797. All Paths From Source to Target

Medium

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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]]:
        target = len(graph)-1
        result = []
        def recursion(node, path):
            # Base Condition
            if node == target:
                result.append(path)
            for adj in graph[node]:
                path.append(adj)
                recursion(adj, path[:])
                path.pop()
        recursion(0, [0])
        return result