Prims algorithm to Dijkstra algorithm

Question

I am trying to make my existing implementation of Prim's algorithm to keep track distances from source . Since prim's and Dijkstra's algorithm are almost same. I can't figure out where am I missing something.

I know what the problem is but cannot figure it out.

Here is my code, how do I modify it to print the shortest distance from source to all other vertex. Shortest distance is stored in array named : dist[]

Code:

package Graphs;

import java.util.ArrayList;

public class Prims {

    static int no_of_vertices = 0;

    public static void main(String[] args) {
        int[][] graph = {{0, 2, 0, 6, 0},
                {2, 0, 3, 8, 5},
                {0, 3, 0, 0, 7},
                {6, 8, 0, 0, 9},
                {0, 5, 7, 9, 0},
               };
        no_of_vertices = graph.length;
        int [][] result =  new int [no_of_vertices][no_of_vertices];
        boolean[] visited = new boolean[no_of_vertices];
        int dist[] = new int[no_of_vertices];
        for (int i = 0; i < no_of_vertices; i++)
            for (int j = 0; j < no_of_vertices; j++) {
                result[i][j]= 0;
                if (graph[i][j] == 0) {
                    graph[i][j] = Integer.MAX_VALUE;
                }
            }

        for (int i = 0; i < no_of_vertices; i++) {
            visited[i] = false;
            dist[i] = 0;

        }
        ArrayList<String> arr = new ArrayList<String>();
        int min;
        visited[0] = true;
        int counter = 0;
        while (counter < no_of_vertices - 1) {
            min = 999;
            for (int i = 0; i < no_of_vertices; i++) {
                if (visited[i] == true) {
                    for (int j = 0; j < no_of_vertices; j++) {
                        if (!visited[j] && min > graph[i][j]) {
                            min = graph[i][j];
                            dist[i] += min; //  <------ Problem here
                            visited[j] = true;
                            arr.add("Src :" + i + " Destination : " + j
                                    + " Weight : " + min);
                        }
                    }
                }
            }
            counter++;
        }


        for (int i = 0; i < no_of_vertices; i++) {
            System.out.println("Source :  0" + " Destination : " + i
                    + " distance : " + dist[i]);
        }

        for (String str : arr) {
            System.out.println(str);
        }
    }
}

There is a mistake in calculation of distance array as it forgets to add the distance of any intermediate nodes from source to destination.

Answer 1

for (int j = 0; j < no_of_vertices; j++) {
    if (!visited[j] && min > graph[i][j]) {
        min = graph[i][j];
        dist[i] += min; //  <------ Problem here

Of course intermediate edges don't get added, because you only add the current edge. You probably want something like:

if (dist[i] + graph[i][j] < dist[j])
    dist[j] = dist[i] + graph[i][j];

And get rid of the min variable.

Although your algorithm does not look correct to me. You're supposed to pick the node with minimum d[] at each step, and update that node's neighbors as I wrote above, then mark it as picked and never pick it again.