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<p>Algorithm to count paths between two nodes in a directed graph using DFS.
<a href="#details">More...</a></p>
<div class="textblock"><code>#include &lt;vector&gt;</code><br />
<code>#include &lt;iostream&gt;</code><br />
<code>#include &lt;cassert&gt;</code><br />
<code>#include &lt;cstdint&gt;</code><br />
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Include dependency graph for number_of_paths.cpp:</div>
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Namespaces</h2></td></tr>
<tr class="memitem:graph" id="r_graph"><td class="memItemLeft" align="right" valign="top">namespace &#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html">graph</a></td></tr>
<tr class="memdesc:df/dce/namespacegraph"><td class="mdescLeft">&#160;</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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Functions</h2></td></tr>
<tr class="memitem:af99fccdd19e8f223e8749561589a762b" id="r_af99fccdd19e8f223e8749561589a762b"><td class="memItemLeft" align="right" valign="top">std::uint32_t&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#af99fccdd19e8f223e8749561589a762b">graph::count_paths_dfs</a> (const std::vector&lt; std::vector&lt; std::uint32_t &gt; &gt; &amp;A, std::uint32_t u, std::uint32_t v, std::uint32_t n, std::vector&lt; bool &gt; &amp;visited)</td></tr>
<tr class="memdesc:af99fccdd19e8f223e8749561589a762b"><td class="mdescLeft">&#160;</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&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="../../df/dce/namespacegraph.html#a7c3adb1551bc527a7aa93f331b1c0987">graph::count_paths</a> (const std::vector&lt; std::vector&lt; std::uint32_t &gt; &gt; &amp;A, std::uint32_t u, std::uint32_t v, std::uint32_t n)</td></tr>
<tr class="memdesc:a7c3adb1551bc527a7aa93f331b1c0987"><td class="mdescLeft">&#160;</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&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#aa8dca7b867074164d5f45b0f3851269d">test</a> ()</td></tr>
<tr class="memdesc:aa8dca7b867074164d5f45b0f3851269d"><td class="mdescLeft">&#160;</td><td class="mdescRight">Self-test implementations. <br /></td></tr>
<tr class="memitem:ae66f6b31b5ad750f1fe042a706a4e3d4" id="r_ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="memItemLeft" align="right" valign="top">int&#160;</td><td class="memItemRight" valign="bottom"><a class="el" href="#ae66f6b31b5ad750f1fe042a706a4e3d4">main</a> ()</td></tr>
<tr class="memdesc:ae66f6b31b5ad750f1fe042a706a4e3d4"><td class="mdescLeft">&#160;</td><td class="mdescRight">Main function. <br /></td></tr>
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<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>
<dl class="section author"><dt>Author</dt><dd><a href="https://github.com/adi776borate" target="_blank">Aditya Borate</a> </dd></dl>
<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>
<a id="ae66f6b31b5ad750f1fe042a706a4e3d4" name="ae66f6b31b5ad750f1fe042a706a4e3d4"></a>
<h2 class="memtitle"><span class="permalink"><a href="#ae66f6b31b5ad750f1fe042a706a4e3d4">&#9670;&#160;</a></span>main()</h2>
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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>
<div class="line"><span class="lineno"> 150</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><span class="lineno"> 151</span>}</div>
<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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<h2 class="memtitle"><span class="permalink"><a href="#aa8dca7b867074164d5f45b0f3851269d">&#9670;&#160;</a></span>test()</h2>
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<td class="memname">void test </td>
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<td class="paramname"><span class="paramname"><em></em></span></td><td>)</td>
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<p>Self-test implementations. </p>
<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>
