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<div class="headertitle"><div class="title">number_of_paths.cpp</div></div>
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<div class="contents">
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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>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="preprocessor">#include <vector></span> </div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="preprocessor">#include <iostream></span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="preprocessor">#include <cassert></span> </div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="preprocessor">#include <cstdint></span> </div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span></div>
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<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>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span></div>
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<div class="foldopen" id="foldopen00034" data-start="{" data-end="}">
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<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>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> std::uint32_t u, </div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> std::uint32_t v, </div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> std::uint32_t n, </div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span> std::vector<bool>& visited) {</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> <span class="keywordflow">if</span> (u == v) {</div>
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<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>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span> }</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> </div>
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<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>
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<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>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> </div>
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<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>
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<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>
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<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>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> }</div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span> }</div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> </div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> visited[u] = <span class="keyword">false</span>; <span class="comment">// Unmark the current node as visited (backtracking)</span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> <span class="keywordflow">return</span> path_count;</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> }</div>
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</div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> </div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span></div>
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<div class="foldopen" id="foldopen00067" data-start="{" data-end="}">
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<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>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> std::uint32_t u, </div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> std::uint32_t v, </div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> std::uint32_t n) {</div>
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<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>
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<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>
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<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>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> }</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
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<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>
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<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>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> }</div>
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</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> </div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span>} <span class="comment">// namespace graph</span></div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span></div>
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<div class="foldopen" id="foldopen00086" data-start="{" data-end="}">
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<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>
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<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>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> std::vector<std::vector<std::uint32_t>> graph1 = {</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> {0, 1, 0, 1, 0}, </div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> {0, 0, 1, 0, 1}, </div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> {0, 0, 0, 0, 1}, </div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> {0, 0, 1, 0, 0}, </div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> {0, 0, 0, 0, 0} </div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> };</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> std::uint32_t n1 = 5, u1 = 0, v1 = 4;</div>
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<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>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="comment">// Test case 2: No possible path (disconnected graph)</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> std::vector<std::vector<std::uint32_t>> graph2 = {</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> {0, 1, 0, 0, 0}, </div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> {0, 0, 0, 0, 0}, </div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> {0, 0, 0, 0, 1}, </div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> {0, 0, 1, 0, 0}, </div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> {0, 0, 0, 0, 0} </div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> };</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> std::uint32_t n2 = 5, u2 = 0, v2 = 4;</div>
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<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>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> </div>
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<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>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> std::vector<std::vector<std::uint32_t>> graph3 = {</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> {0, 1, 0, 0, 0}, </div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> {0, 0, 1, 1, 0}, </div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> {1, 0, 0, 0, 1}, </div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> {0, 0, 1, 0, 1}, </div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> {0, 0, 0, 0, 0} </div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> };</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> std::uint32_t n3 = 5, u3 = 0, v3 = 4;</div>
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<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>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
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<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>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> std::vector<std::vector<std::uint32_t>> graph4 = {</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> {0}</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> };</div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> std::uint32_t n4 = 1, u4 = 0, v4 = 0;</div>
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<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>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> </div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <span class="comment">// Test case 5: Empty graph (no nodes, no paths)</span></div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span> std::vector<std::vector<std::uint32_t>> graph5 = {{}};</div>
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<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>
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<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>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> </div>
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<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>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> std::vector<std::vector<std::uint32_t>> graph6 = {</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> {0, 1, 0}, </div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> {0, 0, 1}, </div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> {0, 0, 0}</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> };</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> <span class="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>
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<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>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> </div>
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<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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