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.

Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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

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// 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;      path.push_back(src);      q.push(path);      while (!q.empty()) {          path = q.front();          q.pop();          int last = path[path.size() - 1];             // if last vertex is the desired destination          // then print the path          if (last == dst)               printpath(path);                     // 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);                  newpath.push_back(g[last][i]);                  q.push(newpath);              }          }      } }    // driver program int main() {      vector<vector< int > > g;      // number of vertices      int v = 4;      g.resize(4);         // construct a graph      g[0].push_back(3);      g[0].push_back(1);      g[0].push_back(2);      g[1].push_back(3);      g[2].push_back(0);      g[2].push_back(1);         int src = 2, dst = 3;      cout << "path from src " << src           << " to dst " << dst << " are \n" ;         // function for finding the paths      findpaths(g, src, dst, v);         return 0; }

Output:

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

This article is contributed by Mandeep Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to [email protected]. See your article appearing on the GeeksforGeeks main page and help other Geeks.