 0} </div>
|
||||
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> };</div>
|
||||
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> std::uint32_t n1 = 5, u1 = 0, v1 = 4;</div>
|
||||
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph1, u1, v1, n1) == 3); <span class="comment">// There are 3 paths from node 0 to 4</span></div>
|
||||
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
|
||||
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// Test case 2: No possible path (disconnected graph)</span></div>
|
||||
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> std::vector<std::vector<std::uint32_t>> graph2 = {</div>
|
||||
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> {0, 1, 0, 0, 0}, </div>
|
||||
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> {0, 0, 0, 0, 0}, </div>
|
||||
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> {0, 0, 0, 0, 1}, </div>
|
||||
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> {0, 0, 1, 0, 0}, </div>
|
||||
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> {0, 0, 0, 0, 0} </div>
|
||||
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> };</div>
|
||||
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> std::uint32_t n2 = 5, u2 = 0, v2 = 4;</div>
|
||||
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph2, u2, v2, n2) == 0); <span class="comment">// No path from node 0 to 4</span></div>
|
||||
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
|
||||
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="comment">// Test case 3: Cyclic graph with multiple paths</span></div>
|
||||
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> std::vector<std::vector<std::uint32_t>> graph3 = {</div>
|
||||
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> {0, 1, 0, 0, 0}, </div>
|
||||
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> {0, 0, 1, 1, 0}, </div>
|
||||
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> {1, 0, 0, 0, 1}, </div>
|
||||
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> {0, 0, 1, 0, 1}, </div>
|
||||
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> {0, 0, 0, 0, 0} </div>
|
||||
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> };</div>
|
||||
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> std::uint32_t n3 = 5, u3 = 0, v3 = 4;</div>
|
||||
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph3, u3, v3, n3) == 3); <span class="comment">// There are 3 paths from node 0 to 4</span></div>
|
||||
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
|
||||
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="comment">// Test case 4: Single node graph (self-loop)</span></div>
|
||||
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> std::vector<std::vector<std::uint32_t>> graph4 = {</div>
|
||||
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> {0}</div>
|
||||
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> };</div>
|
||||
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> std::uint32_t n4 = 1, u4 = 0, v4 = 0;</div>
|
||||
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph4, u4, v4, n4) == 1); <span class="comment">// There is self-loop, so 1 path from node 0 to 0</span></div>
|
||||
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
|
||||
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// Test case 5: Empty graph (no nodes, no paths)</span></div>
|
||||
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> std::vector<std::vector<std::uint32_t>> graph5 = {{}};</div>
|
||||
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> <span class="keywordtype">int</span> n5 = 0, u5 = 0, v5 = 0;</div>
|
||||
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph5, u5, v5, n5) == 0); <span class="comment">// There are no paths in an empty graph</span></div>
|
||||
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
|
||||
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <span class="comment">// Test case 6: Invalid nodes (out of bounds)</span></div>
|
||||
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> std::vector<std::vector<std::uint32_t>> graph6 = {</div>
|
||||
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> {0, 1, 0}, </div>
|
||||
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> {0, 0, 1}, </div>
|
||||
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> {0, 0, 0}</div>
|
||||
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> };</div>
|
||||
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="keywordtype">int</span> n6 = 3, u6 = 0, v6 = 5; <span class="comment">// Node `v` is out of bounds (n = 3, so valid indices are 0, 1, 2)</span></div>
|
||||
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> assert(<a class="code hl_function" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a>(graph6, u6, v6, n6) == 0); <span class="comment">// Should return 0 because `v = 5` is invalid</span></div>
|
||||
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
|
||||
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> std::cout << <span class="stringliteral">"All tests have successfully passed!\n"</span>;</div>
