LeetCode 310. Minimum Height Trees

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]

题目描述：
给出一个无环无向图，如果选择图中的一个顶点作为root节点，那么这个图就可以变成一棵树。题目要求我们找出使得树的高度最低的root节点的集合。

解题思路：
对于一个无环无向图，要找到其中使得树高度最低的root节点，可以想象成是从一个图的边缘顶点(度为1的顶点)一直往图的里面寻找的过程。类似地，对于一个圆，到圆的边界任何一点最近的点就是圆心。所以这里对于一个图，我们的目标就是找到一个类似圆心的顶点，就是使得树高度最低的root节点。
这个过程首先从图的所有边缘点同时开始出发，并删掉这些边缘点，之后图中会出现一些新的边缘点，直到图中剩下的点的个数不超过2。题目的给出的例子比较简单，下面我以自己设定的例子来解析这个过程。

上图中红色点表示当前的边缘点，每次找到边缘点之后去掉再继续找边缘点，最后图中只剩下顶点1和顶点4，此时不管用顶点1还是顶点4作为树的root节点，得到的树的高度都是最小的。分别以顶点1和顶点4为root节点的树结构如下图所示，可以看到两棵树的高度都为4。

代码：

////  main.cpp//  310. Minimum Height Trees////  Created by mingjc on 2017/4/2.//  Copyright © 2017年 mingjc. All rights reserved.//#include <iostream>#include <vector>#include <unordered_set>using namespace std;class Solution {public:    vector<int> findMinHeightTrees(int n, vector<pair<int, int>>& edges) {        vector<unordered_set<int>> adjList(n);        unordered_set<int> vSet;        for (int i = 0; i < n; i++) {            vSet.insert(i);        }        for (int i = 0; i < edges.size(); i++) {            adjList[edges[i].first].insert(edges[i].second);            adjList[edges[i].second].insert(edges[i].first);        }        while (vSet.size() > 2) {            vector<int> temp;            for (int i = 0; i < adjList.size(); i++) {                if (adjList[i].size() == 1) {  //判断是否叶子结点                    temp.push_back(i);                    temp.push_back(*adjList[i].begin());                }            }            for(int i = 0; i < temp.size(); i+=2) {                int adj0 = temp[i];                int adj1 = temp[i + 1];                adjList[adj0].erase(adj1);                adjList[adj1].erase(adj0);                vSet.erase(adj0);                // cout << "erase " << adj0 << endl;            }        }        vector<int> result(vSet.begin(), vSet.end());        return result;    }};int main(int argc, const char * argv[]) {    vector<pair<int, int>> edges;    edges.push_back(make_pair<int, int>(3, 0));    edges.push_back(make_pair<int, int>(3, 1));    edges.push_back(make_pair<int, int>(3, 2));    edges.push_back(make_pair<int, int>(3, 4));    edges.push_back(make_pair<int, int>(5, 4));    Solution sln;    vector<int> result = sln.findMinHeightTrees(6, edges);    return 0;}