<div class="fragment"><div class="line"><span class="lineno"> 86</span> {</div>
<div class="line"><span class="lineno"> 87</span> <span class="comment">// Test case 1: Simple directed graph with multiple paths</span></div>
<div class="line"><span class="lineno"> 88</span> std::vector&lt;std::vector&lt;std::uint32_t&gt;&gt; graph1 = {</div>
<div class="line"><span class="lineno"> 89</span> {0, 1, 0, 1, 0}, </div>
<div class="line"><span class="lineno"> 90</span> {0, 0, 1, 0, 1}, </div>
<div class="line"><span class="lineno"> 91</span> {0, 0, 0, 0, 1}, </div>
<div class="line"><span class="lineno"> 92</span> {0, 0, 1, 0, 0}, </div>
<div class="line"><span class="lineno"> 93</span> {0, 0, 0, 0, 0} </div>
<div class="line"><span class="lineno"> 94</span> };</div>
<div class="line"><span class="lineno"> 95</span> std::uint32_t n1 = 5, u1 = 0, v1 = 4;</div>
<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>
<div class="line"><span class="lineno"> 97</span> </div>
<div class="line"><span class="lineno"> 98</span> <span class="comment">// Test case 2: No possible path (disconnected graph)</span></div>
<div class="line"><span class="lineno"> 99</span> std::vector&lt;std::vector&lt;std::uint32_t&gt;&gt; graph2 = {</div>
<div class="line"><span class="lineno"> 100</span> {0, 1, 0, 0, 0}, </div>
<div class="line"><span class="lineno"> 101</span> {0, 0, 0, 0, 0}, </div>
<div class="line"><span class="lineno"> 102</span> {0, 0, 0, 0, 1}, </div>
<div class="line"><span class="lineno"> 103</span> {0, 0, 1, 0, 0}, </div>
<div class="line"><span class="lineno"> 104</span> {0, 0, 0, 0, 0} </div>
<div class="line"><span class="lineno"> 105</span> };</div>
<div class="line"><span class="lineno"> 106</span> std::uint32_t n2 = 5, u2 = 0, v2 = 4;</div>
<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>
<div class="line"><span class="lineno"> 108</span> </div>
<div class="line"><span class="lineno"> 109</span> <span class="comment">// Test case 3: Cyclic graph with multiple paths</span></div>
<div class="line"><span class="lineno"> 110</span> std::vector&lt;std::vector&lt;std::uint32_t&gt;&gt; graph3 = {</div>
<div class="line"><span class="lineno"> 111</span> {0, 1, 0, 0, 0}, </div>
<div class="line"><span class="lineno"> 112</span> {0, 0, 1, 1, 0}, </div>
<div class="line"><span class="lineno"> 113</span> {1, 0, 0, 0, 1}, </div>
<div class="line"><span class="lineno"> 114</span> {0, 0, 1, 0, 1}, </div>
<div class="line"><span class="lineno"> 115</span> {0, 0, 0, 0, 0} </div>
<div class="line"><span class="lineno"> 116</span> };</div>
<div class="line"><span class="lineno"> 117</span> std::uint32_t n3 = 5, u3 = 0, v3 = 4;</div>
<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>
<div class="line"><span class="lineno"> 119</span> </div>
<div class="line"><span class="lineno"> 120</span> <span class="comment">// Test case 4: Single node graph (self-loop)</span></div>
<div class="line"><span class="lineno"> 121</span> std::vector&lt;std::vector&lt;std::uint32_t&gt;&gt; graph4 = {</div>
<div class="line"><span class="lineno"> 122</span> {0}</div>
<div class="line"><span class="lineno"> 123</span> };</div>
<div class="line"><span class="lineno"> 124</span> std::uint32_t n4 = 1, u4 = 0, v4 = 0;</div>
<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>
<div class="line"><span class="lineno"> 126</span> </div>
<div class="line"><span class="lineno"> 127</span> <span class="comment">// Test case 5: Empty graph (no nodes, no paths)</span></div>
<div class="line"><span class="lineno"> 128</span> std::vector&lt;std::vector&lt;std::uint32_t&gt;&gt; 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&lt;std::vector&lt;std::uint32_t&gt;&gt; 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 &lt;&lt; <span class="stringliteral">&quot;All tests have successfully passed!\n&quot;</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&lt; std::vector&lt; std::uint32_t &gt; &gt; &amp;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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