programming-examples/java/Graph_Problems_Algorithms/Java Program to Find MST(Minimum Spanning Tree) using Prim’s Algorithm.java

/*This Java program is to find MST using Prim’s algorithm.In computer science, Prim’s algorithm is a greedy algorithm that finds a minimum spanning tree for a connected weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.*/

import java.util.InputMismatchException;
import java.util.Scanner;

public class Prims
{
    private boolean unsettled[];
    private boolean settled[];
    private int numberofvertices;
    private int adjacencyMatrix[][];
    private int key[];
    public static final int INFINITE = 999;
    private int parent[];

    public Prims(int numberofvertices)
    {
        this.numberofvertices = numberofvertices;
        unsettled = new boolean[numberofvertices + 1];
        settled = new boolean[numberofvertices + 1];
        adjacencyMatrix = new int[numberofvertices + 1][numberofvertices + 1];
        key = new int[numberofvertices + 1];
        parent = new int[numberofvertices + 1];
    }

    public int getUnsettledCount(boolean unsettled[])
    {
        int count = 0;
        for (int index = 0; index < unsettled.length; index++)
            {
                if (unsettled[index])
                    {
                        count++;
                    }
            }
        return count;
    }

    public void primsAlgorithm(int adjacencyMatrix[][])
    {
        int evaluationVertex;
        for (int source = 1; source <= numberofvertices; source++)
            {
                for (int destination = 1; destination <= numberofvertices; destination++)
                    {
                        this.adjacencyMatrix[source][destination] = adjacencyMatrix[source][destination];
                    }
            }
        for (int index = 1; index <= numberofvertices; index++)
            {
                key[index] = INFINITE;
            }
        key[1] = 0;
        unsettled[1] = true;
        parent[1] = 1;
        while (getUnsettledCount(unsettled) != 0)
            {
                evaluationVertex = getMimumKeyVertexFromUnsettled(unsettled);
                unsettled[evaluationVertex] = false;
                settled[evaluationVertex] = true;
                evaluateNeighbours(evaluationVertex);
            }
    }

    private int getMimumKeyVertexFromUnsettled(boolean[] unsettled2)
    {
        int min = Integer.MAX_VALUE;
        int node = 0;
        for (int vertex = 1; vertex <= numberofvertices; vertex++)
            {
                if (unsettled[vertex] == true && key[vertex] < min)
                    {
                        node = vertex;
                        min = key[vertex];
                    }
            }
        return node;
    }

    public void evaluateNeighbours(int evaluationVertex)
    {
        for (int destinationvertex = 1; destinationvertex <= numberofvertices; destinationvertex++)
            {
                if (settled[destinationvertex] == false)
                    {
                        if (adjacencyMatrix[evaluationVertex][destinationvertex] != INFINITE)
                            {
                                if (adjacencyMatrix[evaluationVertex][destinationvertex] < key[destinationvertex])
                                    {
                                        key[destinationvertex] = adjacencyMatrix[evaluationVertex][destinationvertex];
                                        parent[destinationvertex] = evaluationVertex;
                                    }
                                unsettled[destinationvertex] = true;
                            }
                    }
            }
    }

    public void printMST()
    {
        System.out.println("SOURCE  : DESTINATION = WEIGHT");
        for (int vertex = 2; vertex <= numberofvertices; vertex++)
            {
                System.out.println(parent[vertex] + "\t:\t" + vertex +"\t=\t"+ adjacencyMatrix[parent[vertex]][vertex]);
            }
    }

    public static void main(String... arg)
    {
        int adjacency_matrix[][];
        int number_of_vertices;
        Scanner scan = new Scanner(System.in);
        try
            {
                System.out.println("Enter the number of vertices");
                number_of_vertices = scan.nextInt();
                adjacency_matrix = new int[number_of_vertices + 1][number_of_vertices + 1];
                System.out.println("Enter the Weighted Matrix for the graph");
                for (int i = 1; i <= number_of_vertices; i++)
                    {
                        for (int j = 1; j <= number_of_vertices; j++)
                            {
                                adjacency_matrix[i][j] = scan.nextInt();
                                if (i == j)
                                    {
                                        adjacency_matrix[i][j] = 0;
                                        continue;
                                    }
                                if (adjacency_matrix[i][j] == 0)
                                    {
                                        adjacency_matrix[i][j] = INFINITE;
                                    }
                            }
                    }
                Prims prims = new Prims(number_of_vertices);
                prims.primsAlgorithm(adjacency_matrix);
                prims.printMST();
            }
        catch (InputMismatchException inputMismatch)
            {
                System.out.println("Wrong Input Format");
            }
        scan.close();
    }
}

/*
Enter the number of vertices
5
Enter the Weighted Matrix for the graph
0 4 0 0 5
4 0 3 6 1
0 3 0 6 2
0 6 6 0 7
5 1 2 7 0
SOURCE  : DESTINATION   =    WEIGHT
1       :      2        =       4
5       :      3        =       2
2       :      4        =       6
2       :      5        =       1