JavaAlgorithms/DataStructures/Graphs/PrimMST.java

package 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] == 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;
    }

    // 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] = 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++)

        // graph[u][v] is non zero only for adjacent vertices of m
        // mstSet[v] is false for vertices not yet included in MST
        // Update the key only if graph[u][v] is smaller than key[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) {
    /* 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);
  }
}