【NOI2012】美食节

题面

https://www.luogu.org/problemnew/show/P2050

题解

费用流+动态加点。

#include<cstdio>
#include<cstring>
#include<iostream>
#include<vector>
#include<queue>
#include<cstdlib>
#define LL long long
#define N 2000
#define INF 1000000007
#define S 0
#define T (sumn+m+1)
#define ri register int
using namespace std;

int n,m,sumn,cc;
int typ[N],cai[N];
int p[200][200];

struct graph {
  vector<int> to,w,c;
  vector<int> ed[N];
  LL dis[N]; int cur[N];
  bool vis[N];
  void add_edge(int a,int b,int aw,int ac) {
    to.push_back(b); w.push_back(aw); c.push_back(ac);  ed[a].push_back(to.size()-1);
    to.push_back(a); w.push_back(0);  c.push_back(-ac); ed[b].push_back(to.size()-1);
  }
  bool spfa() {
    memset(dis,0x2f,sizeof(dis));
    memset(vis,0,sizeof(vis));
    queue<int> q;
    dis[S]=0;q.push(S);vis[S]=1;
    while (!q.empty()) {
      int x=q.front(); q.pop();
      for (ri i=0;i<ed[x].size();i++) {
        int e=ed[x][i];
        if (dis[to[e]]>dis[x]+c[e] && w[e]) {
          dis[to[e]]=dis[x]+c[e];
          if (!vis[to[e]]) vis[to[e]]=1,q.push(to[e]);
        }
      }
      vis[x]=0;
    }
    return dis[T]<INF;
  }
  int dfs(int x,int lim) {
    if (!lim) return lim;
    LL sum=0; vis[x]=1;
    for (ri &i=cur[x];i<ed[x].size();i++) {
      int e=ed[x][i];
      if (dis[x]+c[e]==dis[to[e]] && w[e] && !vis[to[e]]) {
        int f;
        if (to[e]==T) {
          //puts("54");
          f=lim; ++cc; typ[cc]=typ[x];
          for (ri j=0;j<ed[x].size();j++) {
            int je=ed[x][j];
            if (je%2==1) {
              add_edge(to[je],cc,1,c[je^1]+p[cai[to[je]]][typ[cc]]);
              //cout<<-c[je]+p[cai[to[je]]][typ[cc]]<<endl;
            }
          }
          add_edge(cc,T,1,0);
        }
        else 
          f=dfs(to[e],min(lim,w[e]));
        w[e]-=f; w[1^e]+=f;
        lim-=f; sum+=f;
        if (!lim) return sum;
      }
    }
    return sum;
  }
  LL zkw() {
    LL ret=0;
    while (spfa()) {
      memset(vis,0,sizeof(vis));
      memset(cur,0,sizeof(cur));
      ret+=dfs(S,INF)*dis[T];
    }
    return ret;
  }
} G;

int main() {
  int x;
  scanf("%d %d",&n,&m);
  sumn=0;
  for (ri i=1;i<=n;i++) {
    scanf("%d",&x);
    cai[i]=i;
    G.add_edge(S,i,x,0);
  }
  sumn=n;
  for (ri i=1;i<=n;i++) 
    for (ri j=1;j<=m;j++) scanf("%d",&p[i][j]);
  for (ri i=1;i<=m;i++) {
    G.add_edge(sumn+i,T,1,0);
    typ[sumn+i]=i;
  }
  for (ri i=1;i<=sumn;i++)
    for (ri j=1;j<=m;j++) G.add_edge(i,sumn+j,1,p[cai[i]][j]);
  cc=T;
  cout<<G.zkw()<<endl;
}