problem.md

Problem 310: Minimum Height Trees

Difficulty: Medium

Problem

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

	
**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.