floyd warshall.cpp

The Floyd Warshall Algorithm is for solving the All Pairs Shortest Path problem. The problem is to find shortest distances between every pair of vertices in a given edge weighted directed Graph.

Author: steffinstanly

DP/Floyd Warshall Algorithm/Floyd Warshall Algorithm.cpp

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+// C Program for Floyd Warshall Algorithm 
+#include<stdio.h> 
+  
+// Number of vertices in the graph 
+#define V 4 
+  
+/* Define Infinite as a large enough value. This value will be used 
+  for vertices not connected to each other */
+#define INF 99999 
+  
+// A function to print the solution matrix 
+void printSolution(int dist[][V]); 
+  
+// Solves the all-pairs shortest path problem using Floyd Warshall algorithm 
+void floydWarshall (int graph[][V]) 
+{ 
+    /* dist[][] will be the output matrix that will finally have the shortest  
+      distances between every pair of vertices */
+    int dist[V][V], i, j, k; 
+  
+    /* Initialize the solution matrix same as input graph matrix. Or  
+       we can say the initial values of shortest distances are based 
+       on shortest paths considering no intermediate vertex. */
+    for (i = 0; i < V; i++) 
+        for (j = 0; j < V; j++) 
+            dist[i][j] = graph[i][j]; 
+  
+    /* Add all vertices one by one to the set of intermediate vertices. 
+      ---> Before start of an iteration, we have shortest distances between all 
+      pairs of vertices such that the shortest distances consider only the 
+      vertices in set {0, 1, 2, .. k-1} as intermediate vertices. 
+      ----> After the end of an iteration, vertex no. k is added to the set of 
+      intermediate vertices and the set becomes {0, 1, 2, .. k} */
+    for (k = 0; k < V; k++) 
+    { 
+        // Pick all vertices as source one by one 
+        for (i = 0; i < V; i++) 
+        { 
+            // Pick all vertices as destination for the 
+            // above picked source 
+            for (j = 0; j < V; j++) 
+            { 
+                // If vertex k is on the shortest path from 
+                // i to j, then update the value of dist[i][j] 
+                if (dist[i][k] + dist[k][j] < dist[i][j]) 
+                    dist[i][j] = dist[i][k] + dist[k][j]; 
+            } 
+        } 
+    } 
+  
+    // Print the shortest distance matrix 
+    printSolution(dist); 
+} 
+  
+/* A utility function to print solution */
+void printSolution(int dist[][V]) 
+{ 
+    printf ("The following matrix shows the shortest distances"
+            " between every pair of vertices \n"); 
+    for (int i = 0; i < V; i++) 
+    { 
+        for (int j = 0; j < V; j++) 
+        { 
+            if (dist[i][j] == INF) 
+                printf("%7s", "INF"); 
+            else
+                printf ("%7d", dist[i][j]); 
+        } 
+        printf("\n"); 
+    } 
+} 
+  
+// driver program to test above function 
+int main() 
+{ 
+    /* Let us create the following weighted graph 
+            10 
+       (0)------->(3) 
+        |         /|\ 
+      5 |          | 
+        |          | 1 
+       \|/         | 
+       (1)------->(2) 
+            3           */
+    int graph[V][V] = { {0,   5,  INF, 10}, 
+                        {INF, 0,   3, INF}, 
+                        {INF, INF, 0,   1}, 
+                        {INF, INF, INF, 0} 
+                      }; 
+  
+    // Print the solution 
+    floydWarshall(graph); 
+    return 0; 
+}