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

## C++

`// C++ 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;` `}` |

## Python3

`# Python3 program to print all paths of` `# source to destination in given graph` `from` `typing ` `import` `List` `from` `collections ` `import` `deque` `# Utility function for printing` `# the found path in graph` `def` `printpath(path: ` `List` `[` `int` `]) ` `-` `> ` `None` `:` ` ` ` ` `size ` `=` `len` `(path)` ` ` `for` `i ` `in` `range` `(size):` ` ` `print` `(path[i], end ` `=` `" "` `)` ` ` ` ` `print` `()` `# Utility function to check if current` `# vertex is already present in path` `def` `isNotVisited(x: ` `int` `, path: ` `List` `[` `int` `]) ` `-` `> ` `int` `:` ` ` `size ` `=` `len` `(path)` ` ` `for` `i ` `in` `range` `(size):` ` ` `if` `(path[i] ` `=` `=` `x):` ` ` `return` `0` ` ` ` ` `return` `1` `# Utility function for finding paths in graph` `# from source to destination` `def` `findpaths(g: ` `List` `[` `List` `[` `int` `]], src: ` `int` `,` ` ` `dst: ` `int` `, v: ` `int` `) ` `-` `> ` `None` `:` ` ` ` ` `# Create a queue which stores` ` ` `# the paths` ` ` `q ` `=` `deque()` ` ` `# Path vector to store the current path` ` ` `path ` `=` `[]` ` ` `path.append(src)` ` ` `q.append(path.copy())` ` ` ` ` `while` `q:` ` ` `path ` `=` `q.popleft()` ` ` `last ` `=` `path[` `len` `(path) ` `-` `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` `i ` `in` `range` `(` `len` `(g[last])):` ` ` `if` `(isNotVisited(g[last][i], path)):` ` ` `newpath ` `=` `path.copy()` ` ` `newpath.append(g[last][i])` ` ` `q.append(newpath)` `# Driver code` `if` `__name__ ` `=` `=` `"__main__"` `:` ` ` ` ` `# Number of vertices` ` ` `v ` `=` `4` ` ` `g ` `=` `[[] ` `for` `_ ` `in` `range` `(` `4` `)]` ` ` `# Construct a graph` ` ` `g[` `0` `].append(` `3` `)` ` ` `g[` `0` `].append(` `1` `)` ` ` `g[` `0` `].append(` `2` `)` ` ` `g[` `1` `].append(` `3` `)` ` ` `g[` `2` `].append(` `0` `)` ` ` `g[` `2` `].append(` `1` `)` ` ` `src ` `=` `2` ` ` `dst ` `=` `3` ` ` `print` `(` `"path from src {} to dst {} are"` `.` `format` `(` ` ` `src, dst))` ` ` `# Function for finding the paths` ` ` `findpaths(g, src, dst, v)` `# This code is contributed by sanjeev2552` |

**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 contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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