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.

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