洛谷P2050 [NOI2012]美食节

动态加边网络流

 #include<cstdio>
 #include<cstdlib>
 #include<algorithm>
 #include<cstring>
 #include<vector>
 #include<queue>
 #define rint register int
 #define ll int
 #define MAXN 100005+10
 #define pb push_back
 #define INF 0x7f7f7f7f
 #define oo 0x7f7f7f7f7f7f7f7f
 #define pil pair<int,ll>
 #define mp make_pair
 #define ft first
 #define sc second
 using namespace std;
 int read(){
     int x=,f=;char ch=getchar();
     while(ch<''||ch>''){if('-'==ch)f=-;ch=getchar();}
     while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
     return x*f;
 }
 struct E{
     int from,to,cap,flow;
     ll cost;
     E(int x=,int y=,int c=,int f=,ll w=0LL){
         from=x,to=y,cap=c,flow=f,cost=w;
     }
 };
 int N,M,s,t=MAXN-;
 vector<E> es;
 vector<int> G[MAXN];
 void add(int x,int y,int cap,ll cost){
     es.pb(E(x,y,cap,,cost));
     es.pb(E(y,x,,,-cost));
     M=es.size();
     G[x].pb(M-),G[y].pb(M-);
 }
 int p[MAXN],a[MAXN];
 ll d[MAXN];
 int b[MAXN];
 bool SPFA(int &flow,ll &cost){
     p[s]=,a[s]=INF;
     memset(d,0x7f,sizeof(d));
     d[s]=;
     memset(b,,sizeof(b));
     b[s]=;
     queue<int> q;
     q.push(s);
     while(!q.empty()){
         int x=q.front();q.pop();b[x]=;
         for(rint i=;i<G[x].size();i++){
             E &e=es[G[x][i]];
             if(e.cap>e.flow&&d[e.to]>d[x]+e.cost){
                 p[e.to]=G[x][i];
                 a[e.to]=min(a[x],e.cap-e.flow);
                 d[e.to]=d[x]+e.cost;
                 if(!b[e.to]){
                     b[e.to]=;
                     q.push(e.to);
                 }
             }
         }
     }
     if(oo==d[t]){
         return ;
     }
     flow+=a[t];
     cost+=a[t]*d[t];
     for(rint i=t;i!=s;i=es[p[i]].from){
         es[p[i]].flow+=a[t];
         es[p[i]^].flow-=a[t];
     }
     return ;
 }
 pil MaxfMinc(){
     int flow=;
     ll cost=0LL;
     while(SPFA(flow,cost));
     return mp(flow,cost);
 }
 int n,m;
 int P[],T[][],now[];
 int sum,L;
 int cook[MAXN],cnt[MAXN];
 int id[][];
 int work(int x,int y){
     add(id[x][y],t,,);
     for(rint i=;i<=n;i++){
         add(L+i,id[x][y],,T[i][x]*y);
     }
 }
 void init(){
     n=read(),m=read();
     for(rint i=;i<=n;i++){
         P[i]=read();
         sum+=P[i];
     }
     for(rint i=;i<=n;i++){
         for(rint j=;j<=m;j++){
             T[i][j]=read();
         }
     }
     L=m*sum;
     int idx=;
     for(rint i=;i<=m;i++){
         for(rint j=;j<=sum;j++){
             id[i][j]=++idx;
             cook[idx]=i,cnt[idx]=j;
         }
     }
     for(rint i=;i<=n;i++){
         add(s,L+i,P[i],);
     }
     for(rint i=;i<=m;i++){
         work(i,);
         now[i]=;
     }
 }
 void solve(){     int flow=;ll cost=0LL;
     while(SPFA(flow,cost)){
         if(flow==sum){
             printf("%lld\n",cost);
             break;
         }
         int x=es[p[t]].from;
         now[cook[x]]++;
         work(cook[x],now[cook[x]]);
     }
 }
 int main()
 {
 //    freopen("data.in","r",stdin);
     init();
     solve();
     return ;
 }