programming-examples/c++/11_Numerical_Problems/C++ Program to Find Path Between Two Nodes in a Graph.cpp

#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;
}

// Driver program to test methods of graph class
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);
    cout << "Enter the source and destination vertices: (0-3)";
    int u, v;
    cin >> u >> v;
    if (g.isReachable(u, v))
        cout << "\nThere is a path from " << u << " to " << v;
    else
        cout << "\nThere is no path from " << u << " to " << v;
    int temp;
    temp = u;
    u = v;
    v = temp;
    if (g.isReachable(u, v))
        cout << "\nThere is a path from " << u << " to " << v;
    else
        cout << "\nThere is no path from " << u << " to " << v;
    return 0;
}

/*
Enter the source and destination vertices: (0-3)
1 3

There is a path from 1 to 3
There is no path from 3 to 1

Enter the source and destination vertices: (0-3)
2 3

There is a path from 2 to 3
There is no path from 3 to 2