797. All Paths From Source to Target

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]).

 

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]]

 

Constraints:

  • n == graph.length
  • 2 <= n <= 15
  • 0 <= graph[i][j] < n
  • graph[i][j] != i (i.e., there will be no self-loops).
  • The input graph is guaranteed to be a DAG.

Rust Solution

struct Solution;

impl Solution {
    fn all_paths_source_target(graph: Vec<Vec<i32>>) -> Vec<Vec<i32>> {
        let mut res = vec![];
        let mut path: Vec<i32> = vec![];
        let n = graph.len();
        Self::dfs(0, &mut path, &mut res, &graph, n);
        res
    }

    fn dfs(u: i32, path: &mut Vec<i32>, paths: &mut Vec<Vec<i32>>, graph: &[Vec<i32>], n: usize) {
        path.push(u);
        if u as usize == n - 1 {
            paths.push(path.clone());
        } else {
            for &v in &graph[u as usize] {
                Self::dfs(v, path, paths, graph, n);
            }
        }
        path.pop();
    }
}

#[test]
fn test() {
    let graph = vec_vec_i32![[1, 2], [3], [3], []];
    let res = vec_vec_i32![[0, 1, 3], [0, 2, 3]];
    assert_eq!(Solution::all_paths_source_target(graph), res);
}

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