Print all paths from a given source to a destination using BFS

Given a directed graph, a source vertex ‘src’ and a destination vertex ‘dst’, print all paths from given ‘src’ to ‘dst’.

Consider the following directed graph. Let the src be 2 and dst be 3. There are 3 different paths from 2 to 3.

We have already discussed Print all paths from a given source to a destination using DFS.

Below is BFS based solution.

Algorithm :

create a queue which will store path(s) of type vector
initialise the queue with first path starting from src

Now run a loop till queue is not empty
   get the frontmost path from queue
   check if the lastnode of this path is destination
       if true then print the path
   run a loop for all the vertices connected to the
   current vertex i.e. lastnode extracted from path
      if the vertex is not visited in current path
         a) create a new path from earlier path and 
             append this vertex
         b) insert this new path to queue
// CPP program to print all paths of source to
// destination in given graph
#include <bits/stdc++.h>
using namespace std;
// utility function for printing
// the found path in graph
void printpath(vector<int>& path)
    int size = path.size();
    for (int i = 0; i < size; i++) 
        cout << path[i] << " ";    
    cout << endl;
// utility function to check if current
// vertex is already present in path
int isNotVisited(int x, vector<int>& path)
    int size = path.size();
    for (int i = 0; i < size; i++) 
        if (path[i] == x) 
            return 0; 
    return 1;
// utility function for finding paths in graph
// from source to destination
void findpaths(vector<vector<int> >&g, int src, 
                                 int dst, int v)
    // create a queue which stores
    // the paths
    queue<vector<int> > q;
    // path vector to store the current path
    vector<int> path;
    while (!q.empty()) {
        path = q.front();
        int last = path[path.size() - 1];
        // if last vertex is the desired destination
        // then print the path
        if (last == dst) 
        // traverse to all the nodes connected to 
        // current vertex and push new path to queue
        for (int i = 0; i < g[last].size(); i++) {
            if (isNotVisited(g[last][i], path)) {
                vector<int> newpath(path);
// driver program
int main()
    vector<vector<int> > g;
    // number of vertices
    int v = 4;
    // construct a graph
    int src = 2, dst = 3;
    cout << "path from src " << src
         << " to dst " << dst << " are ";
    // function for finding the paths
    findpaths(g, src, dst, v);
    return 0;



path from src 2 to dst 3 are 
2 0 3 
2 1 3 
2 0 1 3

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

This article is attributed to GeeksforGeeks.org

You Might Also Like

leave a comment



load comments

Subscribe to Our Newsletter