C++ Program to Check whether Graph is Biconnected or Not

This C++ Program checks whether Graph is Biconnected.

Here is source code of the C++ Program to check whether Graph is Biconnected. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below.

```
/*
```

 * C++ Program to Check whether Graph is Biconnected

```
 */
```
```
#include <iostream>
```
```
#include <list>
```
```
#define NIL -1
```
```
using namespace std;
```
```
 
```
```
/*
```
```
 * Class Declaration
```
```
 */
```
```
class Graph
```
```
{
```
```
    private:
```
```
        int V;
```
```
        list<int> *adj;
```

        bool isBCUtil(int v, bool visited[], int disc[], int low[],int parent[]);

```
    public:
```
```
        Graph(int V)
```
```
        {
```
```
            this->V = V;
```
```
            adj = new list<int>[V]; 
```
```
        }
```
```
        void addEdge(int v, int w);
```
```
        bool isBC();
```
```
};
```
```
 
```
```
/*
```
```
 * Add Edge to connect v and w
```
```
 */
```
```
void Graph::addEdge(int v, int w)
```
```
{
```
```
    adj[v].push_back(w);
```
```
    adj[w].push_back(v);
```
```
}
```
```
 
```
```
/*
```

 *  A recursive function that returns true if there is an articulation

 *  point in given graph, otherwise returns false

```
 */
```

bool Graph::isBCUtil(int u, bool visited[], int disc[],int low[],int parent[])

```
{
```
```
 
```
```
    static int time = 0;
```
```
    int children = 0;
```
```
    visited[u] = true;
```
```
    disc[u] = low[u] = ++time;
```
```
    list<int>::iterator i;
```

    for (i = adj[u].begin(); i != adj[u].end(); ++i)

```
    {
```
```
        int v = *i;
```
```
        if (!visited[v])
```
```
        {
```
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            children++;
```
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            parent[v] = u;
```

            if (isBCUtil(v, visited, disc, low, parent))

```
                return true;
```

            low[u]  = min(low[u], low[v]);

            if (parent[u] == NIL && children > 1)

```
                return true;
```

            if (parent[u] != NIL && low[v] >= disc[u])

```
                return true;
```
```
        }
```
```
 
```
```
        else if (v != parent[u])
```

            low[u]  = min(low[u], disc[v]);

```
    }
```
```
    return false;
```
```
}
```
```
 
```
```
/*
```

 * returns true if graph is Biconnected, otherwise false.

```
 */
```
```
bool Graph::isBC()
```
```
{
```
```
    bool *visited = new bool[V];
```
```
    int *disc = new int[V];
```
```
    int *low = new int[V];
```
```
    int *parent = new int[V];
```
```
 
```
```
    for (int i = 0; i < V; i++)
```
```
    {
```
```
        parent[i] = NIL;
```
```
        visited[i] = false;
```
```
    }
```
```
 
```

    if (isBCUtil(0, visited, disc, low, parent) == true)

```
        return false;
```
```
 
```
```
    for (int i = 0; i < V; i++)
```
```
        if (visited[i] == false)
```
```
            return false;
```
```
 
```
```
    return true;
```
```
}
```
```
 
```
```
/*
```
```
 * Main Contains Menu
```
```
 */
```
```
int main()
```
```
{
```
```
    Graph g1(2);
```
```
    g1.addEdge(0, 1);
```
```
    if (g1.isBC())
```

        cout<<"The Graph is BiConnected"<<endl;

```
    else
```

        cout<<"The Graph is not BiConnected"<<endl;

```
 
```
```
    Graph g2(5);
```
```
    g2.addEdge(1, 0);
```
```
    g2.addEdge(0, 2);
```
```
    g2.addEdge(2, 1);
```
```
    g2.addEdge(0, 3);
```
```
    g2.addEdge(3, 4);
```
```
    g2.addEdge(2, 4);
```
```
    if (g2.isBC())
```

        cout<<"The Graph is BiConnected"<<endl;

```
    else
```

        cout<<"The Graph is not BiConnected"<<endl;

```
 
```
```
    Graph g3(3);
```
```
    g3.addEdge(0, 1);
```
```
    g3.addEdge(1, 2);
```
```
    if (g3.isBC())
```

        cout<<"The Graph is BiConnected"<<endl;

```
    else
```

        cout<<"The Graph is not BiConnected"<<endl;

```
 
```
```
    Graph g4(5);
```
```
    g4.addEdge(1, 0);
```
```
    g4.addEdge(0, 2);
```
```
    g4.addEdge(2, 1);
```
```
    g4.addEdge(0, 3);
```
```
    g4.addEdge(3, 4);
```
```
    if (g4.isBC())
```

        cout<<"The Graph is BiConnected"<<endl;

```
    else
```

        cout<<"The Graph is not BiConnected"<<endl;

```
 
```
```
    Graph g5(3);
```
```
    g5.addEdge(0, 1);
```
```
    g5.addEdge(1, 2);
```
```
    g5.addEdge(2, 0);
```
```
    if (g5.isBC())
```

        cout<<"The Graph is BiConnected"<<endl;

```
    else
```

        cout<<"The Graph is not BiConnected"<<endl;

```
 
```
```
    return 0;
```
```
}
```

$ g++ biconnected.cpp
$ a.out
The Graph is BiConnected
The Graph is BiConnected
The Graph is not BiConnected
The Graph is not BiConnected
The Graph is BiConnected
 
 
------------------
(program exited with code: 0)
Press return to continue

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