方格取数加强版[网络流]

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luogu的第一篇题解

 

#include<bits/stdc++.h>
#define N 5000
#define M N*4
#define inf 0x3fffffff
using namespace std;
int Map[N],n,k,st,ed,dis[N],vis[N],from[M],froms[M];
int first[M],next[M],to[M],w[M],v[M],tot=1;
void add(int x,int y,int z,int q){
//  cout<<"From "<<x<<" To "<<y<<" with the flow of "<<z<<" and the cost of "<<q<<endl;
  next[++tot]=first[x],first[x]=tot,to[tot]=y,w[tot]=z,v[tot]=q;
  next[++tot]=first[y],first[y]=tot,to[tot]=x,w[tot]=0,v[tot]=-q;
}
bool spfa(){
  memset(dis,127,sizeof(dis)); int Inf=dis[0];
  memset(vis,0,sizeof(vis)); queue<int> q;
  dis[st]=0 , vis[st]=0 , q.push(st);
  while(!q.empty()){
    int x=q.front(); q.pop(); vis[x]=0; 
    for(int i=first[x];i;i=next[i]){
      int t=to[i];
      if(w[i] && dis[t] > dis[x] + v[i]){
        from[t] = x , froms[t] = i;
        dis[t] = dis[x] + v[i];
        if(!vis[t]) q.push(t) , vis[t]=1;
      }
    } 
  }return dis[ed]!=Inf;
}
int calc(){
  int now = ed , flow=inf;
  while(now != st){
    flow = min(flow , w[froms[now]]);
    now = from[now];
  }
  now = ed;
  while(now !=st){
    w[froms[now]] -= flow;
    w[froms[now]^1] += flow;
    now = from[now];
  }return flow;
}
int dinic(){
  int ans=0;
  while(spfa()){
    if(dis[ed]==0) break;
    ans += calc() * dis[ed];
  }return ans;
}
int main(){
  scanf("%d%d",&n,&k); st=0 , ed=n*n*2+1;
  add(0,1,k,0); add(n*n*2,ed,k,0);
  for(int i=0;i<n;i++)
    for(int j=1;j<=n;j++)
      scanf("%d",&Map[i*n+j]);
  for(int i=1;i<=n*n;i++){
    add(i,i+n*n,1,-Map[i]);
    add(i,i+n*n,inf,0);
  }
  for(int i=0;i<n;i++){
    for(int j=1;j<=n;j++){
      int pos=i*n+j;
      if(j<n) add(pos+n*n,pos+1,inf,0);
      if(i<n-1) add(pos+n*n,pos+n,inf,0);
    }
  }
  printf("%d",-dinic()); return 0;
}