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 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.

一刷
思路是，用一个list记录所有的node, list[i]为一个set,装有所有与i相邻点的编号。如果set的size为1，表示为叶子节点，移去。即每次移去最外层（相同深度）的叶子。最终剩下来的为满足条件的root

public class Solution {
    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        if(n == 1) return Collections.singletonList(0);
        List<Set<Integer>> adj = new ArrayList<>(n);
        
        for(int i=0; i<n; i++) adj.add(new HashSet<Integer>());
        for(int[] edge : edges){
            adj.get(edge[0]).add(edge[1]);
            adj.get(edge[1]).add(edge[0]);
        }
        
        List<Integer> leaves = new ArrayList<>();
        for(int i=0; i<n; i++)
            if(adj.get(i).size() == 1) leaves.add(i);
        
        while(n>2){
            n -= leaves.size();
            List<Integer> newLeaves = new ArrayList<>();
            for(int i:leaves){
                int j = adj.get(i).iterator().next();
                adj.get(j).remove(i);
                if(adj.get(j).size() == 1) newLeaves.add(j);
            }
            leaves = newLeaves;
        }
        return leaves;
    }
}

二刷
同上

class Solution {
    public List<Integer> findMinHeightTrees(int n, int[][] edges) {
        if(n == 1) return Collections.singletonList(0);
        List<Set<Integer>> adj = new ArrayList<>();
        for(int i=0; i<n; i++) adj.add(new HashSet<Integer>());
        for(int[] edge : edges){
            adj.get(edge[0]).add(edge[1]);
            adj.get(edge[1]).add(edge[0]);
        }
        
        List<Integer> leaves = new ArrayList<>();
        for(int i=0; i<n; i++){
            if(adj.get(i).size() == 1) leaves.add(i);
        }
        
        while(n>2){
            n -= leaves.size();
            List<Integer> newLeaves = new ArrayList<>();
            for(int i:leaves){
                int j = adj.get(i).iterator().next();
                adj.get(j).remove(i);
                if(adj.get(j).size() == 1) newLeaves.add(j);
            }
            leaves = newLeaves; 
        }
        return leaves;
    }
}