 ### C++ program to implement Prims algorithm

C++ Program to find the minimum spanning tree of the given graph using Prims algorithm. Prim’s algorithm is a greedy algorithm that finds a minimum spanning tree for a connected weighted undirected graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized.
Program:
#include <stdio.h>
#include <limits.h>
#include <iostream>

using namespace std;

// Number of vertices in the graph
#define 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[], bool mstSet[])
{
// Initialize min value
int min = INT_MAX, min_index;

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[]
int printMST(int parent[], int n, int graph[V][V])
{
cout<<"Edge   Weight\n";
for (int i = 1; i < V; i++)
printf("%d - %d    %d \n", parent[i], i, graph[i][parent[i]]);
return 0;
}

// Function to construct and print MST for a graph represented using adjacency
// matrix representation
void primMST(int graph[V][V])
{
int parent[V]; // Array to store constructed MST
int key[V]; // Key values used to pick minimum weight edge in cut
bool mstSet[V]; // To represent set of vertices not yet included in MST

// Initialize all keys as INFINITE
for (int i = 0; i < V; i++)
key[i] = INT_MAX, mstSet[i] = false;

// Always include first 1st vertex in MST.
key = 0; // Make key 0 so that this vertex is picked as first vertex
parent = -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] && mstSet[v] == false && graph[u][v] < key[v])
parent[v] = u, key[v] = graph[u][v];
}

// print the constructed MST
printMST(parent, V, graph);
}

// driver program to test above function
int main()
{
/* Let us create the following graph
2    3
(0)--(1)--(2)
|   / \   |
6| 8/   \5 |7
| /     \ |
(3)-------(4)
9          */
int graph[V][V] = { { 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
primMST(graph);

return 0;
}
Output:
Edge   Weight
0 - 1    2
1 - 2    3
0 - 3    6
1 - 4    5 #### More Articles of Shaik Aftab Ahmed:

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