## 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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