求最大流
#include<cstdio> #include<cstring> #include<cstdlib> #include<cmath> #include<algorithm> #include<iostream> #define maxn 210 #define maxm 100010 #define inf 1000000000 using namespace std; int head[maxn],to[maxm],c[maxm],next[maxm],q[maxn],d[maxn],in[maxn],cnt[maxn]; double a[maxn][maxn]; int n,m,num,s,t,S,T,ans; void addedge(int x,int y,int z) { num++;to[num]=y;c[num]=z;next[num]=head[x];head[x]=num; num++;to[num]=x;c[num]=0;next[num]=head[y];head[y]=num; } bool bfs() { memset(d,-1,sizeof(d)); int l=0,r=1; q[1]=S;d[S]=0; while (l<r) { int x=q[++l]; for (int p=head[x];p;p=next[p]) if (c[p] && d[to[p]]==-1) { d[to[p]]=d[x]+1; q[++r]=to[p]; } } if (d[T]==-1) return 0; else return 1; } int find(int x,int low) { if (x==T || low==0) return low; int totflow=0; for (int p=head[x];p;p=next[p]) if (c[p] && d[to[p]]==d[x]+1) { int a=find(to[p],min(c[p],low)); c[p]-=a;c[p^1]+=a; low-=a;totflow+=a; if (low==0) return totflow; } if (low) d[x]=-1; return totflow; } void Dinic() { int ans=0; while (bfs()) ans+=find(S,inf); } bool check(int x) { num=1;s=0;t=2*n+1;S=t+1;T=S+1; memset(head,0,sizeof(head)); memset(in,0,sizeof(in)); memset(cnt,0,sizeof(cnt)); in[s]+=x;in[t]-=x;addedge(t,s,inf); for (int i=1;i<n;i++) { if (a[i][n]!=(int)a[i][n]) addedge(s,i,1); in[s]-=(int)a[i][n];in[i]+=(int)a[i][n]; } for (int i=1;i<n;i++) { if (a[n][i]!=(int)a[n][i]) addedge(i+n,t,1); in[i+n]-=(int)a[n][i];in[t]+=(int)a[n][i]; } for (int i=1;i<n;i++) for (int j=1;j<n;j++) { if (a[i][j]!=(int)a[i][j]) addedge(i,j+n,1); in[i]-=(int)a[i][j];in[j+n]+=(int)a[i][j]; } for (int i=s;i<=t;i++) if (in[i]>0) cnt[i]=num+1,addedge(S,i,in[i]); else if (in[i]<0) cnt[i]=num+1,addedge(i,T,-in[i]); Dinic(); for (int i=s;i<=t;i++) if (cnt[i] && c[cnt[i]]) return 0; return 1; } int main() { scanf("%d",&n); for (int i=1;i<=n;i++) for (int j=1;j<=n;j++) scanf("%lf",&a[i][j]); int l=0,r=inf,ans=-1; while (l<=r) { int mid=(l+r)/2; if (check(mid)) ans=mid,l=mid+1; else r=mid-1; } if (ans==-1) printf("No\n"); else printf("%d\n",ans*3); return 0; }