POJ - 1419 （最大独立集 最大团问题）

Graph Coloring

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 5414		Accepted: 2526		Special Judge

Description

You are to write a program that tries to find an optimal coloring for a given graph. Colors are applied to the nodes of the graph and the only available colors are black and white. The coloring of the graph is called optimal if a maximum of nodes is black. The coloring is restricted by the rule that no two connected nodes may be black. 


 
Figure 1: An optimal graph with three black nodes 

Input

The graph is given as a set of nodes denoted by numbers 1...n, n <= 100, and a set of undirected edges denoted by pairs of node numbers (n1, n2), n1 != n2. The input file contains m graphs. The number m is given on the first line. The first line of each graph contains n and k, the number of nodes and the number of edges, respectively. The following k lines contain the edges given by a pair of node numbers, which are separated by a space.

Output

The output should consists of 2m lines, two lines for each graph found in the input file. The first line of should contain the maximum number of nodes that can be colored black in the graph. The second line should contain one possible optimal coloring. It is given by the list of black nodes, separated by a blank.

Sample Input

1
6 8
1 2
1 3
2 4
2 5
3 4
3 6
4 6
5 6

Sample Output

3
1 4 5

Source

Southwestern European Regional Contest 1995

解题思路：求解无向图的最大独立集。无向图最大独立集=该无向图的补图的最大团。所以用最大团求解。关于最大团网上有很多介绍了。直接暴力搜索解即可。详见代码

//最大团做法

#include 
#include 
#include 
#include 

//最大独立集做法（实际上就是把0改成1,1改成0）

#include 
#include 
#include 
#include