网络流(二分)：BZOJ 3993: [SDOI2015]星际战争

  1 #include <iostream>
  2 #include <cstring>
  3 #include <cstdio>
  4 #include <cmath>
  5 using namespace std;
  6 const int maxn=2510;
  7 const int maxm=6010;
  8 const double eps=1e-8;
  9 int cnt=1,fir[maxn],to[maxm],nxt[maxm];
 10 double cap[maxm];
 11 void addedge(int a,int b){
 12     nxt[++cnt]=fir[a];fir[a]=cnt;to[cnt]=b;
 13 }
 14 
 15 int G[51][51];
 16 int A[51],B[51];
 17 
 18 void Build(double k,int n,int m){
 19     int ct=1;
 20     for(int i=1;i<=m;i++)
 21         for(int j=1;j<=n;j++)
 22             if(G[i][j])
 23                 cap[++ct]=1e20,cap[++ct]=0.0;
 24     
 25     for(int i=1;i<=m;i++)
 26         cap[++ct]=1.0*B[i]*k,cap[++ct]=0.0;
 27     
 28     for(int i=1;i<=n;i++)
 29         cap[++ct]=1.0*A[i],cap[++ct]=0.0;                        
 30 }
 31 
 32 int dis[maxn],gap[maxn],q[maxn],front,back;
 33 
 34 void BFS(int S,int T){
 35     memset(dis,0,sizeof(dis));
 36     front=back=1;
 37     dis[T]=1;q[back++]=T;
 38     while(front<back){
 39         int node=q[front++];
 40         for(int i=fir[node];i;i=nxt[i]){
 41             if(dis[to[i]])continue;
 42             dis[to[i]]=dis[node]+1;
 43             q[back++]=to[i];
 44         }
 45     }
 46 }
 47 double mid;
 48 int path[maxn],fron[maxn];
 49 double ISAP(int S,int T){
 50     double ret=0.0;
 51     BFS(S,T);
 52     for(int i=S;i<=T;i++)gap[dis[i]]++;
 53     int p=S;
 54     double f;
 55     memcpy(fron,fir,sizeof(fir));
 56     while(dis[S]<=T+1){
 57         if(p==T){
 58             f=1e20;
 59             while(p!=S){
 60                 f=min(f,cap[path[p]]);
 61                 p=to[path[p]^1];
 62             }
 63             p=T;ret+=f;
 64             while(p!=S){
 65                 cap[path[p]]-=f;
 66                 cap[path[p]^1]+=f;
 67                 p=to[path[p]^1];
 68             }
 69         }
 70         int &ii=fron[p];
 71         for(;ii;ii=nxt[ii])
 72             if(cap[ii]&&dis[p]==dis[to[ii]]+1)
 73                 break;    
 74         if(ii)
 75             path[p=to[ii]]=ii;
 76         else{
 77             if(--gap[dis[p]]==0)break;
 78             int minn=T+1;
 79             for(int i=fir[p];i;i=nxt[i])
 80                 if(cap[i])
 81                     minn=min(minn,dis[to[i]]);
 82             
 83             ii=fir[p];
 84             ++gap[dis[p]=minn+1];        
 85             if(p!=S)
 86                 p=to[path[p]^1];
 87         }        
 88     }
 89     return ret;
 90 }
 91 
 92 int main(){
 93     int n,m;
 94     scanf("%d%d",&n,&m);
 95     for(int i=1;i<=n;i++)
 96         scanf("%d",&A[i]);
 97     for(int i=1;i<=m;i++)
 98         scanf("%d",&B[i]);
 99         
100     for(int i=1;i<=m;i++)
101         for(int j=1;j<=n;j++)
102             scanf("%d",&G[i][j]);
103     
104     for(int i=1;i<=m;i++)
105         for(int j=1;j<=n;j++)
106             if(G[i][j]){
107                 addedge(i,j+m);
108                 addedge(j+m,i);
109             }
110     
111     for(int i=1;i<=m;i++)
112         addedge(0,i),addedge(i,0);
113     
114     double tot=0.0;
115     for(int i=1;i<=n;i++){
116         addedge(i+m,n+m+1);
117         addedge(n+m+1,i+m);
118         tot+=A[i];
119     }
120     double lo=0,hi=1e5;
121     while(hi-lo>=1e-4){
122         mid=(lo+hi)/2.0;
123         Build(mid,n,m);
124         if(fabs(ISAP(0,n+m+1)-tot)<eps)
125             hi=mid;
126         else
127             lo=mid;
128     }
129     printf("%.4lf\n",hi);
130     return 0;
131 }