For a undirected graph with tree characteristics, we can choose any node as the root. The result graph is then a rooted tree. Among all possible rooted trees, those with minimum height are called minimum height trees (MHTs). Given such a graph, write a function to find all the MHTs and return a list of their root labels.

Format
The graph contains n nodes which are labeled from 0 to n - 1. You will be given the number n and a list of undirected edges (each edge is a pair of labels).

You can assume that no duplicate edges will appear in edges. Since all edges are undirected, [0, 1] is the same as [1, 0] and thus will not appear together in edges.

Example 1:

Given n = 4edges = [[1, 0], [1, 2], [1, 3]]

        0
|
1
/ \
2 3

return [1]

Example 2:

Given n = 6edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]

     0  1  2
\ | /
3
|
4
|
5

return [3, 4]

Show Hint

Note:

(1) According to the definition of tree on Wikipedia: “a tree is an undirected graph in which any two vertices are connected by exactly one path. In other words, any connected graph without simple cycles is a tree.”

(2) The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.

 
 
vector<int> findMinHeightTrees(int n, vector<pair<int, int>>& edges) {
//corner case
if ( n <= ) return {}; //construct a edges search data stucture
vector<unordered_set<int>> graph(n);
for (auto e : edges) {
graph[e.first].insert(e.second);
graph[e.second].insert(e.first);
} //find all of leaf nodes
vector<int> current;
for (int i=; i<graph.size(); i++){
if (graph[i].size() == ) current.push_back(i);
} // BFS the graph
while (true) {
vector<int> next;
for (int node : current) {
for (int neighbor : graph[node]) {
graph[neighbor].erase(node);
if (graph[neighbor].size() == ) next.push_back(neighbor);
}
}
if (next.empty()) break;
current = next;
}
return current;
}

每次去掉最外面一圈叶子节点。最后剩下的节点集合即为所求。

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