Add to List 310. Minimum Height Trees

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

        0
        |
        1
       / \
      2   3

return [1]

Example 2:

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

     0  1  2
      \ | /
        3
        |
        4
        |
        5

return [3, 4]

Note:

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

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

关键是一层一层把叶子节点去掉直到剩下1/2个节点。

class Solution {
    public:
        
        struct Node
        {
            unordered_set<int> neighbor;
            bool isLeaf()const{return neighbor.size()==1;}
        };
        
        vector<int> findMinHeightTrees(int n, vector<pair<int, int>>& edges) {
            
            vector<int> buffer1;
            vector<int> buffer2;
            vector<int>* pB1 = &buffer1;
            vector<int>* pB2 = &buffer2;
            if(n==1)
            {
                buffer1.push_back(0);
                return buffer1;
            }
            if(n==2)
            {
                buffer1.push_back(0);
                buffer1.push_back(1);
                return buffer1;
            }
            
            // build the graph
            vector<Node> nodes(n);
            for(auto p:edges)
            {
                nodes[p.first].neighbor.insert(p.second);
                nodes[p.second].neighbor.insert(p.first);
            }
            
            // find all leaves
            for(int i=0; i<n; ++i)
            {
                if(nodes[i].isLeaf()) pB1->push_back(i);
            }

            // remove leaves layer-by-layer            
            while(1)
            {
                for(int i : *pB1)
                {
                    for(auto n: nodes[i].neighbor)
                    {
                        nodes[n].neighbor.erase(i);
                        if(nodes[n].isLeaf()) pB2->push_back(n);
                    }
                }
                if(pB2->empty())
                {
                    return *pB1;
                }
                pB1->clear();
                swap(pB1, pB2);
            }
            
        }
    };