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/*This is a Java Program to Implement Warshall Transitive closure Algorithm. Warshall’s Transitive closure algorithm is used to determine if a path exists from vertex a to vertex b for all vertex pairs (a, b) in a graph.*/
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/**
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** Java Program to Implement Warshall Algorithm
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**/
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import java.util.Scanner;
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/** Class Warshall **/
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public class Warshall
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{
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private int V;
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private boolean[][] tc;
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/** Function to make the transitive closure **/
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public void getTC(int[][] graph)
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{
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this.V = graph.length;
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tc = new boolean[V][V];
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for (int i = 0; i < V; i++)
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{
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for (int j = 0; j < V; j++)
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if (graph[i][j] != 0)
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tc[i][j] = true;
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tc[i][i] = true;
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}
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for (int i = 0; i < V; i++)
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{
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for (int j = 0; j < V; j++)
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{
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if (tc[j][i])
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for (int k = 0; k < V; k++)
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if (tc[j][i] && tc[i][k])
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tc[j][k] = true;
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}
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}
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}
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/** Funtion to display the trasitive closure **/
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public void displayTC()
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{
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System.out.println("\nTransitive closure :\n");
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System.out.print(" ");
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for (int v = 0; v < V; v++)
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System.out.print(" " + v );
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System.out.println();
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for (int v = 0; v < V; v++)
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{
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System.out.print(v +" ");
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for (int w = 0; w < V; w++)
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{
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if (tc[v][w])
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System.out.print(" * ");
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else
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System.out.print(" ");
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}
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System.out.println();
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}
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}
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/** Main function **/
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public static void main (String[] args)
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{
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Scanner scan = new Scanner(System.in);
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System.out.println("Warshall Algorithm Test\n");
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/** Make an object of Warshall class **/
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Warshall w = new Warshall();
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/** Accept number of vertices **/
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System.out.println("Enter number of vertices\n");
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int V = scan.nextInt();
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/** get graph **/
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System.out.println("\nEnter matrix\n");
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int[][] graph = new int[V][V];
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for (int i = 0; i < V; i++)
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for (int j = 0; j < V; j++)
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graph[i][j] = scan.nextInt();
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w.getTC(graph);
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w.displayTC();
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}
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}
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/*
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Enter number of vertices
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6
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Enter matrix
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0 1 0 0 0 1
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0 0 0 0 0 0
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1 0 0 1 0 0
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0 0 0 0 0 0
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0 0 0 1 0 0
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0 0 0 0 1 0
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Transitive closure :
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0 1 2 3 4 5
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0 * * * * *
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1 *
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2 * * * * * *
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3 *
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4 * *
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5 * * *
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