# 797. All Paths From Source to Target

## Medium

***

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:**

![](https://assets.leetcode.com/uploads/2020/09/28/all_1.jpg)

```
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:**

![](https://assets.leetcode.com/uploads/2020/09/28/all_2.jpg)

```
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**.

**Solution**

```python
class Solution:
    def allPathsSourceTarget(self, graph: List[List[int]]) -> List[List[int]]:
        target = len(graph)-1
        result = []
        def recursion(node, path):
            # Base Condition
            if node == target:
                result.append(path)
            for adj in graph[node]:
                path.append(adj)
                recursion(adj, path[:])
                path.pop()
        recursion(0, [0])
        return result
```