bzoj2530 [Poi2011]Party

Posted 2020-10-09 zbtrs

2530: [Poi2011]Party

Time Limit: 10 Sec  Memory Limit: 128 MBSec  Special Judge
Submit: 342  Solved: 196
[Submit][Status][Discuss]

Description

Byteasar intends to throw up a party. Naturally, he would like it to be a success. Furthermore, Byteasar is quite certain that to make it so it suffices if all invited guests know each other. He is currently trying to come up with a list of his friends he would like to invite. Byteasar has friends, where is divisible by 3. Fortunately, most of Byteasar‘s friends know one another. Furthermore, Byteasar recalls that he once attended a party where there were2/3 n of his friends, and where everyone knew everyone else. Unfortunately, Byteasar does not quite remember anything else from that party... In particular, he has no idea which of his friends attended it. Byteasar does not feel obliged to throw a huge party, but he would like to invite at least n/3of his friends. He has no idea how to choose them, so he asks you for help.

给定一张N（保证N是3的倍数）个节点M条边的图，并且保证该图存在一个大小至少为2N/3的团。

请输出该图的任意一个大小为N/3的团。 一个团的定义为节点的一个子集，该子集中的点两两有直接连边。 输入： 第一行是两个整数N,M。 接下来有M行，每行两个整数A,B，表示A和B有连边。保证无重边。 输出： N/3个整数，表示你找到的团。 数据范围： 

3<=N<=3000,[3/2 n(2/3 n -1)]/2<=M<=[n(n-1)/2]

Input

In the first line of the standard input two integers, n and M(3<=N<=3000,[3/2 n(2/3 n -1)]/2<=M<=[n(n-1)/2]), are given, separated by a single space. These denote the number of Byteasar‘s friends and the number of pairs of his friends who know each other, respectively. Byteasar‘s friends are numbered from 1 to . Each of the following lines holds two integers separated by a single space. The numbers in line no.i+1(for i=1,2,...,m) are Ai and Bi(1<=Ai<Bi<=N), separated by a single space, which denote that the persons Ai and Bi now each other. Every pair of numbers appears at most once on the input.

Output

In the first and only line of the standard output your program should print N/3numbers, separated by single spaces, in increasing order. These number should specify the numbers of Byteasar‘s friends whom he should invite to the party. As there are multiple solutions, pick one arbitrarily.

Sample Input

6 10
2 5
1 4
1 5
2 4
1 3
4 5
4 6
3 5
3 4
3 6

Sample Output

2 4

HINT

Explanation of the example: Byteasar‘s friends numbered 1, 3, 4, 5 know one another. However, any pair of Byteasar‘s friends who know each other, like 2 and 4 for instance, constitutes a correct solution, i.e., such a pair needs not be part of aforementioned quadruple.

Source

鸣谢 Object022&suhang

分析：一道构造题，每次找一对没有连边的点,这一对点中至少有一个不在团中，都删掉，打上标记，就能防止删除一定在团中的点，因为有一个不超过2n/3的团，所以最多删掉2n/3个点，最后剩下的点个数一定大于等于n/3.