PrimMST.java

package com.thealgorithms.datastructures.graphs;

/**
 * A Java program for Prim's Minimum Spanning Tree (MST) algorithm. adjacency
 * matrix representation of the graph
 */
class PrimMST {

    // Number of vertices in the graph

    private static final int V = 5;

    // A utility function to find the vertex with minimum key
    // value, from the set of vertices not yet included in MST
    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] && 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] = Boolean.FALSE;
        }

        // Always include first 1st vertex in MST.
        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

        // The MST will have V vertices
        for (int count = 0; count < V - 1; count++) {
            // Pick thd minimum key vertex from the set of vertices
            // not yet included in MST
            int u = minKey(key, mstSet);

            // Add the picked vertex to the MST Set
            mstSet[u] = Boolean.TRUE;

            // Update key value and parent index of the adjacent
            // vertices of the picked vertex. Consider only those
            // vertices which are not yet included in MST
            for (int v = 0; v < V; v++) // Update the key only if graph[u][v] is smaller than key[v] // mstSet[v] is
                                        // false for vertices not yet included in MST // graph[u][v] is non zero only
                                        // for adjacent vertices of m
            {
                if (graph[u][v] != 0 && !mstSet[v] && 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) {
        /* Let us create the following graph
       2    3
    (0)--(1)--(2)
    |    / \   |
    6| 8/   \5 |7
    | /      \ |
    (3)-------(4)
         9          */
        PrimMST t = new PrimMST();
        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);
    }
}