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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="preprocessor">#include <climits></span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="preprocessor">#include <cstddef></span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="preprocessor">#include <iostream></span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span> </div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="keyword">using </span>std::cin;</div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="keyword">using </span>std::cout;</div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="keyword">using </span>std::endl;</div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span> </div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// Wrapper class for storing a graph</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="keyword">class </span><a class="code hl_class" href="../../da/d9a/class_graph.html">Graph</a> {</div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> <span class="keywordtype">int</span> vertexNum;</div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> <span class="keywordtype">int</span> **edges;</div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span> </div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> <span class="comment">// Constructs a graph with V vertices and E edges</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span> Graph(<span class="keywordtype">int</span> V) {</div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> this->vertexNum = V;</div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span> this->edges = <span class="keyword">new</span> <span class="keywordtype">int</span> *[V];</div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < V; i++) {</div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span> this->edges[i] = <span class="keyword">new</span> <span class="keywordtype">int</span>[V];</div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < V; j++) this->edges[i][j] = INT_MAX;</div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span> this->edges[i][i] = 0;</div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> }</div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> }</div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span> </div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> ~Graph() {</div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < vertexNum; i++) {</div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keyword">delete</span>[] edges[i];</div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span> }</div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span> <span class="keyword">delete</span>[] edges;</div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> }</div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> </div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="comment">// Adds the given edge to the graph</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordtype">void</span> addEdge(<span class="keywordtype">int</span> src, <span class="keywordtype">int</span> dst, <span class="keywordtype">int</span> weight) {</div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> this->edges[src][dst] = weight;</div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> }</div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span>};</div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// Utility function to print distances</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="keywordtype">void</span> print(<span class="keyword">const</span> std::vector<int>& dist, <span class="keywordtype">int</span> V) {</div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> cout << <span class="stringliteral">"\nThe Distance matrix for Floyd - Warshall"</span> << <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < V; i++) {</div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < V; j++) {</div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">if</span> (dist[i * V + j] != INT_MAX)</div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> cout << dist[i * V + j] << <span class="stringliteral">"\t"</span>;</div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span> <span class="keywordflow">else</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> cout << <span class="stringliteral">"INF"</span></div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span> << <span class="stringliteral">"\t"</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> cout << <a class="code hl_define" href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a>;</div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> }</div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span>}</div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">// The main function that finds the shortest path from a vertex</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// to all other vertices using Floyd-Warshall Algorithm.</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="keywordtype">void</span> FloydWarshall(<a class="code hl_class" href="../../da/d9a/class_graph.html">Graph</a> <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>) {</div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span> std::size_t V = <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.vertexNum;</div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span> std::vector<std::vector<int> > dist(V, std::vector<int>(V));</div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> </div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="comment">// Initialise distance array</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < V; i++)</div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < V; j++) dist[i][j] = <a class="code hl_namespace" href="../../df/dce/namespacegraph.html">graph</a>.edges[i][j];</div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> </div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// Calculate distances</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 0; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a> < V; <a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>++)</div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span> <span class="comment">// Choose an intermediate vertex</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < V; i++)</div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span> <span class="comment">// Choose a source vertex for given intermediate</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < V; j++)</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> <span class="comment">// Choose a destination vertex for above source vertex</span></div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> </div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> <span class="keywordflow">if</span> (dist[i][k] != INT_MAX && dist[k][j] != INT_MAX &&</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> dist[i][k] + dist[k][j] < dist[i][j])</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> <span class="comment">// If the distance through intermediate vertex is less than</span></div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> <span class="comment">// direct edge then update value in distance array</span></div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> dist[i][j] = dist[i][<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>] + dist[<a class="code hl_function" href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">k</a>][j];</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> </div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> <span class="comment">// Convert 2d array to 1d array for print</span></div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> std::vector<int> dist1d(V * V);</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < V; i++)</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < V; j++) dist1d[i * V + j] = dist[i][j];</div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> </div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> print(dist1d, V);</div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span>}</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span> </div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="comment">// Driver Function</span></div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="keywordtype">int</span> <a class="code hl_function" href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a>() {</div>
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<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> <span class="keywordtype">int</span> V, E;</div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordtype">int</span> src, dst, weight;</div>
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<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> cout << <span class="stringliteral">"Enter number of vertices: "</span>;</div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> cin >> V;</div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> cout << <span class="stringliteral">"Enter number of edges: "</span>;</div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> cin >> E;</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> <a class="code hl_class" href="../../da/d9a/class_graph.html">Graph</a> G(V);</div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < E; i++) {</div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> cout << <span class="stringliteral">"\nEdge "</span> << i + 1 << <span class="stringliteral">"\nEnter source: "</span>;</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> cin >> src;</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> cout << <span class="stringliteral">"Enter destination: "</span>;</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> cin >> dst;</div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> cout << <span class="stringliteral">"Enter weight: "</span>;</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> cin >> weight;</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> G.addEdge(src, dst, weight);</div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> }</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> FloydWarshall(G);</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="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span>}</div>
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<div class="ttc" id="aclass_graph_html"><div class="ttname"><a href="../../da/d9a/class_graph.html">Graph</a></div><div class="ttdef"><b>Definition</b> <a href="../../df/d14/bellman__ford_8cpp_source.html#l00014">bellman_ford.cpp:14</a></div></div>
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<div class="ttc" id="acomposite__simpson__rule_8cpp_html_a1b74d828b33760094906797042b89442"><div class="ttname"><a href="../../d4/d18/composite__simpson__rule_8cpp.html#a1b74d828b33760094906797042b89442">numerical_methods::simpson_method::k</a></div><div class="ttdeci">double k(double x)</div><div class="ttdoc">Another test function.</div><div class="ttdef"><b>Definition</b> <a href="../../d4/d18/composite__simpson__rule_8cpp_source.html#l00117">composite_simpson_rule.cpp:117</a></div></div>
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<div class="ttc" id="agenerate__parentheses_8cpp_html_gae66f6b31b5ad750f1fe042a706a4e3d4"><div class="ttname"><a href="../../dd/d1e/generate__parentheses_8cpp.html#gae66f6b31b5ad750f1fe042a706a4e3d4">main</a></div><div class="ttdeci">int main()</div><div class="ttdoc">Main function.</div><div class="ttdef"><b>Definition</b> <a href="../../dd/d1e/generate__parentheses_8cpp_source.html#l00110">generate_parentheses.cpp:110</a></div></div>
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<div class="ttc" id="amatrix__exponentiation_8cpp_html_a600eaf353befc174637855795f12d258"><div class="ttname"><a href="../../d7/d35/matrix__exponentiation_8cpp.html#a600eaf353befc174637855795f12d258">endl</a></div><div class="ttdeci">#define endl</div><div class="ttdef"><b>Definition</b> <a href="../../d7/d35/matrix__exponentiation_8cpp_source.html#l00036">matrix_exponentiation.cpp:36</a></div></div>
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<div class="ttc" id="anamespacegraph_html"><div class="ttname"><a href="../../df/dce/namespacegraph.html">graph</a></div><div class="ttdoc">Graph Algorithms.</div></div>
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