# 310 Minimum Height Trees

### 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 1:

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

``````    0
|
1
/ \
2   3
``````

return 

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]

Hint:

How many MHTs can a graph have at most? 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.

### Solutions:

``````public class Solution {
public List<Integer> findMinHeightTrees(int n, int[][] edges) {
}
}
if (leaves.size() == 0) {
return leaves;
}
while (n > 2) {
n = n - leaves.size();
for (Integer i:leaves) {
}
}
leaves = newLeaves;
}
return leaves;
}
for (int i = 0; i < n; i ++) {