797. All Paths From Source to Target
Đề Bài
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.length2 <= n <= 150 <= graph[i][j] < ngraph[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.
Thuật Toán & Kỹ Thuật
⏱️ Thời gian
O(V+E)
💾 Không gian
O(V)
Lời Giải
C++
0797-all-paths-from-source-to-target.cpp
class Solution {
private:
int n;
vector<vector<int>> ans, adj;
vector<int> tmp;
public:
void backTracking(vector<vector<int>>& graph, int u) {
if (u == n - 1) {
ans.push_back(tmp);
return;
}
for (int v : graph[u]) {
tmp.push_back(v);
backTracking(graph, v);
tmp.pop_back();
}
}
vector<vector<int>> allPathsSourceTarget(vector<vector<int>>& graph) {
this->n = graph.size();
adj.resize(n);
tmp.push_back(0);
backTracking(graph, 0);
return ans;
}
};
Python
0797-all-paths-from-source-to-target.py
class Solution:
def allPathsSourceTarget(self, graph: List[List[int]]) -> List[List[int]]:
ans = []
n = len(graph)
def dfs(u: int, path: List[int]) -> None:
if u == n - 1:
ans.append(path)
return
for v in graph[u]:
dfs(v, path + [v])
dfs(0, [0])
return ans