Minimum Spanning Trees: Growing a Minimum Spanning Tree Explained

#include <stdio.h>
#include <stdbool.h>
#include <limits.h>

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

// Function to find the vertex with minimum key value
int minKey(int key[], bool mstSet[]) {
    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
void printMST(int parent[], int graph[V][V]) {
    printf("Edge \tWeight\n");
    for (int i = 1; i < V; i++) {
        printf("%d - %d \t%d \n", parent[i], i, graph[i][parent[i]]);
    }
}

// Function to construct and print MST using Prim's algorithm
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
    bool mstSet[V];     // To represent set of vertices included in MST

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

    // Always include first vertex in MST
    key[0] = 0;         // Make key 0 so this vertex is picked first
    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 vertices not yet 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 adjacent vertices
        for (int v = 0; v < V; v++) {
            // Update key only if graph[u][v] is not 0 (adjacent), 
            // v is not in mstSet, and graph[u][v] is smaller than current 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);
}

int main() {
    /* Example graph represented as adjacency matrix
          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}
    };

    primMST(graph);

    return 0;
}