C++ Program to Check if an Directed Graph is a Tree or Not Using DFS

Code:

#include    iostream
#include    list
#include    limits.h

using namespace std;

class Graph
{
        int V; // No. of vertices
        list *adj; // Pointer to an array containing adjacency lists
        bool isCyclicUtil(int v, bool visited[], bool *rs); // used by isCyclic()
    public:
        Graph(int V); // Constructor
        void addEdge(int v, int w); // to add an edge to graph
        bool isCyclic(); // returns true if there is a cycle in this graph
};

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

void Graph::addEdge(int v, int w)
{
    adj[v].push_back(w); // Add w to v’s list.
}

// This function is a variation of DFSUytil() in http://www.geeksforgeeks.org/archives/18212
bool Graph::isCyclicUtil(int v, bool visited[], bool *recStack)
{
    if (visited[v] == false)
    {
        // Mark the current node as visited and part of recursion stack
        visited[v] = true;
        recStack[v] = true;

        // Recur for all the vertices adjacent to this vertex
        list::iterator i;
        for (i = adj[v].begin(); i != adj[v].end(); ++i)
        {
            if (!visited[*i] && isCyclicUtil(*i, visited, recStack))
                return true;
            else if (recStack[*i])
                return true;
        }

    }
    recStack[v] = false; // remove the vertex from recursion stack
    return false;
}

// Returns true if the graph contains a cycle, else false.
// This function is a variation of DFS() in http://www.geeksforgeeks.org/archives/18212
bool Graph::isCyclic()
{
    // Mark all the vertices as not visited and not part of recursion
    // stack
    bool *visited = new bool[V];
    bool *recStack = new bool[V];
    for (int i = 0; i < V; i++)
    {
        visited[i] = false;
        recStack[i] = false;
    }

    // Call the recursive helper function to detect cycle in different
    // DFS trees
    for (int i = 0; i < V; i++)
        if (isCyclicUtil(i, visited, recStack))
            return true;

    return false;
}

int main()
{
    // Create a graph given in the above diagram
    Graph g(4);
    g.addEdge(0, 1);
    g.addEdge(0, 2);
    g.addEdge(1, 2);
    g.addEdge(2, 0);
    g.addEdge(2, 3);
    g.addEdge(3, 3);

    if (g.isCyclic())
        cout << "Directed Graph isn't a tree";
    else
        cout << "Directed Graph is a tree";
    return 0;
}


Output:

Directed Graph isn't a tree

------------------
(program exited with code: 0)
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