C Program to Find a Good Feedback Edge Set in a Graph

This is a C Program to find feednack arc set. This is the set which contains edges which when removed from the graph, graph becomes directed acyclic graph.

Here is source code of the C Program to Find a Good Feedback Edge Set in a Graph. The C program is successfully compiled and run on a Linux system. The program output is also shown below.

```
#include<stdio.h>
```
```
#include<stdlib.h>
```
```
#include<conio.h>
```
```
 
```
```
int c = 0;
```
```
 
```
```
struct adj_list {
```
```
    int dest;
```
```
    struct adj_list *next;
```

}*np = NULL, *np1 = NULL, *p = NULL, *q = NULL;

```
 
```
```
struct Graph {
```
```
    int v;
```
```
    struct adj_list *ptr;
```
```
} array[6];
```
```
 
```

void addReverseEdge(int src, int dest) {

    np1 = malloc(sizeof(struct adj_list));

```
    np1->dest = src;
```
```
    np1->next = NULL;
```
```
    if (array[dest].ptr == NULL) {
```
```
        array[dest].ptr = np1;
```
```
        q = array[dest].ptr;
```
```
        q->next = NULL;
```
```
    } else {
```
```
        q = array[dest].ptr;
```
```
        while (q->next != NULL) {
```
```
            q = q->next;
```
```
        }
```
```
        q->next = np1;
```
```
    }
```
```
}
```
```
void addEdge(int src, int dest) {
```

    np = malloc(sizeof(struct adj_list));

```
    np->dest = dest;
```
```
    np->next = NULL;
```
```
    if (array[src].ptr == NULL) {
```
```
        array[src].ptr = np;
```
```
        p = array[src].ptr;
```
```
        p->next = NULL;
```
```
    } else {
```
```
        p = array[src].ptr;
```
```
        while (p->next != NULL) {
```
```
            p = p->next;
```
```
        }
```
```
        p->next = np;
```
```
    }
```
```
    //addReverseEdge(src, dest);
```
```
}
```
```
void print_graph(int n) {
```
```
    int i;
```
```
    for (i = 0; i < n; i++) {
```

        printf("Adjacency List of %d: ", array[i].v);

```
        while (array[i].ptr != NULL) {
```

            printf("%d ", (array[i].ptr)->dest);

            array[i].ptr = (array[i].ptr)->next;

```
        }
```
```
        printf("\n");
```
```
    }
```
```
}
```
```
 
```
```
int checkDAG(int n) {
```
```
    int count = 0;
```
```
    int size = n - 1, i, j;
```
```
    for (i = 0; i < n; i++) {
```

        //cout << "Adjacency List of " << array[i].v << ": ";

```
        if (count == size) {
```
```
            return 0;
```
```
        }
```
```
        if (array[i].ptr == NULL) {
```
```
            count++;
```
```
            for (j = 0; j < n; j++) {
```
```
 
```

                while (array[j].ptr != NULL) {

                    if ((array[j].ptr)->dest == (array[i].ptr)->dest) {

                        (array[j].ptr)->dest = -1;

```
                    }
```

                    array[i].ptr = (array[i].ptr)->next;

```
                }
```
```
            }
```
```
 
```
```
        }
```
```
    }
```

    printf("After checking whether the graph is DAG.");

```
    int visited[n + 1];
```
```
    for (i = 0; i < n; i++) {
```
```
        while (array[i].ptr != NULL) {
```

            printf("%d ", (array[i].ptr)->dest);

```
            visited[i] = 1;
```
```
            for (j = 0; j < n; j++) {
```
```
 
```

                while (array[j].ptr != NULL) {

                    printf("%d ", (array[j].ptr)->dest);

                    if (visited[array[j].v] == 1) {

                        printf("%d - %d", array[i].v, array[j].v);

```
                    }
```

                    array[j].ptr = (array[j].ptr)->next;

```
                }
```
```
                printf("\n");
```
```
            }
```
```
 
```

            array[i].ptr = (array[i].ptr)->next;

```
        }
```
```
        printf("\n");
```
```
    }
```
```
 
```
```
    return 1;
```
```
}
```
```
int main() {
```
```
    int n = 6, i;
```

    printf("Number of vertices: %d\n", n);

```
 
```
```
    for (i = 0; i < n; i++) {
```
```
        array[i].v = i;
```
```
        array[i].ptr = NULL;
```
```
    }
```
```
    addEdge(0, 1);
```
```
    addEdge(1, 2);
```
```
    addEdge(1, 3);
```
```
    addEdge(3, 4);
```
```
    addEdge(4, 5);
```
```
    addEdge(3, 5);
```
```
    addEdge(5, 2);
```
```
    print_graph(n);
```
```
    printf("Feedback arc Set: ");
```
```
    if (checkDAG(n) == 0)
```
```
        printf("None");
```
```
 
```
```
    return 0;
```
```
}
```

Output:

$ gcc FeedbackArcSet.c
$ ./a.out
 
Number of vertices: 6
Adjacency List of 0: 1 
Adjacency List of 1: 2 3 
Adjacency List of 2: 
Adjacency List of 3: 4 5 
Adjacency List of 4: 5 
Adjacency List of 5: 2 
Feedback arc Set: None

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