C++ Program to Find the Edge Connectivity of a Graph

Code:

#include   iostream
#include   list
#define NIL -1
using namespace std;

// A class that represents an undirected graph
class Graph
{
        int V; // No. of vertices
        list *adj; // A dynamic array of adjacency lists
        void bridgeUtil(int v, bool visited[], int disc[], int low[],
                int parent[]);
    public:
        Graph(int V); // Constructor
        void addEdge(int v, int w); // function to add an edge to graph
        void bridge(); // prints all bridges
};

Graph::Graph(int V)
{
    this->V = V;
    adj = new list [V];
}

void Graph::addEdge(int v, int w)
{
    adj[v].push_back(w);
    adj[w].push_back(v); // Note: the graph is undirected
}

void Graph::bridgeUtil(int u, bool visited[], int disc[], int low[],
        int parent[])
{
    // A static variable is used for simplicity, we can avoid use of static
    // variable by passing a pointer.
    static int time = 0;

    // Mark the current node as visited
    visited[u] = true;

    // Initialize discovery time and low value
    disc[u] = low[u] = ++time;

    // Go through all vertices aadjacent to this
    list::iterator i;
    for (i = adj[u].begin(); i != adj[u].end(); ++i)
    {
        int v = *i; // v is current adjacent of u

        // If v is not visited yet, then recur for it
        if (!visited[v])
        {
            parent[v] = u;
            bridgeUtil(v, visited, disc, low, parent);

            // Check if the subtree rooted with v has a connection to
            // one of the ancestors of u
            low[u] = min(low[u], low[v]);

            // If the lowest vertex reachable from subtree under v is
            // below u in DFS tree, then u-v is a bridge
            if (low[v] > disc[u])
                cout << u << " " << v << endl;
        }

        // Update low value of u for parent function calls.
        else if (v != parent[u])
            low[u] = min(low[u], disc[v]);
    }
}

// DFS based function to find all bridges. It uses recursive function bridgeUtil()
void Graph::bridge()
{
    // Mark all the vertices as not visited
    bool *visited = new bool[V];
    int *disc = new int[V];
    int *low = new int[V];
    int *parent = new int[V];

    // Initialize parent and visited arrays
    for (int i = 0; i < V; i++)
    {
        parent[i] = NIL;
        visited[i] = false;
    }

    // Call the recursive helper function to find Bridges
    // in DFS tree rooted with vertex 'i'
    for (int i = 0; i < V; i++)
        if (visited[i] == false)
            bridgeUtil(i, visited, disc, low, parent);
}

// Driver program to test above function
int main()
{
    // Create graphs given in above diagrams
    cout << "\nBridges in first graph \n";
    Graph g1(5);
    g1.addEdge(1, 0);
    g1.addEdge(0, 2);
    g1.addEdge(2, 1);
    g1.addEdge(0, 3);
    g1.addEdge(3, 4);
    g1.bridge();

    cout << "\nBridges in second graph \n";
    Graph g2(4);
    g2.addEdge(0, 1);
    g2.addEdge(1, 2);
    g2.addEdge(2, 3);
    g2.bridge();

    cout << "\nBridges in third graph \n";
    Graph g3(7);
    g3.addEdge(0, 1);
    g3.addEdge(1, 2);
    g3.addEdge(2, 0);
    g3.addEdge(1, 3);
    g3.addEdge(1, 4);
    g3.addEdge(1, 6);
    g3.addEdge(3, 5);
    g3.addEdge(4, 5);
    g3.bridge();

    return 0;
}


Output:

Bridges in first graph 
3 4
0 3

Bridges in second graph 
2 3
1 2
0 1

Bridges in third graph 
1 6
------------------
(program exited with code: 0)
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