## Program to implement prim’s algorithm

Objective: C program to find the minimum spanning tree to design prim’s algorithm using greedy method

Time Complexities: The time required by algorithm Prim is O(n²), where n is the number of vertices in the graph G.

				
#include<stdio.h>
#include<conio.h>
int n, cost[10][10];
void prim() {
int i, j, startVertex, endVertex;
int k, nr[10], temp, minimumCost = 0, tree[10][3];
/* For first smallest edge */
temp = cost[0][0];
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
if (temp > cost[i][j]) {
temp = cost[i][j];
startVertex = i;
endVertex = j;
}
}
}
/* Now we have fist smallest edge in graph */
tree[0][0] = startVertex;
tree[0][1] = endVertex;
tree[0][2] = temp;
minimumCost = temp;
/* Now we have to find min dis of each vertex from eitherstartVertex or endVertex by initialising nr[] array */
for (i = 0; i < n; i++) {
if (cost[i][startVertex] < cost[i][endVertex])
nr[i] = startVertex;
else
nr[i] = endVertex;
}
/* To indicate visited vertex initialise nr[] for them to 100 */
nr[startVertex] = 100;
nr[endVertex] = 100;
/* Now find out remaining n-2 edges */
temp = 99;
for (i = 1; i < n - 1; i++) {
for (j = 0; j < n; j++) {
if (nr[j] != 100 && cost[j][nr[j]] < temp) {
temp = cost[j][nr[j]];
k = j;
}
}
/* Now i have got next vertex */
tree[i][0] = k;
tree[i][1] = nr[k];
tree[i][2] = cost[k][nr[k]];
minimumCost = minimumCost + cost[k][nr[k]];
nr[k] = 100;
/* Now find if k is nearest to any vertex
than its previous near value */
for (j = 0; j < n; j++) {
if (nr[j] != 100 && cost[j][nr[j]] > cost[j][k])
nr[j] = k;
}
temp = 99;
}
/* Now i have the answer, just going to print it */
printf("\nThe min spanning tree is:- ");
for (i = 0; i < n - 1; i++) {
for (j = 0; j < 3; j++)
printf("%d", tree[i][j]);
printf("\n");
}
printf("\nMin cost : %d", minimumCost);
}
void main() {
int i, j;
clrscr();
printf("\nEnter the no. of vertices :");
scanf("%d", &n);
printf("\nEnter the costs of edges in matrix form :");
for (i = 0; i < n; i++)
for (j = 0; j < n; j++) {
scanf("%d", &cost[i][j]);
}
printf("\nThe matrix is : ");
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) {
printf("%d\t", cost[i][j]);
}
printf("\n");
}
prim();
getch();
}