# 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
*S*is 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.

- remove an edge with minimum weight from

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

## C source code

#include<stdio.h> #include<stdlib.h> 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; } printArray(a,n); } void printArray(int a[][100],int n){ int i,j; for(i=0;i<n;i++) { for(j=0;j<n;j++) { printf("%d\t",a[i][j]); } printf("\n"); } } 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; else 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; k++; sum += min; union_ij(i,j,p); } 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"); scanf("%d",&n); AdjacencyMatrix(a,n); kruskal(a,n); return 0; }

## Content of Makefile

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

## Comments

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.

thnx

good post :) thanks for help

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

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

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.

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

youer gaidence very useful thanks for me

lelo ji lelo ......

There is an error at the code. The line

while(count < n)

should be:

while (count < num_of_Edges)

Thanks for your wonderful code.

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

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