Prim’s Algorithm Objective: Implement Prim’s algorithm and run it on a weighted

Question

Prim’s Algorithm

Objective:

Implement Prim’s algorithm and run it on a weighted graph of your own creation. The algorithm is used to find the minimum spanning tree in a graph. This is a greedy algorithm traverses each edge of the graph only keeping the smallest connections to each node. For more information look here:

http://en.wikipedia.org/wiki/Prim%27s_algorithm

Demonstrate the algorithm works by printing out every edge with weights in your graph, and then printing out the minimum spanning tree.

Explanation / Answer

Program:

import java.util.*;
import java.lang.*;
import java.io.*;

class MST
{
private static final int V=5;

int minKey(int key[], Boolean mstSet[])
{
// Initialize min value
int min = Integer.MAX_VALUE, min_index=-1;

for (int v = 0; v < V; v++)
if (mstSet[v] == false && key[v] < min)
{
min = key[v];
min_index = v;
}

return min_index;
}

// A utility function to print the constructed MST stored in
// parent[]
void printMST(int parent[], int n, int graph[][])
{
System.out.println("Edge Weight");
for (int i = 1; i < V; i++)
System.out.println(parent[i]+" - "+ i+" "+
graph[i][parent[i]]);
}

// Function to construct and print MST for a graph represented
// using adjacency matrix representation
void primMST(int graph[][])
{
// Array to store constructed MST
int parent[] = new int[V];

// Key values used to pick minimum weight edge in cut
int key[] = new int [V];

// To represent set of vertices not yet included in MST
Boolean mstSet[] = new Boolean[V];

// Initialize all keys as INFINITE
for (int i = 0; i < V; i++)
{
key[i] = Integer.MAX_VALUE;
mstSet[i] = false;
}

key[0] = 0; // Make key 0 so that this vertex is
// picked as first vertex
parent[0] = -1; // First node is always root of MST
for (int count = 0; count < V-1; count++)
{

int u = minKey(key, mstSet);
mstSet[u] = true;

  
for (int v = 0; v < V; v++)
if (graph[u][v]!=0 && mstSet[v] == false && graph[u][v] < key[v])
{
parent[v] = u;
key[v] = graph[u][v];
}
}

// print the constructed MST
printMST(parent, V, graph);
}

public static void main (String[] args)
{
  
MST t = new MST();
int graph[][] = new int[][] {{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},
};

// Print the solution
t.primMST(graph);
}
}

Result:

Edge Weight
0 - 1 2
1 - 2 3
0 - 3 6
1 - 4 5

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