|
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span>}</div>
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</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span></div>
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<div class="foldopen" id="foldopen00148" data-start="{" data-end="}">
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"><a class="line" href="../../d2/d32/number__of__paths_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4"> 148</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="../../d2/d32/number__of__paths_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <a class="code hl_function" href="../../d2/d32/number__of__paths_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a>(); <span class="comment">// Run self-test implementations</span></div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span>}</div>
|
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</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="anamespacegraph_html_a7c3adb1551bc527a7aa93f331b1c0987"><div class="ttname"><a href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a></div><div class="ttdeci">std::uint32_t count_paths(const std::vector< std::vector< std::uint32_t > > &A, std::uint32_t u, std::uint32_t v, std::uint32_t n)</div><div class="ttdoc">Counts the number of paths from node u to node v in a directed graph using Depth First Search (DFS)</div><div class="ttdef"><b>Definition</b> <a href="#l00067">number_of_paths.cpp:67</a></div></div>
|
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<div class="ttc" id="anamespacegraph_html_af99fccdd19e8f223e8749561589a762b"><div class="ttname"><a href="../../df/dce/namespacegraph.html#af99fccdd19e8f223e8749561589a762b">graph::count_paths_dfs</a></div><div class="ttdeci">std::uint32_t count_paths_dfs(const std::vector< std::vector< std::uint32_t > > &A, std::uint32_t u, std::uint32_t v, std::uint32_t n, std::vector< bool > &visited)</div><div class="ttdoc">Helper function to perform DFS and count the number of paths from node u to node v</div><div class="ttdef"><b>Definition</b> <a href="#l00034">number_of_paths.cpp:34</a></div></div>
|
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<div class="ttc" id="anumber__of__paths_8cpp_html_aa8dca7b867074164d5f45b0f3851269d"><div class="ttname"><a href="../../d2/d32/number__of__paths_8cpp.html#aa8dca7b867074164d5f45b0f3851269d">test</a></div><div class="ttdeci">static void test()</div><div class="ttdoc">Self-test implementations.</div><div class="ttdef"><b>Definition</b> <a href="#l00086">number_of_paths.cpp:86</a></div></div>
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<div class="ttc" id="anumber__of__paths_8cpp_html_ae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../d2/d32/number__of__paths_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="#l00148">number_of_paths.cpp:148</a></div></div>
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<tr class="memdesc:a8e1b547cd407c0774e63f0dc95cda9e7"><td class="mdescLeft"> </td><td class="mdescRight">function to check whether the passed graph is bipartite or not <br /></td></tr>
|
||||
<tr class="memitem:a84b0551489c613a681cc83b34450da4b" id="r_a84b0551489c613a681cc83b34450da4b"><td class="memItemLeft" align="right" valign="top">bool </td><td class="memItemRight" valign="bottom"><a class="el" href="#a84b0551489c613a681cc83b34450da4b">isBipartite</a> (const std::vector< std::vector< int64_t > > &graph)</td></tr>
|
||||
<tr class="memdesc:a84b0551489c613a681cc83b34450da4b"><td class="mdescLeft"> </td><td class="mdescRight">returns true if the given graph is bipartite else returns false <br /></td></tr>
|
||||
<tr class="memitem:af99fccdd19e8f223e8749561589a762b" id="r_af99fccdd19e8f223e8749561589a762b"><td class="memItemLeft" align="right" valign="top">std::uint32_t </td><td class="memItemRight" valign="bottom"><a class="el" href="#af99fccdd19e8f223e8749561589a762b">count_paths_dfs</a> (const std::vector< std::vector< std::uint32_t > > &A, std::uint32_t u, std::uint32_t v, std::uint32_t n, std::vector< bool > &visited)</td></tr>
|
||||
<tr class="memdesc:af99fccdd19e8f223e8749561589a762b"><td class="mdescLeft"> </td><td class="mdescRight">Helper function to perform DFS and count the number of paths from node <span class="tt">u</span> to node <span class="tt">v</span> <br /></td></tr>
|
||||
<tr class="memitem:a7c3adb1551bc527a7aa93f331b1c0987" id="r_a7c3adb1551bc527a7aa93f331b1c0987"><td class="memItemLeft" align="right" valign="top">std::uint32_t </td><td class="memItemRight" valign="bottom"><a class="el" href="#a7c3adb1551bc527a7aa93f331b1c0987">count_paths</a> (const std::vector< std::vector< std::uint32_t > > &A, std::uint32_t u, std::uint32_t v, std::uint32_t n)</td></tr>
|
||||
<tr class="memdesc:a7c3adb1551bc527a7aa93f331b1c0987"><td class="mdescLeft"> </td><td class="mdescRight">Counts the number of paths from node <span class="tt">u</span> to node <span class="tt">v</span> in a directed graph using Depth First Search (DFS) <br /></td></tr>
