package graphs;

import java.lang.*;

// Problem Title => Implement Prims Algorithms

public class Graph_Problem_20 {

// 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[][] graph) {

System.out.println("Edge \tWeight");

for (int i = 1; i < V; i++)

System.out.println(parent[i] + " - " + i + "\t" + 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 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] && graph[u][v] < key[v]) {

parent[v] = u;

key[v] = graph[u][v];

}

}

// print the constructed MST

printMST(parent, 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 */

Graph_Problem_19 t = new Graph_Problem_19();

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);

}

}