All Paths From Source to Target

#leetcode #dsa #theabbie

Given a directed acyclic graph (DAG) of n nodes labeled from 0 to n - 1, find all possible paths from node 0 to node n - 1 and return them in any order.

The graph is given as follows: graph[i] is a list of all nodes you can visit from node i (i.e., there is a directed edge from node i to node graph[i][j]).

Example 1:

Input: graph = [[1,2],[3],[3],[]]
Output: [[0,1,3],[0,2,3]]
Explanation: There are two paths: 0 -> 1 -> 3 and 0 -> 2 -> 3.

Example 2:

Input: graph = [[4,3,1],[3,2,4],[3],[4],[]]
Output: [[0,4],[0,3,4],[0,1,3,4],[0,1,2,3,4],[0,1,4]]

Constraints:

n == graph.length
2 <= n <= 15
0 <= graph[i][j] < n
graph[i][j] != i (i.e., there will be no self-loops).
All the elements of graph[i] are unique.
The input graph is guaranteed to be a DAG.

SOLUTION:

class Solution:
    def allPathsSourceTarget(self, graph: List[List[int]]) -> List[List[int]]:
        n = len(graph)
        op = []
        paths = [([0], {0})]
        while len(paths) > 0:
            curr, visited = paths.pop()
            if curr[-1] == n - 1:
                op.append(curr)
            for newcurr in graph[curr[-1]]:
                if newcurr not in visited:
                    paths.append((curr + [newcurr], visited.union({newcurr})))
        return op