C++ program to implement Prims algorithm














































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] = 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] && 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 



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