prim.cpp

//Prim's Minimum Spanning Tree (MST) algorithm using adjacency matrix representation
#include <bits/stdc++.h> 

using namespace std; 

  
// Number of vertices in the graph  
#define V 5  

  
// function to find the vertex with minimum key value, from the set of vertices   

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;  
}  

  
// function to print the constructed MST stored in parent[]  

void printMST(int parent[], int graph[V][V])  
{  

    cout<<"Edge \tWeight\n";  

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

        cout<<parent[i]<<" - "<<i<<" \t"<<graph[i][parent[i]]<<" \n";  
}  

  
// Function to construct and print MST for  
// a graph represented using adjacency matrix

void primMST(int graph[V][V])  
{  

    // Array to store constructed MST  

    int parent[V];  

      

    // Key values used to pick minimum weight edge in cut  

    int key[V];  

      

    // To represent set of vertices not yet included in MST  

    bool mstSet[V];  

  

    // Initialize all keys as INFINITE  

    for (int i = 0; i < V; i++)  

        key[i] = INT_MAX, mstSet[i] = false;  

  

    // Always include first vertex in MST

    key[0] = 0;  

    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 the 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, graph);  
}  

  
// Driver code 

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);  

  
 	cout<<"\n\n";
 	system("pause");
    return 0;  
}