poj 1419 Graph Coloring

Posted 2020-10-17 日拱一卒 功不唐捐

http://poj.org/problem?id=1419

 

题意：

一张图黑白染色，相邻点不能都染黑色，最多能染几个黑色点

 

最大点独立集

但是图不能同构为二分图，不能用二分图匹配来做

那就爆搜吧

 

还可以转化为补图的最大团问题

 

#include<cstdio>
#include<cstring>
#include<iostream>

using namespace std;

bool map[101][101];
int color[101],res[101];

int n,ans,cnt;

void read(int &x)
{
    x=0; char c=getchar();
    while(!isdigit(c)) c=getchar();
    while(isdigit(c)) { x=x*10+c-‘0‘; c=getchar(); }
}

bool can(int s)
{
    for(int i=1;i<=n;++i)
    {
        if(map[s][i] && color[i]==1) return false;
    }
    return true;
}

void dfs(int p)
{
    if(p>n)
    {
        ans=cnt;
        int k=0;
        for(int i=1;i<=n;++i)
        {
            if(color[i]==1) res[++k]=i;
        }
        return;
    }
    if(cnt+n-p+1<=ans) return;
    if(can(p))
    {
        cnt++;
        color[p]=1;
        dfs(p+1);
        cnt--;
    }
    color[p]=2;
    dfs(p+1);
}

int main()
{
    int T;
    read(T);
    int m,x,y;
    while(T--)
    {
        read(n); read(m);
        memset(map,false,sizeof(map));
        memset(color,0,sizeof(color));
        while(m--)
        {
            read(x); read(y);
            map[x][y]=map[y][x]=true;
        }
        ans=cnt=0;
        dfs(1);
        cout<<ans<<‘\n‘;
        for(int i=1;i<ans;++i) cout<<res[i]<<‘ ‘;
        cout<<res[ans]<<‘\n‘;
    }
}

 

Graph Coloring

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 5384		Accepted: 2515		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