All Paths from Source to Target

Problem

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]]

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

class Solution {
    public List<List<Integer>> allPathsSourceTarget(int[][] graph) {
        var ans = new ArrayList<List<Integer>>();
        solve(graph, List.of(0), ans);
        return ans;
    }

    public void solve(int[][] graph, List<Integer> curr, List<List<Integer>> ans) {
        var n = curr.get(curr.size() - 1);
        if (n == graph.length - 1) {
            ans.add(curr);
            return;
        }

        for (var e : graph[n]) {
            var l = new ArrayList<>(curr);
            l.add(e);
            solve(graph, l, ans);
        }
    }
}