All Paths From Source to Target (M)

题目

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.

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题意

在一个有向无环图中找到所有从结点0到结点n-1的路径。

思路

回溯法。

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代码实现

Java

class Solution {
    public List<List<Integer>> allPathsSourceTarget(int[][] graph) {
        List<List<Integer>> ans = new ArrayList<>();
        dfs(graph, 0, graph.length - 1, new ArrayList<>(), ans);
        return ans;
    }

    private void dfs(int[][] graph, int u, int v, List<Integer> tmp, List<List<Integer>> ans) {
        tmp.add(u);

        if (u == v) {
            ans.add(new ArrayList<>(tmp));
        } else {
            for (int i = 0; i < graph[u].length; i++) {
                dfs(graph, graph[u][i], v, tmp, ans);
            }
        }

        tmp.remove(tmp.size() - 1);
    }
}