Leetcode: All Paths From Source to Target

All Paths From Source to Target



Similar Problems:


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.

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.


## Blog link: https://code.dennyzhang.com/all-paths-from-source-to-target
## Basic Ideas: dfs
## Complexity: Time O(n!), Space O(n)
class Solution:
    def allPathsSourceTarget(self, graph):
        """
        :type graph: List[List[int]]
        :rtype: List[List[int]]
        """
        length = len(graph)
        if length == 0: return []
        if length == 1: return [[0]]

        self.res, self.l = [], []
        self.dfs(0, graph)
        return self.res

    def dfs(self, node, graph):
        if node == len(graph) - 1:
            self.res.append(self.l + [node])
            return
        self.l.append(node)
        for edge in graph[node]:
            self.dfs(edge, graph)
        self.l.pop(-1)
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