You are provided one skeleton program named Graph2.java. Implement the prim(int r) function for minimum spanning tree using PRIORITY QUEUE. You should return an integer that indicates the total weight of the minimum spanning tree. In order to associate each node with a weight and place it into the queue, you may need to create another class.

PLEASE TRY TO FOLLOW THE PSEUDO CODE AND THE INSTRUCTIONS. Thank you

package graph;

public class Graph2 {

public int n; /umber of vertice

public int[][] A;//the adjacency matrix

public Graph2 () {

n = 0;

A = null;

}

public Graph2 (int _n, int[][] _A) {

this.n = _n;

this.A = _A;

}

public int prim (int r) {

}

/**

* @param args

*/

public static void main(String[] args) {

// TODO Auto-generated method stub

int n = 9;

int A[][] = {

{0, 4, 0, 0, 0, 0, 0, 8, 0},

{4, 0, 8, 0, 0, 0, 0, 11, 0},

{0, 8, 0, 7, 0, 4, 0, 0, 2},

{0, 0, 7, 0, 9, 14, 0, 0, 0},

{0, 0, 0, 9, 0, 10, 0, 0, 0},

{0, 0, 4, 14, 10, 0, 2, 0, 0},

{0, 0, 0, 0, 0, 2, 0, 1, 6},

{8, 11, 0, 0, 0, 0, 1, 0, 7},

{0, 0, 2, 0, 0, 0, 6, 7, 0}

};

Graph2 g = new Graph2(n, A);

System.out.println(g.prim(0));

}

}

Minimum Spanning Tree MST-PRIM (G, w, r) Key idea: 1 for each u e G. V 2 Take r as the root of the tree. In each iteration, add one edge to the tree until it covers all the nodes 6 while Q 7 u ExTRACT-MIN ) 8 for each v E G.Adj[u] The min-priority queue Q includes all nodes that are not in the tree yet, where each node's key value is the minimum weight of any edge ifv e Q and w(u, v)