797 - All Paths From Source to Target

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]).

Examples

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.

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]]

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

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

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).

• All the elements of graph[i] are unique.

• The input graph is guaranteed to be a DAG.

Java Solution (Backtracking)

class Solution {
    public List<List<Integer>> allPathsSourceTarget(int[][] graph) {
        List<List<Integer>> result = new ArrayList<>();
        int target = graph.length-1;
        LinkedList<Integer> path = new LinkedList<Integer>();
        path.addLast(0);
        
        backtrack(0, path, target, result, graph);
        return result;
    }
    
    private void backtrack(int currNode, LinkedList<Integer> path, int target, List<List<Integer>> result, int[][] graph){
        if (currNode == target) {
            result.add(new ArrayList<Integer>(path));
            return;
        }
        for (int nextNode : graph[currNode]) {
            path.addLast(nextNode);
            backtrack(nextNode, path, target, result, graph);
            path.removeLast();
        }
    }
}