|
||||
<tr class="memitem:ab7706341d006e20d1ae58274187a3346" id="r_ab7706341d006e20d1ae58274187a3346"><td class="memItemLeft" align="right" valign="top">int </td><td class="memItemRight" valign="bottom"><a class="el" href="#ab7706341d006e20d1ae58274187a3346">TravellingSalesmanProblem</a> (std::vector< std::vector< uint32_t > > *cities, int32_t src, uint32_t V)</td></tr>
|
||||
<tr class="memdesc:ab7706341d006e20d1ae58274187a3346"><td class="mdescLeft"> </td><td class="mdescRight">Function calculates the minimum path distance that will cover all the cities starting from the source. <br /></td></tr>
|
||||
</table>
|
||||
@@ -164,6 +168,7 @@ Functions</h2></td></tr>
|
||||
<p>A bipartite graph is the one whose nodes can be divided into two disjoint sets in such a way that the nodes in a set are not connected to each other at all, i.e. no intra-set connections. The only connections that exist are that of inter-set, i.e. the nodes from one set are connected to a subset of nodes in the other set. In this implementation, using a graph in the form of adjacency list, check whether the given graph is a bipartite or not.</p>
|
||||
<p>References used: <a href="https://www.geeksforgeeks.org/bipartite-graph/" target="_blank">GeeksForGeeks</a> </p><dl class="section author"><dt>Author</dt><dd><a href="https://github.com/tushar2407" target="_blank">tushar2407</a> for assert for IO operations for queue data structure for vector data structure</dd></dl>
|
||||
<p>Graphical algorithms</p>
|
||||
<p>for std::vector for IO operations for assert for fixed-size integer types (e.g., std::uint32_t)</p>
|
||||
<p>for std::min for IO operations for limits of integral types for std::vector</p>
|
||||
<p><a class="el" href="../../dc/d61/classgraph_1_1_graph.html">Graph</a> Algorithms </p>
|
||||
</div><a name="doc-func-members" id="doc-func-members"></a><h2 id="header-doc-func-members" class="groupheader">Function Documentation</h2>
|
||||
@@ -379,6 +384,129 @@ Functions</h2></td></tr>
|
||||
</div><!-- fragment -->
|
||||
</div>
|
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<a id="a7c3adb1551bc527a7aa93f331b1c0987" name="a7c3adb1551bc527a7aa93f331b1c0987"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#a7c3adb1551bc527a7aa93f331b1c0987">◆ </a></span>count_paths()</h2>
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<div class="memproto">
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||||
<table class="memname">
|
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<td class="memname">std::uint32_t graph::count_paths </td>
|
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<td>(</td>
|
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<td class="paramtype">const std::vector< std::vector< std::uint32_t > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
|
||||
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|
||||
<tr>
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<td class="paramkey"></td>
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<td class="paramtype">std::uint32_t</td> <td class="paramname"><span class="paramname"><em>u</em></span>, </td>
|
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<td class="paramkey"></td>
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<tr>
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<td class="paramkey"></td>
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<td></td>
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<td class="paramtype">std::uint32_t</td> <td class="paramname"><span class="paramname"><em>n</em></span> )</td>
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</div><div class="memdoc">
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|
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<p>Counts the number of paths from node <span class="tt">u</span> to node <span class="tt">v</span> in a directed graph using Depth First Search (DFS) </p>
|
||||
<dl class="params"><dt>Parameters</dt><dd>
|
||||
<table class="params">
|
||||
<tr><td class="paramname">A</td><td>adjacency matrix representing the graph (1: edge exists, 0: no edge) </td></tr>
|
||||
<tr><td class="paramname">u</td><td>the starting node </td></tr>
|
||||
<tr><td class="paramname">v</td><td>the destination node </td></tr>
|
||||
<tr><td class="paramname">n</td><td>the number of nodes in the graph </td></tr>
|
||||
</table>
|
||||
</dd>
|
||||
</dl>
|
||||
<dl class="section return"><dt>Returns</dt><dd>the number of paths from node <span class="tt">u</span> to node <span class="tt">v</span> </dd></dl>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../d2/d32/number__of__paths_8cpp_source.html#l00067">67</a> of file <a class="el" href="../../d2/d32/number__of__paths_8cpp_source.html">number_of_paths.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 70</span> {</div>
|
||||
<div class="line"><span class="lineno"> 71</span> <span class="comment">// Check for invalid nodes or empty graph</span></div>
|
||||
