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; 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
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