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円 |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);
 }
}