<div class="line"><span class="lineno"> 72</span> <span class="keywordflow">if</span> (u >= n || v >= n || A.empty() || A[0].empty()) {</div>
|
||||
<div class="line"><span class="lineno"> 73</span> <span class="keywordflow">return</span> 0; <span class="comment">// No valid paths if graph is empty or nodes are out of bounds</span></div>
|
||||
<div class="line"><span class="lineno"> 74</span> }</div>
|
||||
<div class="line"><span class="lineno"> 75</span> </div>
|
||||
<div class="line"><span class="lineno"> 76</span> std::vector<bool> visited(n, <span class="keyword">false</span>); <span class="comment">// Initialize a visited vector for tracking nodes</span></div>
|
||||
<div class="line"><span class="lineno"> 77</span> <span class="keywordflow">return</span> <a class="code hl_function" href="#af99fccdd19e8f223e8749561589a762b">count_paths_dfs</a>(A, u, v, n, visited); <span class="comment">// Start DFS</span></div>
|
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<div class="line"><span class="lineno"> 78</span> }</div>
|
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<div class="ttc" id="anamespacegraph_html_af99fccdd19e8f223e8749561589a762b"><div class="ttname"><a href="#af99fccdd19e8f223e8749561589a762b">graph::count_paths_dfs</a></div><div class="ttdeci">std::uint32_t count_paths_dfs(const std::vector< std::vector< std::uint32_t > > &A, std::uint32_t u, std::uint32_t v, std::uint32_t n, std::vector< bool > &visited)</div><div class="ttdoc">Helper function to perform DFS and count the number of paths from node u to node v</div><div class="ttdef"><b>Definition</b> <a href="../../d2/d32/number__of__paths_8cpp_source.html#l00034">number_of_paths.cpp:34</a></div></div>
|
||||
</div><!-- fragment -->
|
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</div>
|
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</div>
|
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<a id="af99fccdd19e8f223e8749561589a762b" name="af99fccdd19e8f223e8749561589a762b"></a>
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<h2 class="memtitle"><span class="permalink"><a href="#af99fccdd19e8f223e8749561589a762b">◆ </a></span>count_paths_dfs()</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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<td class="memname">std::uint32_t graph::count_paths_dfs </td>
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<td class="paramtype">const std::vector< std::vector< std::uint32_t > > &</td> <td class="paramname"><span class="paramname"><em>A</em></span>, </td>
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<p>Helper function to perform DFS and count the number of paths from node <span class="tt">u</span> to node <span class="tt">v</span> </p>
|
||||
<dl class="params"><dt>Parameters</dt><dd>
|
||||
<table class="params">
|
||||
<tr><td class="paramname">A</td><td>adjacency matrix representing the graph (1: edge exists, 0: no edge) </td></tr>
|
||||
<tr><td class="paramname">u</td><td>the starting node </td></tr>
|
||||
<tr><td class="paramname">v</td><td>the destination node </td></tr>
|
||||
<tr><td class="paramname">n</td><td>the number of nodes in the graph </td></tr>
|
||||
<tr><td class="paramname">visited</td><td>a vector to keep track of visited nodes in the current DFS path </td></tr>
|
||||
</table>
|
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</dd>
|
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</dl>
|
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<dl class="section return"><dt>Returns</dt><dd>the number of paths from node <span class="tt">u</span> to node <span class="tt">v</span> </dd></dl>
|
||||
|
||||
<p class="definition">Definition at line <a class="el" href="../../d2/d32/number__of__paths_8cpp_source.html#l00034">34</a> of file <a class="el" href="../../d2/d32/number__of__paths_8cpp_source.html">number_of_paths.cpp</a>.</p>
|
||||
<div class="fragment"><div class="line"><span class="lineno"> 38</span> {</div>
|
||||
<div class="line"><span class="lineno"> 39</span> <span class="keywordflow">if</span> (u == v) {</div>
|
||||
<div class="line"><span class="lineno"> 40</span> <span class="keywordflow">return</span> 1; <span class="comment">// Base case: Reached the destination node</span></div>
|
||||
<div class="line"><span class="lineno"> 41</span> }</div>
|
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<div class="line"><span class="lineno"> 42</span> </div>
|
||||
<div class="line"><span class="lineno"> 43</span> visited[u] = <span class="keyword">true</span>; <span class="comment">// Mark the current node as visited</span></div>
|
||||
<div class="line"><span class="lineno"> 44</span> std::uint32_t path_count = 0; <span class="comment">// Count of all paths from `u` to `v`</span></div>
|
||||
<div class="line"><span class="lineno"> 45</span> </div>
|
||||
<div class="line"><span class="lineno"> 46</span> <span class="keywordflow">for</span> (std::uint32_t i = 0; i < n; i++) {</div>
|
||||
