all-paths-from-source-to-target.py

# Time:  O(p + r * n), p is the count of all the possible paths in graph,
#                      r is the count of the result.
# Space: O(n)

# 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.

class Solution(object):
    def allPathsSourceTarget(self, graph):
        """
        :type graph: List[List[int]]
        :rtype: 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()
                    
        result = []
        dfs(graph, 0, [0], result)
        return result