Find if there is a path between two vertices in a directed graph

Given a Directed Graph and two vertices in it, check whether there is a path from the first given vertex to second. For example, in the following graph, there is a path from vertex 1 to 3. As another example, there is no path from 3 to 0.

We can either use Breadth First Search (BFS) or Depth First Search (DFS) to find path between two vertices. Take the first vertex as source in BFS (or DFS), follow the standard BFS (or DFS). If we see the second vertex in our traversal, then return true. Else return false.

Following is C++ code that uses BFS for finding reachability of second vertex from first vertex.

// Program to check if there is exist a path between two vertices of a graph.
#include<iostream>
#include <list>
 
using namespace std;
 
// This class represents a directed graph using adjacency list representation
class Graph
{
    int V;    // No. of vertices
    list<int> *adj;    // Pointer to an array containing adjacency lists
public:
    Graph(int V);  // Constructor
    void addEdge(int v, int w); // function to add an edge to graph
    bool isReachable(int s, int d);  // returns true if there is a path from s to d
};
 
Graph::Graph(int V)
{
    this->V = V;
    adj = new list<int>[V];
}
 
void Graph::addEdge(int v, int w)
{
    adj[v].push_back(w); // Add w to v’s list.
}
 
// A BFS based function to check whether d is reachable from s.
bool Graph::isReachable(int s, int d)
{
    // Base case
    if (s == d)
      return true;
 
    // Mark all the vertices as not visited
    bool *visited = new bool[V];
    for (int i = 0; i < V; i++)
        visited[i] = false;
 
    // Create a queue for BFS
    list<int> queue;
 
    // Mark the current node as visited and enqueue it
    visited[s] = true;
    queue.push_back(s);
 
    // it will be used to get all adjacent vertices of a vertex
    list<int>::iterator i;
 
    while (!queue.empty())
    {
        // Dequeue a vertex from queue and print it
        s = queue.front();
        queue.pop_front();
 
        // Get all adjacent vertices of the dequeued vertex s
        // If a adjacent has not been visited, then mark it visited
        // and enqueue it
        for (i = adj[s].begin(); i != adj[s].end(); ++i)
        {
            // If this adjacent node is the destination node, then return true
            if (*i == d)
                return true;
 
            // Else, continue to do BFS
            if (!visited[*i])
            {
                visited[*i] = true;
                queue.push_back(*i);
            }
        }
    }
 
    return false;
}

From:

http://www.geeksforgeeks.org/find-if-there-is-a-path-between-two-vertices-in-a-given-graph/