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PrimMST.java

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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);

}

}