leetcode Minimum Height Trees - 细语呢喃

leetcode Minimum Height Trees - 细语呢喃

leetcode Minimum Height Trees

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]]

Python

0 | 1 / \ 2 3

1 2 3 4 5

0         |         1        / \       2   3

return [1]

Example 2:

Given n = 6, edges = [[0, 3], [1, 3], [2, 3], [4, 3], [5, 4]]

Python

0 1 2 \ | / 3 | 4 | 5

1 2 3 4 5 6 7

0  1  2       \ | /         3         |         4         |         5

return [3, 4]

Hint:

1. 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.

 

今天新出的题 leetcode Minimum Height Trees

题意：

给定一个n个结点n-1条边的无向图（就是树啦），让你找从哪个点出发，到其他结点的最长距离最小？（返回所有答案）

思路：

一开始类似RIP来更新距离，结果TLE。证明O(n^2)的复杂度太大

只好想其他的方法。

答案一定是最长距离的中间结点位置上。

我们要的是中间结点，沿着树的外围每次把叶子结点砍掉，那么，最后剩下的不就是中间结点了么？

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