Add Prim's Algorithm with easy-to-understand comments

[Mayank29903]

#include
#include
#include // for INT_MAX
using namespace std;

// Prim's Algorithm: Find Minimum Spanning Tree (MST)
void primsAlgorithm(int V, vector<vector> &graph) {
vector key(V, INT_MAX); // Minimum weight edge for each vertex
vector mstSet(V, false); // True if vertex included in MST
vector parent(V, -1); // To store MST structure

key[0] = 0; // Start from vertex 0

for (int count = 0; count < V - 1; count++) {
    int minKey = INT_MAX, u;

    // Pick the vertex with the smallest key value not yet included in MST
    for (int v = 0; v < V; v++) {
        if (!mstSet[v] && key[v] < minKey) {
            minKey = key[v];
            u = v;
        }
    }

    mstSet[u] = true; // Include this vertex in MST

    // Update the key and parent of adjacent vertices
    for (int v = 0; v < V; v++) {
        // graph[u][v] != 0 means there is an edge
        if (graph[u][v] && !mstSet[v] && graph[u][v] < key[v]) {
            parent[v] = u;
            key[v] = graph[u][v];
        }
    }
}

// Print the Minimum Spanning Tree
cout << "Edge \tWeight\n";
for (int i = 1; i < V; i++)
    cout << parent[i] << " - " << i << "\t" << graph[i][parent[i]] << "\n";

}

int main() {
int V;
cout << "Enter number of vertices: ";
cin >> V;

vector<vector<int>> graph(V, vector<int>(V));
cout << "Enter adjacency matrix (0 if no edge):\n";
for (int i = 0; i < V; i++)
    for (int j = 0; j < V; j++)
        cin >> graph[i][j];

primsAlgorithm(V, graph);
return 0;

}