[最大权闭合子图] BZOJ4873: [Shoi2017] 寿司餐厅

#include <cstdio>
#include <iostream>
#include <algorithm>
#include <queue>

using namespace std;

const int N=100010,inf=1<<29;

int n,m,S,T,a
,cnt=1,G
,d[110][110],g[110][110],v[1010],t;
struct edge{
int t,nx,f;
}E[N<<2];

inline void link(int x,int y,int f){
E[++cnt].t=y; E[cnt].nx=G[x]; E[cnt].f=f; G[x]=cnt;
E[++cnt].t=x; E[cnt].nx=G[y]; E[cnt].f=0; G[y]=cnt;
}

queue<int> Q;
int dis
,cur
;

inline bool bfs(){
while(!Q.empty()) Q.pop();
for(int i=S;i<=T;i++) dis[i]=-1;
dis[S]=0; Q.push(S);
while(!Q.empty()){
int x=Q.front(); Q.pop();
for(int i=G[x];i;i=E[i].nx)
if(E[i].f && !~dis[E[i].t]){
dis[E[i].t]=dis[x]+1;
if(E[i].t==T) return true;
Q.push(E[i].t);
}
}
return false;
}

int dfs(int x,int f){
if(x==T || !f) return f;
int used=0,w;
for(int &i=cur[x];i;i=E[i].nx)
if(E[i].f && dis[E[i].t]==dis[x]+1){
w=dfs(E[i].t,min(f-used,E[i].f));
E[i].f-=w; E[i^1].f+=w;
if((used+=w)==f) return used;
}
if(!used) dis[x]=-1;
return used;
}

int main(){
scanf("%d%d",&n,&m); T=1;
for(int i=1;i<=n;i++){
scanf("%d",&a[i]);
if(!v[a[i]]) v[a[i]]=T++;
}
for(int i=1;i<=n;i++)
for(int j=i;j<=n;j++)
scanf("%d",&d[i][j]),g[i][j]=T++;
for(int i=1;i<=1000;i++)
if(v[i]) link(v[i],T,m*i*i);
int ans=0;
for(int i=1;i<=n;i++)
for(int j=i;j<=n;j++){
if(i==j){
if(d[i][j]-a[i]>=0)
link(S,g[i][j],d[i][j]-a[i]),ans+=d[i][j]-a[i];
else
link(g[i][j],T,a[i]-d[i][j]);
link(g[i][j],v[a[i]],inf);
}
else{
if(d[i][j]>=0)
link(S,g[i][j],d[i][j]),ans+=d[i][j];
else
link(g[i][j],T,-d[i][j]);
link(g[i][j],g[i+1][j],inf); link(g[i][j],g[i][j-1],inf);
}
}
while(bfs()){
for(int i=S;i<=T;i++) cur[i]=G[i];
ans-=dfs(S,inf);
}
printf("%d\n",ans);
return 0;
}