<div class="line"><span class="lineno"> 47</span> <span class="keywordflow">if</span> (A[u][i] == 1 && !visited[i]) { <span class="comment">// Check if there is an edge and the node is not visited</span></div>
|
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<div class="line"><span class="lineno"> 48</span> path_count += <a class="code hl_function" href="#af99fccdd19e8f223e8749561589a762b">count_paths_dfs</a>(A, i, v, n, visited); <span class="comment">// Recursively explore paths from `i` to `v`</span></div>
|
||||
<div class="line"><span class="lineno"> 49</span> }</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>
|
||||
<div class="line"><span class="lineno"> 52</span> visited[u] = <span class="keyword">false</span>; <span class="comment">// Unmark the current node as visited (backtracking)</span></div>
|
||||
<div class="line"><span class="lineno"> 53</span> <span class="keywordflow">return</span> path_count;</div>
|
||||
<div class="line"><span class="lineno"> 54</span> }</div>
|
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</div><!-- fragment -->
|
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</div>
|
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</div>
|
||||
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|
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<h2 class="memtitle"><span class="permalink"><a href="#ab5428a3519267a28bba4b4310cfbb6ae">◆ </a></span>depth_first_search()</h2>
|
||||
|
||||
|
||||
@@ -8,6 +8,8 @@ var namespacegraph =
|
||||
[ "addEdge", "df/dce/namespacegraph.html#ad4016cfc80485a43748895a2c26c7d08", null ],
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[ "addEdge", "df/dce/namespacegraph.html#a0e30e0dca68cb6e4f671440819b35b6a", null ],
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[ "depth_first_search", "df/dce/namespacegraph.html#ab5428a3519267a28bba4b4310cfbb6ae", null ],
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||||
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||||
|
||||
@@ -147,6 +147,8 @@ Files</h2></td></tr>
|
||||
<tr class="memitem:lowest_5Fcommon_5Fancestor_2Ecpp" id="r_lowest_5Fcommon_5Fancestor_2Ecpp"><td class="memItemLeft" align="right" valign="top"><a href="de/dde/lowest__common__ancestor_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a> </td><td class="memItemRight" valign="bottom"><a class="el" href="de/dde/lowest__common__ancestor_8cpp.html">lowest_common_ancestor.cpp</a></td></tr>
|
||||
<tr class="memdesc:de/dde/lowest__common__ancestor_8cpp"><td class="mdescLeft"> </td><td class="mdescRight">Data structure for finding the lowest common ancestor of two vertices in a rooted tree using binary lifting. <br /></td></tr>
|
||||
<tr class="memitem:max_5Fflow_5Fwith_5Fford_5Ffulkerson_5Fand_5Fedmond_5Fkarp_5Falgo_2Ecpp" id="r_max_5Fflow_5Fwith_5Fford_5Ffulkerson_5Fand_5Fedmond_5Fkarp_5Falgo_2Ecpp"><td class="memItemLeft" align="right" valign="top"><a href="d2/d48/max__flow__with__ford__fulkerson__and__edmond__karp__algo_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a> </td><td class="memItemRight" valign="bottom"><b>max_flow_with_ford_fulkerson_and_edmond_karp_algo.cpp</b></td></tr>
|
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<tr class="memitem:number_5Fof_5Fpaths_2Ecpp" id="r_number_5Fof_5Fpaths_2Ecpp"><td class="memItemLeft" align="right" valign="top"><a href="d2/d32/number__of__paths_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a> </td><td class="memItemRight" valign="bottom"><a class="el" href="d2/d32/number__of__paths_8cpp.html">number_of_paths.cpp</a></td></tr>
|
||||
<tr class="memdesc:d2/d32/number__of__paths_8cpp"><td class="mdescLeft"> </td><td class="mdescRight">Algorithm to count paths between two nodes in a directed graph using DFS. <br /></td></tr>
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<tr class="memdesc:d8/db9/topological__sort_8cpp"><td class="mdescLeft"> </td><td class="mdescRight"><a href="https://en.wikipedia.org/wiki/Topological_sorting" target="_blank">Topological Sort Algorithm</a> <br /></td></tr>
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|
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@@ -17,6 +17,7 @@ var dir_12552d7fa429bf94a2e32e5cf39f7e69 =
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@@ -264,10 +264,11 @@ solve-a-rat-in-a-maze-c-java-pytho/" target="_blank">Rat in a Maze</a> algorithm
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<tr id="row_9_14_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="d9/d1c/kruskal_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><b>kruskal.cpp</b></td><td class="desc"></td></tr>
|
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<tr id="row_9_15_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="de/dde/lowest__common__ancestor_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="de/dde/lowest__common__ancestor_8cpp.html" target="_self">lowest_common_ancestor.cpp</a></td><td class="desc">Data structure for finding the lowest common ancestor of two vertices in a rooted tree using binary lifting </td></tr>
