Tuesday, 14 May 2013

12. WARSHALL'S ALGORITHM (ALL PAIRS SHORTEST PATH)


Code:
import java.io.*;
class AllPairsShortestPath(Warshalls)
{
            public static BufferedReader br =new BufferedReader(new InputStreamReader(System.in));
                       
            static int [][] G;
            static int n;
            public static void main (String[] args) throws IOException
            {
                        System.out.println("\t\t\t\tAll Pairs Shortest Path");
                        System.out.print("\nEnter the number of the vertices: ");
                        n = Integer.parseInt(br.readLine());
                        G = new int[n+1][n+1];
                        System.out.print("\nIf edge between the start and end nodes and its distance (enter -1               to quit) :\n");
                        for(int i=1;i<=n;i++)
                                    for(int j=1;j<=n;j++)
                                    {
                                                if(i != j)
                                                            G[i][j]= 400000;//+ve infinity
                                                else
                                                            G[i][j] = 0;
                                    }          
                        int i =0, j=0;
                        do{
                                    System.out.print("Enter start node: ");
                                    i = Integer.parseInt(br.readLine());
                                    if((i<=0)||(i>n))
                                    {
                                                if(i==-1)
                                                            break;
                                                System.out.println("Invalid start node!");
                                                continue;
                                    }
                                    System.out.print("Enter end node: ");
                                    j = Integer.parseInt(br.readLine());
                                   
                                    if((j<=0)||(j>n))
                                    {
                                                if(j==-1)
                                                            break;
                                                System.out.println("Invalid end node!");
                                                continue;
                                    }
                                    if(j == i)
                                    {
                                                System.out.println("Start and end node cant be same!");
                                                continue;
                                    }
                                               
                                    System.out.print("Enter distance between "+i+" and "+j+": ");
                                    G[i][j] = Integer.parseInt(br.readLine());
           
                        }while( (i !=-1 ) && (j!=-1) );
                       
                        System.out.println("\n\nSolution :");
                        APSP();
            }
            static void APSP()
            {
                                    int [][] A = new int[n+1][n+1];
                                    for(int i=1; i<=n; i++)
                                                for(int j=1; j<= n; j++)
                                                            A[i][j] = G[i][j];

                                    for(int k=1; k<=n; k++)
                                                for(int i=1; i<= n; i++)
                                                            for(int j=1; j<= n; j++)
                                                                        A[i][j] = Math.min(A[i][j], A[i][k]+A[k][j]);
                                                                       
                                    for(int i=1; i<=n; i++)
                                    {
                                                for(int j=1; j<= n; j++)
                                                {
                                                            System.out.print(A[i][j]+"\t");
                                                }
                                                System.out.println();
                                    }

            }
}



OUTPUT:
Enter the number of the vertices: 4

If edge between the start and end nodes and its distance (enter -1 to quit) :
Enter start node: 0
Invalid start node!
Enter start node: 1
Enter end node: 3
Enter distance between 1 and 3: 3
Enter start node: 2
Enter end node: 1
Enter distance between 2 and 1: 2
Enter start node: 4
Enter end node: 1
Enter distance between 4 and 1: 6
Enter start node: 3
Enter end node: 2
Enter distance between 3 and 2: 7
Enter start node: 3
Enter end node: 4
Enter distance between 3 and 4: 1
Enter start node: -1



Solution :
0       10      3       4
2       0       5       6
7       7       0       1
6       16      9       0





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