c: Prim's Algorithm

/**
 * *****************************************************************************
 * @file        PrimsAlgorithm.c
 * @brief       Prim's Algorithm
 * @author       (geovindu,Geovin Du,涂聚文)
 * @date        2023-09-26
 * @copyright   geovindu
 * *****************************************************************************
 */

#include<stdio.h>
#include<stdbool.h> 
#include "include/PrimsAlgorithm.h"



/**
 * @brief       
 * 
 */
void Prims(int G[V][V])
{
    
    int no_edge;  // number of edge

    // create a array to track selected vertex
    // selected will become true otherwise false
    int selected[V];

    // set selected false initially
    memset(selected, false, sizeof(selected));
    
    // set number of edge to 0
    no_edge = 0;

    // the number of egde in minimum spanning tree will be
    // always less than (V -1), where V is number of vertices in
    //graph

    // choose 0th vertex and make it true
    selected[0] = true;

    int x;  //  row number
    int y;  //  col number

    // print for edge and weight
    printf("\n16.Prim's Algorithm\n Edge : Weight\n");

    while (no_edge < V - 1) {
        //For every vertex in the set S, find the all adjacent vertices
        // , calculate the distance from the vertex selected at step 1.
        // if the vertex is already in the set S, discard it otherwise
        //choose another vertex nearest to selected vertex  at step 1.

        int min = INF;
        x = 0;
        y = 0;

        for (int i = 0; i < V; i++) {
        if (selected[i]) {
            for (int j = 0; j < V; j++) {
            if (!selected[j] && G[i][j]) {  // not in selected and there is an edge
                if (min > G[i][j]) {
                min = G[i][j];
                x = i;
                y = j;
                }
            }
            }
        }
        }
        printf("%d - %d : %d\n", x, y, G[x][y]);
        selected[y] = true;
        no_edge++;


    }
}

    //16 Prim's Algorithm
    int G[V][V] = {
    {0, 9, 75, 0, 0},
    {9, 0, 95, 19, 42},
    {75, 95, 0, 51, 66},
    {0, 19, 51, 0, 31},
    {0, 42, 66, 31, 0}};
    Prims(G);