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POFloyd Warshall algorithm using adjacency list
 

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  1. POFloyd Warshall algorithm using adjacency list
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    <p>I had implemented the Floyd Warshall algorithm using adjacency matrix in C++ as given below, but I used the adjacency matrix representation which made it very convenient to loop over the (i,j,k) indices. Is there a way to accomplish this in adjacency list represtation? I saw that even <a href="http://mcs.uwsuper.edu/sb/425/Prog/FloydWarshall.java" rel="nofollow">http://mcs.uwsuper.edu/sb/425/Prog/FloydWarshall.java</a> this site converts adjacency list into matrix before applying the algorithm.</p> <pre><code>int rowSize = numberOfGraphVertices, colSize = numberOfGraphVertices ; std::vector&lt;int&gt; shortestPathMatrix(rowSize * colSize, 10000000); for (int i = 0; i &lt; rowSize; ++i) shortestPathMatrix[i + i * colSize] = 0 ; cout &lt;&lt; "Done" &lt;&lt; endl ; int numEdges = 0; while(getline(infile, graphString)) // To get you all the lines. { pch = strtok_s(const_cast&lt;char *&gt; (graphString.c_str())," ", &amp;p2); int rowNumber = atoi(pch); //graphListVector[node1] = pch = strtok_s(NULL, " ", &amp;p2); int colNumber = atoi(pch); pch = strtok_s(NULL, " ", &amp;p2); int edgeWeight = atoi(pch); shortestPathMatrix[(rowNumber-1)*colSize + (colNumber-1)] = edgeWeight; ++numEdges; } cout&lt;&lt; "numberOfVertices"&lt;&lt;numberOfGraphVertices&lt;&lt;"NumberOfEdges"&lt;&lt; numEdges &lt;&lt;endl; t = clock(); //for (int i = 0 ; i &lt; 1002 ; ++i) cout &lt;&lt; "Value" &lt;&lt; i &lt;&lt;" " &lt;&lt; shortestPathMatrix[i] &lt;&lt; endl; for (int k = 0 ; k &lt; rowSize ; ++k){ for (int i = 0 ; i &lt; rowSize ; ++i){ for (int j = 0; j &lt; rowSize ; ++j){ if ( shortestPathMatrix[j*colSize + i] + shortestPathMatrix[i*colSize + k] &lt; shortestPathMatrix[j*colSize + k]) shortestPathMatrix[j*colSize + k] = shortestPathMatrix[j*colSize + i] + shortestPathMatrix[i*colSize + k]; } } } for (int i = 0; i &lt; rowSize; ++i) { if (shortestPathMatrix[i + i * colSize] &lt; 0) cout &lt;&lt; "Negative cycle found" &lt;&lt; endl; break; } std::vector&lt;int&gt;::iterator minShortestPathIndex = std::min_element (shortestPathMatrix.begin(), shortestPathMatrix.end()); </code></pre>
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    1. COYes, there is a way. What is your real question? Why do you want to use an adjacency list, rather than an adjacency matrix?
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    2. COJust to save on memory, but I suppose all pairs shortest path would mean, we will have to use memory anyway, right?
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    3. COYeah, you have to allocate O(V^2) for the solution table anyways. You won't save any memory by doing it directly from an adjacency list.
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      1. USkevmo314
 

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