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Floyd.java
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Floyd.java
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/*
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.
/* Let us create the following weighted graph
10
(0)------->(3)
| /|\
5 | |
| | 1
\|/ |
(1)------->(2)
3
Enter number of nodes in the graph :
4
INPUT ADJ MATRIX 4x4
0 5 8 9
999 0 3 4
999 999 0 1
999 999 999 0
SHORTEST PATHS ARE :
0 5 8 9
999 0 3 4
999 999 0 1
999 999 999 0
*/
import java.util.*;
import java.io.*;
class Floyd
{
public static void main(String args[])
{
Scanner s=new Scanner(System.in);
int N;
//Input no of nodes
System.out.println("Enter number of nodes in the graph : ");
N=s.nextInt();
//Input Graph Matrix
int adj_mat[][]=new int[N][N];
System.out.println("\n\nINPUT ADJ MATRIX "+N+"x"+N+"\n\n");
for(int i=0;i<N;i++)
{
for(int j=0;j<N;j++)
adj_mat[i][j]=s.nextInt();
}
//Empty array where solution is stored
int A[][]=new int[N][N];
//Create object and call get_paths()
Floyd F=new Floyd();
F.get_paths(adj_mat,A,N);
}
void get_paths(int cost[][],int A[][],int n)
{
//Copy cost[][] to A[][]
for(int i=0;i<n;i++)
for(int j=0;j<n;j++)
A[i][j]=cost[i][j];
//loop through all pairs of vertices (n-1)times
for(int k=0;k<n;k++)
for(int i=0;i<n;i++)
for(int j=0;j<n;j++)
{ //assign minimum among : to A[i[][j]
//(1)Direct path from i to j i.e- adj[i][j] or
//(2)Path from i to j via k who's cost will be A[i][k]+A[k][j]
A[i][j]=Math.min(A[i][j],A[i][k]+A[k][j]);
}
//print the A[][]
System.out.println("\nSHORTEST PATHS ARE :\n\n");
for(int i=0;i<n;i++)
{
for(int j=0;j<n;j++)
System.out.print(A[i][j]+ " ");
System.out.println();
}
}
}