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Abhishek Chaudhary

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# All Paths From Source to Target

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