used to find the shorthest paths among all pairs of nodes in a graph,

Floyd-Warshall algorithm is a procedure, which is used to find the shorthest (longest) paths among all pairs of nodes in a graph, which does not contain any cycles of negative lenght. The main advantage of Floyd-Warshall algorithm is its simplicity.

Data Structures/Graphs/FloydWarshall.java

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+    import java.util.Scanner;
+
+     
+
+    public class FloydWarshall
+
+    {
+
+        private int distancematrix[][];
+
+        private int numberofvertices;
+
+        public static final int INFINITY = 999;
+
+     
+
+        public FloydWarshall(int numberofvertices)
+
+        {
+
+            distancematrix = new int[numberofvertices + 1][numberofvertices + 1];
+
+            this.numberofvertices = numberofvertices;
+
+        }
+
+     
+
+        public void floydwarshall(int adjacencymatrix[][])
+
+        {
+
+            for (int source = 1; source <= numberofvertices; source++)
+
+            {
+
+                for (int destination = 1; destination <= numberofvertices; destination++)
+
+                {
+
+                    distancematrix[source][destination] = adjacencymatrix[source][destination];
+
+                }
+
+            }
+
+     
+
+            for (int intermediate = 1; intermediate <= numberofvertices; intermediate++)
+
+            {
+
+                for (int source = 1; source <= numberofvertices; source++)
+
+                {
+
+                    for (int destination = 1; destination <= numberofvertices; destination++)
+
+                    {
+
+                        if (distancematrix[source][intermediate] + distancematrix[intermediate][destination]
+
+                             < distancematrix[source][destination])
+
+                            distancematrix[source][destination] = distancematrix[source][intermediate] 
+
+                                + distancematrix[intermediate][destination];
+
+                    }
+
+                }
+
+            }
+
+     
+
+            for (int source = 1; source <= numberofvertices; source++)
+
+                System.out.print("\t" + source);
+
+     
+
+            System.out.println();
+
+            for (int source = 1; source <= numberofvertices; source++)
+
+            {
+
+                System.out.print(source + "\t");
+
+                for (int destination = 1; destination <= numberofvertices; destination++)
+
+                {
+
+                    System.out.print(distancematrix[source][destination] + "\t");
+
+                }
+
+                System.out.println();
+
+            }
+
+        }
+
+     
+
+        public static void main(String... arg)
+
+        {
+
+            int adjacency_matrix[][];
+
+            int numberofvertices;
+
+     
+
+            Scanner scan = new Scanner(System.in);
+
+            System.out.println("Enter the number of vertices");
+
+            numberofvertices = scan.nextInt();
+
+     
+
+            adjacency_matrix = new int[numberofvertices + 1][numberofvertices + 1];
+
+            System.out.println("Enter the Weighted Matrix for the graph");
+
+            for (int source = 1; source <= numberofvertices; source++)
+
+            {
+
+                for (int destination = 1; destination <= numberofvertices; destination++)
+
+                {
+
+                    adjacency_matrix[source][destination] = scan.nextInt();
+
+                    if (source == destination)
+
+                    {
+
+                        adjacency_matrix[source][destination] = 0;
+
+                        continue;
+
+                    }
+
+                    if (adjacency_matrix[source][destination] == 0)
+
+                    {
+
+                        adjacency_matrix[source][destination] = INFINITY;
+
+                    }
+
+                }
+
+            }
+
+     
+
+            System.out.println("The Transitive Closure of the Graph");
+
+            FloydWarshall floydwarshall = new FloydWarshall(numberofvertices);
+
+            floydwarshall.floydwarshall(adjacency_matrix);
+
+            scan.close();
+
+        }
+
+    }