797. All Paths From Source to Target

1. Question

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]).

2. Examples

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]]

Example 3:

Input: graph = [[1],[]]
Output: [[0,1]]

Example 4:

Input: graph = [[1,2,3],[2],[3],[]]
Output: [[0,1,2,3],[0,2,3],[0,3]]

Example 5:

Input: graph = [[1,3],[2],[3],[]]
Output: [[0,1,2,3],[0,3]]

3. 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.

4. References

来源：力扣（LeetCode） 链接：https://leetcode-cn.com/problems/all-paths-from-source-to-target 著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

5. Solutions

dfs

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

    public void dfs(int[][] graph, int index, List<Integer> list) {
        list.add(index);
        if (index == graph.length - 1) {
            lists.add(new ArrayList<>(list));
            return ;
        }
        for (int i : graph[index]) {
            dfs(graph, i, list);
            list.remove(list.size() - 1);   // 不符合条件的要删掉
        }

    }
}