README_EN.md

797. All Paths From Source to Target

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Description

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.

Solutions

Since there is no ring in the graph, you can simply use DFS or BFS to traverse it.

Python3

BFS.

class Solution:
    def allPathsSourceTarget(self, graph: List[List[int]]) -> List[List[int]]:
        n = len(graph)
        q = deque([[0]])
        ans = []
        while q:
            path = q.popleft()
            u = path[-1]
            if u == n - 1:
                ans.append(path)
                continue
            for v in graph[u]:
                q.append(path + [v])
        return ans

DFS:

class Solution:
    def allPathsSourceTarget(self, graph: List[List[int]]) -> List[List[int]]:
        ans = []

        def dfs(t):
            if t[-1] == len(graph) - 1:
                ans.append(t.copy())
                return

            for v in graph[t[-1]]:
                t.append(v)
                dfs(t)
                t.pop()

        dfs([0])
        return ans

Java

BFS:

class Solution {
    public List<List<Integer>> allPathsSourceTarget(int[][] graph) {
        int n = graph.length;
        Queue<List<Integer>> queue = new ArrayDeque<>();
        queue.offer(Arrays.asList(0));
        List<List<Integer>> ans = new ArrayList<>();
        while (!queue.isEmpty()) {
            List<Integer> path = queue.poll();
            int u = path.get(path.size() - 1);
            if (u == n - 1) {
                ans.add(path);
                continue;
            }
            for (int v : graph[u]) {
                List<Integer> next = new ArrayList<>(path);
                next.add(v);
                queue.offer(next);
            }
        }
        return ans;
    }
}

DFS:

class Solution {
    private List<List<Integer>> ans;
    private int[][] graph;

    public List<List<Integer>> allPathsSourceTarget(int[][] graph) {
        ans = new ArrayList<>();
        this.graph = graph;
        List<Integer> t = new ArrayList<>();
        t.add(0);
        dfs(t);
        return ans;
    }

    private void dfs(List<Integer> t) {
        int cur = t.get(t.size() - 1);
        if (cur == graph.length - 1) {
            ans.add(new ArrayList<>(t));
            return;
        }
        for (int v : graph[cur]) {
            t.add(v);
            dfs(t);
            t.remove(t.size() - 1);
        }
    }
}

C++

DFS:

class Solution {
public:
    vector<vector<int>> graph;
    vector<vector<int>> ans;

    vector<vector<int>> allPathsSourceTarget(vector<vector<int>>& graph) {
        this->graph = graph;
        vector<int> path;
        path.push_back(0);
        dfs(0, path);
        return ans;
    }

    void dfs(int i, vector<int> path) {
        if (i == graph.size() - 1)
        {
            ans.push_back(path);
            return;
        }
        for (int j : graph[i])
        {
            path.push_back(j);
            dfs(j, path);
            path.pop_back();
        }
    }
};

Go

DFS:

func allPathsSourceTarget(graph [][]int) [][]int {
	var path []int
	path = append(path, 0)
	var ans [][]int

	var dfs func(i int)
	dfs = func(i int) {
		if i == len(graph)-1 {
			ans = append(ans, append([]int(nil), path...))
			return
		}
		for _, j := range graph[i] {
			path = append(path, j)
			dfs(j)
			path = path[:len(path)-1]
		}
	}

	dfs(0)
	return ans
}

JavaScript

/**
 * @param {number[][]} graph
 * @return {number[][]}
 */
var allPathsSourceTarget = function (graph) {
    const ans = [];
    const t = [0];

    const dfs = t => {
        const cur = t[t.length - 1];
        if (cur == graph.length - 1) {
            ans.push([...t]);
            return;
        }
        for (const v of graph[cur]) {
            t.push(v);
            dfs(t);
            t.pop();
        }
    };

    dfs(t);
    return ans;
};

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