C++ Program to Find All Cross Edges in a Graph

This C++ program, using recursion, displays the number of cross edges in a graph. A cross edge is one in which a node points to another node which has already been fully visited.

Here is the source code of the C++ program to display the cross edges as and when they are encountered. The C++ program is successfully compiled and run on DevCpp, a C++ compiler. The program output is also shown below.

```
/*
```

 * C++ Program to Find all Cross Edges in a Graph

```
 */
```
```
#include<iostream>
```
```
#include<conio.h>
```
```
using namespace std;
```
```
struct node_info
```
```
{
```
```
    int no;
```
```
    int lv_time,st_time;
```
```
}*q = NULL, *r = NULL;
```
```
struct node
```
```
{
```
```
    node_info *pt;
```
```
    node *next;
```
```
}*top = NULL, *p = NULL, *np = NULL;
```
```
struct node1
```
```
{
```
```
    node1 *link;
```
```
    node_info *pt1;
```

}*head = NULL, *m = NULL, *n = NULL, *np1 = NULL;

```
int c = 0;
```
```
void push(node_info *ptr)
```
```
{
```
```
    np = new node;
```
```
    np->pt = ptr;
```
```
    np->next = NULL;
```
```
    if (top == NULL)
```
```
    {
```
```
        top = np;
```
```
    }
```
```
    else
```
```
    {
```
```
        np->next = top;
```
```
        top = np;
```
```
    }
```
```
}
```
```
node_info *pop()
```
```
{
```
```
    if (top == NULL)
```
```
    {
```
```
        cout<<"underflow\n";
```
```
    }
```
```
    else
```
```
    {
```
```
        p = top;
```
```
        top = top->next;
```
```
        return(p->pt);
```
```
        delete(p);
```
```
    }
```
```
}
```
```
void store(node_info *ptr1)
```
```
{
```
```
    np1 = new node1;
```
```
    np1->pt1 = ptr1;
```
```
    np1->link = NULL;
```
```
    if (c == 0)
```
```
    {
```
```
        head = np1;
```
```
        m = head;
```
```
        m->link = NULL;
```
```
        c++;
```
```
    }
```
```
    else
```
```
    {
```
```
        m = head;
```
```
        np1->link = m;
```
```
        head = np1;
```
```
    }
```
```
}
```
```
int search(int j)
```
```
{
```
```
    node1 *t = head;
```
```
    while (t != NULL)
```
```
    {
```
```
        if ((t->pt1)->no == j)
```
```
        {
```
```
            break;
```
```
        }
```
```
        else
```
```
        {
```
```
            t = t->link;
```
```
            continue;
```
```
        }
```
```
    }
```
```
    return (t->pt1)->lv_time;
```
```
}             
```
```
int present_in_stack(int j)
```
```
{
```
```
    int flag = 0;
```
```
    p = top;
```
```
    while (p != NULL)
```
```
    {
```
```
        if ((p->pt)->no == j)
```
```
        {
```
```
            flag = 1;
```
```
            return flag;
```
```
        }
```
```
        p = p->next;
```
```
    }
```
```
    return flag;
```
```
}
```
```
void topo(int *v,int am[][8],int i)
```
```
{
```
```
    q = new node_info;
```
```
    q->no = i;
```
```
    q->st_time = c;
```
```
    push(q);
```
```
    v[i] = 1;
```
```
    for (int j = 0; j < 8; j++)
```
```
    {
```
```
        if (am[i][j] == 0)
```
```
            continue;
```

        else if ((am[i][j] == 1 && v[j] == 1))

```
        {
```

            if (!present_in_stack(j) && q->st_time > search(j))

```
            {
```

                cout<<"Cross edge between "<<i<<" and "<<j<<endl;

```
            }
```
```
            continue;
```
```
        }
```

        else if(am[i][j] == 1 && v[j] == 0)

```
        {
```
```
            c++;
```
```
            topo(v,am,j);
```
```
        }
```
```
    }
```
```
    c++;
```
```
    q = pop();
```
```
    q->lv_time = c;
```
```
    store(q);
```
```
    return;
```
```
}
```
```
int main()
```
```
{
```
```
    int v[8], am[8][8];
```
```
    for (int i = 0; i < 8; i++)
```
```
        v[i] = 0;
```
```
    for (int i = 0; i < 8; i++)
```
```
    {
```

        cout<<"enter the values for adjacency matrix row:"<<i + 1<<endl;

```
        for(int j = 0; j < 8; j++)
```
```
        {
```
```
            cin>>am[i][j];
```
```
        }
```
```
    }
```
```
    topo(v,am,0);
```
```
    getch();
```
```
}
```

Output
 
enter the values for adjacency matrix row:1
0
1
0
0
1
0
0
1
enter the values for adjacency matrix row:2
0
0
1
0
0
0
0
0
enter the values for adjacency matrix row:3
0
0
0
1
0
0
00
0
enter the values for adjacency matrix row:4
0
1
0
0
0
0
0
0
enter the values for adjacency matrix row:5
0
0
0
0
0
1
0
0
enter the values for adjacency matrix row:6
0
0
1
0
0
0
1
1
enter the values for adjacency matrix row:7
 
0
0
0
0
0
0
0
0
enter the values for adjacency matrix row:8
0
0
0
0
0
0
0
0
Cross edge between 5 and 2

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