[JSOI2009] 球队收益 （费用流）

Posted 2021-02-12 siruiyang_sry

终于来发题解啦！

 pdf版题解

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#include<queue>
#include<climits>
using namespace std;
inline int read(){
    int f=1,ans=0;char c=getchar();
    while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
    while(c>=‘0‘&&c<=‘9‘){ans=ans*10+c-‘0‘;c=getchar();}
    return f*ans;
}
queue<int> que;
const int MAXN=400001;
struct node{
    int u,v,w,cost,nex;
}x[MAXN];
int head[MAXN],dis[MAXN],vis[MAXN],S,T,cnt,cost,INF=INT_MAX;
void add(int u,int v,int cost,int w){
//    printf("u:%d v:%d cost:%d w:%d
",u,v,cost,w);
    x[cnt].u=u,x[cnt].v=v,x[cnt].cost=cost,x[cnt].w=w,x[cnt].nex=head[u],head[u]=cnt++;swap(u,v);w=0,cost=-cost;
    x[cnt].u=u,x[cnt].v=v,x[cnt].cost=cost,x[cnt].w=w,x[cnt].nex=head[u],head[u]=cnt++;
} 
bool spfa(){
    memset(vis,0,sizeof(vis));memset(dis,127/3,sizeof(dis));int inf=dis[0];dis[S]=0;
    que.push(S);
    while(!que.empty()){
        int xx=que.front();que.pop();
        for(int i=head[xx];i!=-1;i=x[i].nex){
            if(dis[x[i].v]>dis[xx]+x[i].cost&&x[i].w){
                dis[x[i].v]=dis[xx]+x[i].cost;
                if(!vis[x[i].v]){
                    vis[x[i].v]=1;
                    que.push(x[i].v);
                }
            }
        }vis[xx]=0;
    }return dis[T]!=inf;
}
int dfs(int u,int flow){
    if(u==T) return flow;
    vis[u]=1;int used=0;
    for(int i=head[u];i!=-1;i=x[i].nex){
        if(!vis[x[i].v]&&x[i].w&&dis[x[i].v]==dis[u]+x[i].cost){
            int slow=dfs(x[i].v,min(flow-used,x[i].w));used+=slow;
            x[i].w-=slow,x[i^1].w+=slow;
            cost+=slow*x[i].cost;
            if(flow==used) break;
        }
    }if(!used) dis[u]=-1;
    vis[u]=0;
    return used;
}
int dinic(){
    int ans=0;
    while(spfa()){memset(vis,0,sizeof(vis));ans+=dfs(S,INF);}
    return ans;
}
int n,m,c[MAXN],Sum,d[MAXN],a[MAXN],b[MAXN],sum[MAXN];
int main(){
    memset(head,-1,sizeof(head));
    n=read(),m=read();S=0,T=n+m+1; 
    for(int i=1;i<=n;i++) a[i]=read(),b[i]=read(),c[i]=read(),d[i]=read();
    for(int i=1;i<=m;i++){
        add(S,i,0,1);
        int u=read(),v=read();
        b[u]++,b[v]++;
        sum[u]++,sum[v]++;
        add(i,u+m,0,1),add(i,v+m,0,1);
    }
    for(int i=1;i<=n;i++) Sum+=c[i]*a[i]*a[i]+d[i]*b[i]*b[i];
    for(int i=1;i<=n;i++){
        for(int j=1;j<=sum[i];j++){
            add(i+m,T,c[i]*(2*a[i]+1)-d[i]*(2*b[i]-1),1);
            a[i]++,b[i]--;
        }
    }dinic();
    printf("%d
",Sum+cost); 
}

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