HDU - 6228 Tree （2017ICPC沈阳站 深搜+思维）

Tree

Problem Description

Consider a un-rooted tree T which is not the biological significance of tree or plant, but a tree as an undirected graph in graph theory with n nodes, labelled from 1 to n. If you cannot understand the concept of a tree here, please omit this problem.
Now we decide to colour its nodes with k distinct colours, labelled from 1 to k. Then for each colour i = 1, 2, · · · , k, define Ei as the minimum subset of edges connecting all nodes coloured by i. If there is no node of the tree coloured by a specified colour i, Ei will be empty.
Try to decide a colour scheme to maximize the size of E1 ∩ E2 · · · ∩ Ek, and output its size.

 

Input

The first line of input contains an integer T (1 ≤ T ≤ 1000), indicating the total number of test cases.
For each case, the first line contains two positive integers n which is the size of the tree and k (k ≤ 500) which is the number of colours. Each of the following n - 1 lines contains two integers x and y describing an edge between them. We are sure that the given graph is a tree.
The summation of n in input is smaller than or equal to 200000.

 

Output

For each test case, output the maximum size of E1 ∩ E1 ... ∩ Ek.

 

Sample Input

3 4 2 1 2 2 3 3 4 4 2 1 2 1 3 1 4 6 3 1 2 2 3 3 4 3 5 6 2

 

Sample Output

1 0 1

 

题意：给你一棵树，和K种颜色，用这K种颜色去染色。然后将相同颜色的点连通所需要的最少的边作为一个集合。然后将所有颜色形成的集合做一个交，现在要找到一种染色方案，使得这个交集最大。若不使用某种颜色，那么该颜色的边集为空集。

解题思路：题目看了半天，终于看懂了，一开始往点的方向去想，毫无思路，换成边去想就好了。首先对于某种颜色染色，肯定是只染两个点最好（尽量的省点给其他颜色染）！基于这个思路，我们又想到，为了使集合最大化，肯定是染最远的两个点最好！但是有很多颜色，怎么办呢？其实对于每一条边，他有两个点，或者说两个子树，我们只要看看对于每一条边，它左右两边的子树的大小，是不是都大于K就好了。如果是，那么那条边，肯定在交集里面！（基于我们的最优算法）。所以一个深搜，答案就出来了，具体看代码。

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