Description
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: [1]
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.
Solutions
BFS
采用层层剥茧的方式进行求解：
class Solution(object):
def findMinHeightTrees(self, n, edges):
"""
:type n: int
:type edges: List[List[int]]
:rtype: List[int]
"""
if n == 1:
return [0]
leaves = collections.defaultdict(set)
for u, v in edges:
leaves[u].add(v)
leaves[v].add(u)
que = collections.deque()
for u, vs in leaves.items():
if len(vs) == 1:
que.append(u)
while n > 2:
_len = len(que)
n = _len
for _ in range(_len):
u = que.popleft()
for v in leaves[u]:
leaves[v].remove(u)
if len(leaves[v]) == 1:
que.append(v)
return list(que)
# Runtime: 216 ms, faster than 70.15% of Python online submissions for Minimum Height Trees.
# Memory Usage: 18.4 MB, less than 33.33% of Python online submissions for Minimum Height Trees.