73. Minimum Height Trees

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本文介绍了一种算法，用于解决在给定无向图中寻找所有最小高度树的问题。通过逐步去除叶子节点的方法，最终确定了树的根节点。文章提供了一个具体的C++实现示例。

Minimum Height Trees My Submissions QuestionEditorial Solution
Total Accepted: 12164 Total Submissions: 45386 Difficulty: Medium
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]]

return [1]

Example 2:

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

return [3, 4]

题意：
对于一棵无向树，我们可以选择它的任意节点作为根。得到的结果就是有根树。在所有可能的有根树中，高度最小的称为最小高度树（MHT）。给定一个无向图，编写函数找出所有的最小高度树，并返回其根标号的列表。

思路：逐步去掉相应的叶子节点，那么最后剩下的便是根节点（<=2)
如上图：1.去掉0,1,2,再去掉5

算法如下：
注意：尽量节省时间，否则很容易就time limited!!!!
以下的新一轮叶子节点尽量一次得到，不要再另外扫描，否则超时

class Solution {
public:
    vector<int> findMinHeightTrees(int n, vector<pair<int, int>>& edges) {
        int nsize=edges.size();
        set<int> ps;
        map<int,set<int>> mp;      //类似于邻接表
        for(int i=0;i<nsize;++i){
                mp[edges[i].first].insert(edges[i].second);
                mp[edges[i].second].insert(edges[i].first);
        }
        set<int> leaf;
        auto it = mp.begin();
        while(it!=mp.end()){
            if(it->second.size()==1)leaf.insert(it->first);  //第一次得到叶子节点集合
            ++it;
        }
        while(mp.size()>2){              //当剩下的节点数>2
            set<int> newleaf;
            auto it2 = mp.begin();
            while(it2!=mp.end()){
                if(leaf.count(it2->first)){          //如果当前节点在叶子节点
                    auto itbeg = (it2->second).begin();
                    auto itend = (it2->second).end();
                    while(itbeg!=itend){              //使得和叶子节点相邻的节点不再和叶子节点相连
                        mp[*itbeg].erase(it2->first);
                        if(mp[*itbeg].size()==1)newleaf.insert(*itbeg); //加入到新一轮的叶子节点
                        ++itbeg;
                    }
                    auto it2next = ++it2; //确保迭代器有效
                    --it2;
                    mp.erase(it2);      //删除叶子节点
                    it2 = it2next;
                }
                else ++it2;
            }
            leaf = newleaf;       //更新新一轮的叶子节点
        }
         vector<int> res;
         if(n==1){                //如果n==1要求直接返回0
             res.push_back(0);
             return res;
         }
         auto mit=mp.begin();
         while(mit!=mp.end()){
             res.push_back(mit->first);
             ++mit;
         }
         return res;
    }
};