## Minimum Height Trees 解答

### Question

For an 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 :

```Input: `n = 4`, `edges = [[1, 0], [1, 2], [1, 3]]`

0
|
1
/ \
2   3

Output: ``
```

Example 2 :

```Input: `n = 6`, `edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]`

0  1  2
\ | /
3
|
4
|
5

Output: `[3, 4]````

Note:

• 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.”
• The height of a rooted tree is the number of edges on the longest downward path between the root and a leaf.

### Solution

BFS时间复杂度是O(N)

``` 1 class Solution:
2     def findMinHeightTrees(self, n: int, edges: List[List[int]]) -> List[int]:
3         if n == 1:
4             return 
5         adjacency_list = [set() for i in range(n)]
7         for edge in edges:
10         # Build leaves list
11         leaves = [i for i in range(n) if len(adjacency_list[i]) == 1]
12         # BFS
13         while n > 2:
14             n -= len(leaves)
15             new_leaves = []
16             while leaves:
17                 leaf = leaves.pop()