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<tr id="row_9_16_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="d2/d48/max__flow__with__ford__fulkerson__and__edmond__karp__algo_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><b>max_flow_with_ford_fulkerson_and_edmond_karp_algo.cpp</b></td><td class="desc"></td></tr>
|
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<tr id="row_9_17_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="da/d27/prim_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><b>prim.cpp</b></td><td class="desc"></td></tr>
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<tr id="row_9_18_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="d8/db9/topological__sort_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="d8/db9/topological__sort_8cpp.html" target="_self">topological_sort.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Topological_sorting" target="_blank">Topological Sort Algorithm</a> </td></tr>
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<tr id="row_9_19_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="d1/d1b/topological__sort__by__kahns__algo_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><b>topological_sort_by_kahns_algo.cpp</b></td><td class="desc"></td></tr>
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<tr id="row_9_20_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="de/d88/travelling__salesman__problem_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="de/d88/travelling__salesman__problem_8cpp.html" target="_self">travelling_salesman_problem.cpp</a></td><td class="desc">[Travelling Salesman Problem] (<a href="https://en.wikipedia.org/wiki/Travelling_salesman_problem">https://en.wikipedia.org/wiki/Travelling_salesman_problem</a>) implementation </td></tr>
|
||||
<tr id="row_9_17_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="d2/d32/number__of__paths_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="d2/d32/number__of__paths_8cpp.html" target="_self">number_of_paths.cpp</a></td><td class="desc">Algorithm to count paths between two nodes in a directed graph using DFS </td></tr>
|
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<tr id="row_9_18_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="da/d27/prim_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><b>prim.cpp</b></td><td class="desc"></td></tr>
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<tr id="row_9_19_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="d8/db9/topological__sort_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="d8/db9/topological__sort_8cpp.html" target="_self">topological_sort.cpp</a></td><td class="desc"><a href="https://en.wikipedia.org/wiki/Topological_sorting" target="_blank">Topological Sort Algorithm</a> </td></tr>
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<tr id="row_9_20_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="d1/d1b/topological__sort__by__kahns__algo_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><b>topological_sort_by_kahns_algo.cpp</b></td><td class="desc"></td></tr>
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<tr id="row_9_21_" class="even" style="display:none;"><td class="entry"><span style="width:32px;display:inline-block;"> </span><a href="de/d88/travelling__salesman__problem_8cpp_source.html"><span class="icondoc"><div class="doc-icon"></div></span></a><a class="el" href="de/d88/travelling__salesman__problem_8cpp.html" target="_self">travelling_salesman_problem.cpp</a></td><td class="desc">[Travelling Salesman Problem] (<a href="https://en.wikipedia.org/wiki/Travelling_salesman_problem">https://en.wikipedia.org/wiki/Travelling_salesman_problem</a>) implementation </td></tr>
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File diff suppressed because one or more lines are too long
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<li>circle_area() : <a class="el" href="dd/d47/namespacemath.html#a40e36c67da78d2131408c57ee091ad75">math</a></li>
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||||
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||||
<li>cone_volume() : <a class="el" href="dd/d47/namespacemath.html#a3fe35440c27758ecc2287e08217d63a7">math</a></li>
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||||
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|
||||
<li>cube_surface_perimeter() : <a class="el" href="dd/d47/namespacemath.html#a8998ca7b1886d1d7d00aef3b457a9b1b">math</a></li>
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||||
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@@ -122,6 +122,8 @@ $(function(){initNavTree('namespacemembers_func_c.html','',''); });
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|
||||
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||||
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||||
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|
||||
<li>cube_surface_perimeter() : <a class="el" href="dd/d47/namespacemath.html#a8998ca7b1886d1d7d00aef3b457a9b1b">math</a></li>
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