LOJ117 有源汇有上下界最小流(上下界网络流)
跑出可行流后从原来的汇点向原来的源点跑最大流,原图最小流=inf-maxflow。显然超源超汇的相关边对其也没有影响。原图最小流=可行流-原图新增流量,因为t向s流量增加相当于s向t流量减少。但为什么等于inf-maxflow呢?显然最大流会把这条inf边跑满,这样会增加inf-可行流的流量,然后又继续在原图中增加可增加的流量,移项就可以得到这个式子了。
#include<iostream> #include<cstdio> #include<cmath> #include<cstdlib> #include<cstring> #include<algorithm> using namespace std; int read() { int x=0,f=1;char c=getchar(); while (c<'0'||c>'9') {if (c=='-') f=-1;c=getchar();} while (c>='0'&&c<='9') x=(x<<1)+(x<<3)+(c^48),c=getchar(); return x*f; } #define N 50010 #define M 500000 #define S 0 #define T 50001 #define inf 1000000000 int n,m,w,v,t=-1,p[N],degree[N],l[M],tot=0; int cur[N],d[N],q[N],ans=0; struct data{int to,nxt,cap,flow; }edge[M]; void addedge(int x,int y,int z) { t++;edge[t].to=y,edge[t].nxt=p[x],edge[t].cap=z,edge[t].flow=0,p[x]=t; t++;edge[t].to=x,edge[t].nxt=p[y],edge[t].cap=0,edge[t].flow=0,p[y]=t; } bool bfs(int s,int t) { memset(d,255,sizeof(d));d[s]=0; int head=0,tail=1;q[1]=s; do { int x=q[++head]; for (int i=p[x];~i;i=edge[i].nxt) if (d[edge[i].to]==-1&&edge[i].flow<edge[i].cap) { d[edge[i].to]=d[x]+1; q[++tail]=edge[i].to; } }while (head<tail); return ~d[t]; } int work(int k,int f,int t) { if (k==t) return f; int used=0; for (int i=cur[k];~i;i=edge[i].nxt) if (d[k]+1==d[edge[i].to]) { int w=work(edge[i].to,min(f-used,edge[i].cap-edge[i].flow),t); edge[i].flow+=w,edge[i^1].flow-=w; if (edge[i].flow<edge[i].cap) cur[k]=i; used+=w;if (used==f) return f; } if (used==0) d[k]=-1; return used; } void dinic(int s,int t) { while (bfs(s,t)) { memcpy(cur,p,sizeof(p)); ans+=work(s,inf,t); } } int main() { #ifndef ONLINE_JUDGE freopen("loj117.in","r",stdin); freopen("loj117.out","w",stdout); const char LL[]="%I64d"; #else const char LL[]="%lld"; #endif n=read(),m=read(),w=read(),v=read(); memset(p,255,sizeof(p)); for (int i=1;i<=m;i++) { int x=read(),y=read(),low=read(),high=read(); addedge(x,y,high-low); degree[y]+=low,degree[x]-=low; l[i]=low; } for (int i=1;i<=n;i++) if (degree[i]>0) addedge(S,i,degree[i]),tot+=degree[i]; else if (degree[i]<0) addedge(i,T,-degree[i]); addedge(v,w,inf); dinic(S,T); if (ans<tot) cout<<"please go home to sleep"; else ans=0,dinic(v,w),cout<<inf-ans; return 0; }