Given a directed acyclic graph, with n vertices numbered from 0 to n-1, and an array edges where edges[i] = [fromi, toi] represents a directed edge from node fromi to node toi.
Find the smallest set of vertices from which all nodes in the graph are reachable. It’s guaranteed that a unique solution exists.
Notice that you can return the vertices in any order.
Input:
n = 6, edges = [[0,1],[0,2],[2,5],[3,4],[4,2]]
Output:
[0,3]
Explanation: It's not possible to reach all the nodes from a single vertex. From 0 we can reach [0,1,2,5]. From 3 we can reach [3,4,2,5]. So we output [0,3].
Example 2:
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Input:
n = 5, edges = [[0,1],[2,1],[3,1],[1,4],[2,4]]
Output:
[0,2,3]
Explanation: Notice that vertices 0, 3 and 2 are not reachable from any other node, so we must include them. Also any of these vertices can reach nodes 1 and 4.
The key idea is that in a directed acyclic graph, any node with in-degree zero cannot be reached from any other node. Thus, to reach all nodes, we must start from all nodes with in-degree zero.
classSolution {
public: vector<int> findSmallestSetOfVertices(int n, vector<vector<int>>& edges) {
vector<int> indeg(n);
for (auto& e : edges) indeg[e[1]]++;
vector<int> ans;
for (int i =0; i < n; ++i) if (indeg[i] ==0) ans.push_back(i);
return ans;
}
};
classSolution {
public List<Integer>findSmallestSetOfVertices(int n, List<List<Integer>> edges) {
int[] indeg =newint[n];
for (List<Integer> e : edges) indeg[e.get(1)]++;
List<Integer> ans =new ArrayList<>();
for (int i = 0; i < n; i++) if (indeg[i]== 0) ans.add(i);
return ans;
}
}
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classSolution {
funfindSmallestSetOfVertices(n: Int, edges: List<List<Int>>): List<Int> {
val indeg = IntArray(n)
for (e in edges) indeg[e[1]]++val ans = mutableListOf<Int>()
for (i in0 until n) if (indeg[i] ==0) ans.add(i)
return ans
}
}
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classSolution:
deffindSmallestSetOfVertices(self, n: int, edges: list[list[int]]) -> list[int]:
indeg = [0] * n
for u, v in edges:
indeg[v] +=1return [i for i in range(n) if indeg[i] ==0]
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impl Solution {
pubfnfind_smallest_set_of_vertices(n: i32, edges: Vec<Vec<i32>>) -> Vec<i32> {
let n = n asusize;
letmut indeg =vec![0; n];
for e in edges.iter() {
indeg[e[1] asusize] +=1;
}
letmut ans =vec![];
for i in0..n {
if indeg[i] ==0 {
ans.push(i asi32);
}
}
ans
}
}
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classSolution {
findSmallestSetOfVertices(n: number, edges: number[][]):number[] {
constindeg= Array(n).fill(0);
for (const [_, v] ofedges) indeg[v]++;
constans: number[] = [];
for (leti=0; i<n; i++) if (indeg[i] ===0) ans.push(i);
returnans;
}
}