797.All Paths From Source to Target

tags: Medium,Backtracking,Depth-First Search,Breadth-First Search,Graph

797. All Paths From Source to Target

題目描述

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]).

範例

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.

解答

Python

class Solution:
    def allPathsSourceTarget(self, graph: List[List[int]]) -> List[List[int]]:
        DAG = defaultdict(list)
        paths = []

        for u, node in enumerate(graph):
            for v in node:
                DAG[u].append(v)

        def dfs(u, path):
            if u == len(graph) - 1:
                paths.append(path.copy())
                return

            for v in DAG[u]:
                path.append(v)
                dfs(v, path)
                path.pop()
                
        dfs(0, [0])
        return paths

KobeFri, Dec 30, 2022

Reference

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