Lvat_s Blog

最大流

拆点，男孩和女孩各拆成2个点ix,iy,jx,jy，互相喜欢ix->jx:1 不互相喜欢iy->jy:1

然后ix->iy=k,jy->jx=k,S->ix=ans,jy->T=ans

枚举ans跑最大流，不满流答案就是ans-1

#include<cstdio>
#include<queue>
#include<algorithm>
#include<cstring>
using namespace std;
 
int en,n,k,level[1005],S,T,cur[1005],POINT_N,h[1005];
char s[55][55];
 
struct Edge{
int b,f,back,next;
}e[1000005];
 
void AddEdge(int sa,int sb,int sc){
e[++en].b=sb;
e[en].f=sc;
e[en].back=en+1;
e[en].next=h[sa];
h[sa]=en;
swap(sa,sb);
e[++en].b=sb;
e[en].f=0;
e[en].back=en-1;
e[en].next=h[sa];
h[sa]=en;
}
 
int BFS(){
queue<int> Q;
Q.push(S);
memset(level,0,sizeof(level));
level[S]=1;
while(!Q.empty()){
    int u=Q.front();
    Q.pop();
    for(int i=h[u];i;i=e[i].next){
        int v=e[i].b;
        if(level[v] || !e[i].f)continue;
        level[v]=level[u]+1;
        Q.push(v);
    }
}
return level[T];
}
 
int DFS(int u,int flow){
if(u==T)return flow;
int f=flow;
for(int &i=cur[u];i;i=e[i].next){
    int v=e[i].b,fl;
    if(level[v]==level[u]+1 && e[i].f && (fl=DFS(v,min(f,e[i].f)))){
        e[i].f-=fl;
        e[e[i].back].f+=fl;
        f-=fl;
        if(f==0)return flow;
    }
}
return flow-f;
}
 
int Dinic(){
int ans=0;
while(BFS()){
    for(int i=1;i<=POINT_N;i++)cur[i]=h[i];
    ans+=DFS(S,2100000000);
}
return ans;
}
 
int main(){
freopen("1305.in","r",stdin);
freopen("1305.out","w",stdout);
scanf("%d %d",&n,&k);
for(int i=1;i<=n;i++)scanf("%s",s[i]+1);
S=4*n+1;
T=4*n+2;
POINT_N=4*n+2;
int ans=1;
while(ans<=1000){
    memset(h,0,sizeof(h));
    for(int i=1;i<=n;i++){
        AddEdge(i,i+n,k);
        AddEdge(i+3*n,i+2*n,k);
    }
    for(int i=1;i<=n;i++){
        for(int j=1;j<=n;j++){
            if(s[i][j]=='Y'){
                AddEdge(i,j+2*n,1);
            }
            else {
                AddEdge(i+n,j+3*n,1);
            }
        }
    }
    for(int i=1;i<=n;i++){
        AddEdge(S,i,ans);
        AddEdge(i+2*n,T,ans);
    }
    int an=Dinic();
    //printf("%d\n",ans);
    if(an<ans*n){printf("%d\n",ans-1);return 0;}
    ans++;
}
return 0;
}