algorithm - find minimum spanning tree using depth first search in C

Question

I'm trying to implement an algorithm in c which finds MST using DFS. I've already found the DFS algortihm and i understand it pretty well. I also know that i should follow these steps to achieve my purpose :

1 Run DFS till you find an edge going backwards or DFS stopped. If stopped return G.

2 On the circle that is constructed by the backwards going edge find the heaviest edge and remove it from G.

3 Return to 1.

Here is the DFS code :

#include<stdio.h>
void DFS(int);
int G[10][10],visited[10],n;    //n is no of vertices and graph is sorted in array G[10][10]
void main()
{
    int i,j;

printf("Enter number of vertices:");
scanf("%d",&n);

    //read the adjecency matrix
    printf("
Enter adjecency matrix of the graph:");
    for(i=0;i<n;i++)
        for(j=0;j<n;j++)
            fscanf("%d",&G[i][j]);

    //visited is initialized to zero
    for(i=0;i<n;i++)
        visited[i]=0;

    DFS(0);
}
void DFS(int i)
{
    int j;
printf("
%d",i);
visited[i]=1; // éviter cycle
for(j=0;j<n;j++)
    if(!visited[j]&&G[i][j]==1)
        DFS(j);
}

I need your help to implement the full algorithm or at least some advices. That would be much appreciated. Thank's in advance.

Answer 1

This sounds like homework, so I'll tell you how I would approach the problem.

First, modify your DFS implementation to use an explicit stack instead of recursion. Create a new array int stack[10]; and a variable int stacksize = 0;. The idea is that stack[0], stack[1], ..., stack[stacksize-1] will correspond to the arguments i of the outermost active invocation of DFS to the innermost. I'll leave the details a bit sketchy because I'm sure that there have been other question/answer pairs about this aspect.

Second, whenever the graph has an edge back to a visited vertex, scan from the top of the stack back to the visited vertex, looking for the heaviest edge. Once you find it, delete that edge by modifying G. To restart the depth-first search, pop the stack until you pop one of the endpoints of the deleted edge. Each time you pop something, clear its visited flag. The depth-first search continues from here (a complete restart is not necessary because it would do the same thing up to here).