上下界网络流

最大流(BZOJ1313)

 
#include <cstdio>
#include <cstring>
#include <cmath>
#define LDB long double
using namespace std;
    
  int cnt,nd[10001],dep[10001],sor,tar,dl[10001],n,cur[10001],sta[1000001];
  LDB a[101][101];
  int in[10001],tot;
    
  struct edge{
    int next,des,cap,fr;
  }sid[1000001];
    
  void addedge(int u,int v,int cap){
      sid[cnt].next=nd[u];sid[cnt].des=v;sid[cnt].cap=cap;nd[u]=cnt;sid[cnt].fr=u;cnt++;
      sid[cnt].next=nd[v];sid[cnt].des=u;sid[cnt].cap=0;nd[v]=cnt;sid[cnt].fr=v;cnt++;
  }
     
   int bfs(){
      memset(dep,-1,sizeof(dep));
        
      int head=1,tail=1;
      dep[sor]=0;dl[head]=sor;
      while (head<=tail){
        for (int p=nd[dl[head]];p!=-1;p=sid[p].next)
          if ((dep[sid[p].des]==-1)&&(sid[p].cap)) dep[sid[p].des]=dep[dl[head]]+1,dl[++tail]=sid[p].des;
        head++;  
    }
      
    if (dep[tar]==-1) return(0);else return(1);
  }
    
  int dinic(){
      int maxflow=0;
      while (bfs()){
          for (int i=0;i<=2*n+1;i++) cur[i]=nd[i];
            
          int u=sor,top=0;
          while(1){
              if (u==tar){
                  int mi=1e9,last;
                  for (int i=1;i<=top;i++)
                    if (sid[sta[i]].cap<mi)
                    {mi=sid[sta[i]].cap;last=i;}
                      
                  for (int i=1;i<=top;i++) 
                  sid[sta[i]].cap-=mi,sid[sta[i]^1].cap+=mi;
                u=sid[sta[last]].fr;cur[u]=sid[cur[u]].next;top=last-1;
                maxflow+=mi;
                continue;
            }
              
            while((cur[u]!=-1)&&((sid[cur[u]].cap==0)||(dep[sid[cur[u]].des]!=dep[u]+1)))
              cur[u]=sid[cur[u]].next;
                
            if (cur[u]!=-1){sta[++top]=cur[u];u=sid[cur[u]].des;continue;}
            else{
                if (u==sor) break;
                dep[u]=-1;
                u=sid[sta[top--]].fr;
                continue;
            }       
          }
      }
      return(maxflow);
  }
    
  void build(){
    for (int i=1;i<n;i++){
      if (fabs(a[i][n]-(int)a[i][n])>1e-3) addedge(0,i,1);
      in[0]-=(int)a[i][n];in[i]+=(int)a[i][n];  
    }
    for (int i=1;i<n;i++){
      if (fabs(a[n][i]-(int)a[n][i])>1e-3) addedge(i+n-1,2*n-1,1);
      in[i+n-1]-=(int)a[n][i];in[2*n-1]+=(int)a[n][i];
    }
    for (int i=1;i<n;i++)
     for (int j=1;j<n;j++){
       if (fabs(a[i][j]-(int)a[i][j])>1e-3) addedge(i,n-1+j,1);
       in[i]-=(int)a[i][j];in[n-1+j]+=(int)a[i][j];
     }
    for (int i=0;i<=2*n-1;i++)
      if (in[i]>0) {tot+=in[i];addedge(2*n,i,in[i]);}else
      if (in[i]<0) addedge(i,2*n+1,-in[i]); 
  }
  
  int main(){   
    scanf("%d",&n);
    for (int i=1;i<=n;i++)
      for (int j=1;j<=n;j++)
        scanf("%Lf",&a[i][j]);
  
    for (int i=0;i<=2*n+1;i++) nd[i]=-1;     
    build();
    sor=2*n;tar=2*n+1;
    addedge(2*n-1,0,1e9);
    if (dinic()!=tot) {printf("No\n");return(0);}
    sor=0;tar=2*n-1;
    printf("%d\n",3*dinic()); 
  }