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.


'''

class Solution(object):
    def allPathsSourceTarget(self, graph):
        """
        :type graph: List[List[int]]
        :rtype: List[List[int]]
        """
        dic = {}
        for i in xrange(len(graph)):
            for nex in graph[i]:
                if i in dic:
                    dic[i].append(nex)
                else:
                    dic[i] = [nex]
                    
        res = []
        self.dfs(0, len(graph) - 1, dic, [0], res)
        return res
    
    def dfs(self, start, end, dic, tmp, res):
        if start == end:
            res.append(tmp)
            return
        for nex in dic[start]:
            self.dfs(nex, end, dic, tmp + [nex], res)