Kruskal algorithm implementation in C

Kruskal Algorithm

Kruskal Algorithm

Kruskal's algorithm is an algorithm in graph theory that finds a minimum spanning tree for a connected weighted graph. This means it finds a subset of the edges that forms a tree that includes every vertex, where the total weight of all the edges in the tree is minimized. If the graph is not connected, then it finds a minimum spanning forest (a minimum spanning tree for each connected component). Kruskal's algorithm is an example of a greedy algorithm.

  • create a forest F (a set of trees), where each vertex in the graph is a separate tree
  • create a set S containing all the edges in the graph
  • while Sis nonemptyand F is not yet spanning
    • remove an edge with minimum weight from S
    • if that edge connects two different trees, then add it to the forest, combining two trees into a single tree
    • otherwise discard that edge.

At the termination of the algorithm, the forest has only one component and forms a minimum spanning tree of the graph.

C source code



void printArray(int a[][100],int n);

void AdjacencyMatrix(int a[][100], int n){
	int i,j;
	for(i = 0;i < n; i++)
		for(j = 0;j < i; j++)
			a[i][j] = a[j][i]= rand()%50;
			if( a[i][j]>40)a[i][j]=a[j][i]=999;
	a[i][i] = 999;

void printArray(int a[][100],int n){
	int i,j;

int root(int v,int p[]){

	while(p[v] != v)
		{v = p[v];}
return v;

void union_ij(int i,int j,int p[]){
	if(j > i)
		p[j] = i;
		p[i] = j;

void kruskal(int a[][100],int n){
	int count, i, p[100], min, j, u, v, k, t[100][100], sum;
	count = k = sum = 0;
	for(i = 0; i < n; i++)
		p[i] = i;
	while(count < n)
		min = 999;
		for(i = 0; i < n; i++)
			for(j = 0;j < n; j++)
				if(a[i][j] < min)
					min = a[i][j];
					u = i;
					v = j;
 		if(min != 999)
			i = root(u, p);
			j = root(v, p);
			if (i != j)
				t[k][0] = u;
				t[k][1] = v;
				sum += min;
		a[u][v] = a[v][u] = 999;
		}count +=1;
	if(count != n)
		printf("spanning tree not exist\n");
	if(count == n)
		printf("Adges Spanning tree is\n");
		for(k = 0; k < n-1 ; k++)
			printf(" %d -> %d ",t[k][0],t[k][1]);
	printf("\ncost = %d \n",sum);

int main()
	int a[100][100],n;
	printf("enter the number of vertices\n");
	return 0;

Content of Makefile

a.out:	kruskal.c
	gcc kruskal.c
	rm *~ a.out

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Comments 12 comments

Janus 5 years ago

Thanks for your wonderful code.

However, why did you have this t[100][100],instead of t[100][1].

prabhakar gouda profile image

prabhakar gouda 5 years ago from Bangalore Author

hey good observation ..... but has to be declared as t[100][2] right

Stratos 5 years ago

There is an error at the code. The line

while(count < n)

should be:

while (count < num_of_Edges)

FUCK MASTER'S 5 years ago

lelo ji lelo ......

subbu 5 years ago

youer gaidence very useful thanks for me

carnoot 5 years ago

Nice tutorial, however there are some errors at the end of the kruskal method. With the printing stuff. Stratos is right, though.

Ankit 5 years ago

The concept of parent array(p) is very nice but the running time I think is quite high O(V^3 + E) because you

are searching for the minimum again and again.Instead you sort them once which will require O(VlgV) time.

rajesh subramanian 4 years ago

Ankit is exactly right! we might build a heap to reduce it to O(vlogv)

ezhisai 4 years ago

this was more useful and effective examples.from this, i am full understood.

play 4 years ago

good post :) thanks for help

gohil binal 3 years ago


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bfilipek 2 years ago from Cracow

It would be better if you provide some more examples and description. Graph algorithms are quite hard to understand so the more examples the better person can understand the idea.

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