poj 3692 最大独立点集

题意：男同学间相互认识，女同学间相互认识，再给男女之间的认识关系，找一个集合，使选择的男女之间都相互认识

解法：如果以“认识”关系连线，在左右结合间都会连线，有背于二分图的含义，（线段的一个顶点在左集合，一个在右集合），所以我们可以以“不认识”关系连线，这样就得到了两个合理的集合，以给出的信息补集连线~

最大独立点集=定点数（|x+y|）-最大匹配数

/*
----------------------------------

Love is more than a word.
It says so much.
When I see these four letters,
I almost feel your touch.
This is only happened since
I fell in love with you.
Why this word does this,
I haven't got a clue.

To My Goddess
CY
----------------------------------
*/

#include<iostream>
#include<cstring>
#include<algorithm>
#include<cstdlib>
#include<vector>
#include<cmath>
#include<stdlib.h>
#include<iomanip>
#include<list>
#include<deque>
#include<map>
#include <stdio.h>
#include <queue>

#define maxn 250+5

#define ull unsigned long long
#define ll long long
#define reP(i,n) for(i=1;i<=n;i++)
#define REP(i,a,b) for(i=a;i<=b;i++)
#define rep(i,n) for(i=0;i<n;i++)

#define cle(a) memset(a,0,sizeof(a))
#define clehead(a) rep(i,maxn)a[i]=-1

/*
The time of story :
**  while(1)
{
once upon a time,
there was a mountain,
on top of which there was a temple,
in which there was an old monk and a little monk.
Old monk was telling stories inside the temple.
What was he talking about?
**  }

ÎûÎû
(*^__^*)
*/

#define sci(a) scanf("%d",&a)
#define scd(a) scanf("%lf",&a)
#define pri(a) printf("%d",a)
#define prie(a) printf("%d\n",a)
#define prd(a)  printf("%lf",a)
#define prde(a) printf("%lf\n",a)
#define pre printf("\n")

#define LL(x) x<<1
#define RR(x) x<<|1

#define pb push_back
#define mod 90001
#define PI 3.141592657

const ull INF = 1LL << 61;
const int inf =   int(1e5)+10;
const double eps=1e-5;

using namespace std;

struct node
{
int u,v,w;
int next;
};

bool cmp(int a,int b){
return a>b;
}
bool bmap[maxn][maxn];
bool bmark[10000];
int nx,ny;
int cx[10000];
int cy[10000];
int m,g,b;
int findpath(int u)
{
int i,j,k;
rep(i,ny){
if(bmap[u][i]&&!bmark[i]){
bmark[i]=1;
if(cy[i]==-1||findpath(cy[i]))
{
cy[i]=u;
cx[u]=i;
return 1;
}
}
}
return 0;
}

int maxmatch()
{
int i,j,k;
int res(0);
rep(i,nx)cx[i]=-1;
rep(j,ny)cy[j]=-1;
rep(i,nx){
if(cx[i]==-1){
rep(j,ny)bmark[j]=0;
res+=findpath(i);
}
}
return res;
}
int main()
{
freopen("in.txt","r",stdin);
//freopen("out.txt","w",stdout);
int T=0;
while(cin>>g>>b>>m)
{
if(m+g+b==0)break;
int i,j,k;
memset(bmap,true,sizeof(bmap));
nx=g,ny=b;
rep(i,m)
{
int x,y;
cin>>x>>y;
bmap[x-1][y-1]=false;
}
printf("Case %d: ",++T);
cout<<nx+ny-maxmatch()<<endl;
}
return 0;
}