# LeetCode 797. All Paths From Source to Target

## Description:

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.

## 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.

## 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.

## Solution:

class Path:
last = None
node = -1

def __init__(self, last, node):
self.last = last
self.node = node

class Solution(object):

def allPathsSourceTarget(self, graph):
"""
:type graph: List[List[int]]
:rtype: List[List[int]]
"""
start = 0
end = len(graph) - 1

# bfs
queue = []
queue.append(Path(None, start))

endNode = []

while len(queue) > 0:
front = queue.pop(0)
assert front.node != -1

if front.node == end:
endNode.append(front)
else:
for nextNode in graph[front.node]:
queue.append(Path(front, nextNode))

result = []
for node in endNode:
path = []
obj = node
while obj is not None:
path.append(obj.node)
obj = obj.last
path.reverse()
result.append(path)
return result


Simple bredth first search algorithm.