kruskal.c

#include<stdio.h>
#define MAX 30

typedef struct edge
{
	int u,v,w;
}edge;

typedef struct edgelist
{
	edge data[MAX];
	int n;
}edgelist;

edgelist elist;

int G[MAX][MAX],n;
edgelist spanlist;

void kruskal();
int find(int belongs[],int vertexno);
void union1(int belongs[],int c1,int c2);
void sort();
void print();

void kruskal()
{
	int belongs[MAX],cno1,cno2;
	elist.n=0;

	for(int i=1;i<n;i++)
		for(int j=0;j<i;j++)
		{
			if(G[i][j]!=0)
			{
				elist.data[elist.n].u=i;
				elist.data[elist.n].v=j;
				elist.data[elist.n].w=G[i][j];
				elist.n++;
			}
		}

	sort();

	for(int i=0;i<n;i++)
		belongs[i]=i;

	spanlist.n=0;

	for(int i=0;i<elist.n;i++)
	{
		cno1=find(belongs,elist.data[i].u);
		cno2=find(belongs,elist.data[i].v);

		if(cno1!=cno2)
		{
			spanlist.data[spanlist.n]=elist.data[i];
			spanlist.n=spanlist.n+1;
			union1(belongs,cno1,cno2);
		}
	}
}

int find(int belongs[],int vertexno)
{
	return(belongs[vertexno]);
}

void union1(int belongs[],int c1,int c2)
{
	for(int i=0;i<n;i++)
		if(belongs[i]==c2)
			belongs[i]=c1;
}

void sort()
{
	edge temp;
	for(int i=1;i<elist.n;i++)
		for(int j=0;j<elist.n-1;j++)
			if(elist.data[j].w>elist.data[j+1].w)
			{
				temp=elist.data[j];
				elist.data[j]=elist.data[j+1];
				elist.data[j+1]=temp;
			}
}

void print()
{
	int cost=0;
    for(int i=0;i<spanlist.n;i++)
	{
		printf("\n%d\t%d\t%d",spanlist.data[i].u,spanlist.data[i].v,spanlist.data[i].w);
		cost=cost+spanlist.data[i].w;
	}
    printf("\n\nThe spanning tree cost=%d",cost);
}

int main()
{
	printf("\nEnter number of vertices:");
	scanf("%d",&n);
	printf("\nEnter the adjacency matrix:\n");
	for(int i=0;i<n;i++)
		for(int j=0;j<n;j++)
			scanf("%d",&G[i][j]);

	kruskal();
	print();
}

//Overall time complexity = O(ElogE) + O(ElogN)
//Overall space complexity = O(N^2)
/*
Input
0 3 1 6 0 0
3 0 5 0 3 0
1 5 0 5 6 4
6 0 5 0 0 2
0 3 6 0 0 6
0 0 4 2 6 0

Output
2	0	1
5	3	2
1	0	3
4	1	3
5	2	4

The spanning tree cost = 13
*/