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【LeetCode】310. Minimum Height Trees 解题报告(Python)


id: fuxuemingzhu

个人博客: ​​​http://fuxuemingzhu.cn/​​​


目录


  • ​​题目描述​​
  • ​​题目大意​​
  • ​​解题方法​​
  • ​​BFS​​
  • ​​相似题目​​
  • ​​参考资料​​
  • ​​日期​​


题目地址:​​https://leetcode.com/problems/minimum-height-trees/description/​​

题目描述

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 :

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:


  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.

题目大意

找出以哪些节点为根节点的时候,构建出来的整棵树的高度是最低的。

解题方法

BFS

这个题很优秀啊,是个好题。这个题给定的是个图,但是让我们构建成树,也就是说构建出来的并不是二叉树。题目其实想考我们的是,整个图最靠近中间的节点是什么。我们使用类似与拓扑排序的BFS进行解决。

拓扑排序我们都知道,每次选择入度为0的节点进行删除。在这个题中,因为我们要找到无向图最靠近中间的节点,所以,我们先使用一个字典保存每个节点的所有相邻节点set。每次把所有只有一个邻接的节点(叶子节点,类似于入度为0,但是这是个无向图,入度等于出度)都放入队列,然后遍历队列中的节点u,把和每个节点u相邻的节点v的set删去u,所以这一步操作得到的是去除了叶子节点的新一轮的图。所以我们需要再次进行选择只有一个邻接节点的叶子节点,然后放入队列中,再次操作。最后结束的标准是,整个图只留下了1个或者两个元素。为什么不能是3个呢?因为题目第一句话说了给出的图是具有树的特性的,所以一定没有环存在。

这个题整体的思路就是把所有的叶子节点放入队列中,然后同时向中间遍历,这样最后剩下来的就是整棵树中间的元素。

时间复杂度是O(V),空间复杂度是O(E + V).

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)

相似题目

​​207. Course Schedule​​

​​210. Course Schedule II​​

日期

2018 年 10 月 30 日 —— 啊,十月过完了



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