All Paths From Source to Target.py

'''
Given a directed, acyclic graph of N nodes.  Find all possible paths from node 0 to node N-1, and return them in any order.
The graph is given as follows:  the nodes are 0, 1, ..., graph.length - 1.  graph[i] is a list of all nodes j for which the edge (i, j) exists.

Example:
Input: [[1,2], [3], [3], []] 
Output: [[0,1,3],[0,2,3]] 
Explanation: The graph looks like this:
0--->1
|    |
v    v
2--->3
There are two paths: 0 -> 1 -> 3 and 0 -> 2 -> 3.

Note:
The number of nodes in the graph will be in the range [2, 15].
You can print different paths in any order, but you should keep the order of nodes inside one path.
'''

#Solution: Backtracking

class Solution:
    def allPathsSourceTarget(self, graph: List[List[int]]) -> List[List[int]]:
        def dfs(graph, curr, path, result):
            if curr == len(graph)-1:
                result.append(path[:])
                return
            for node in graph[curr]:
                path.append(node)
                dfs(graph, node, path, result)
                path.pop()

        res = []
        dfs(graph, 0, [0], res)
        return res