[BZOJ3203][SDOI2013]保护出题人(凸包+三分)

https://www.cnblogs.com/Skyminer/p/6435544.html

先不要急于转化成几何模型，先把式子化到底再对应到几何图形中去。

 #include<cstdio>
 #include<algorithm>
 #define rep(i,l,r) for (int i=(l); i<=(r); i++)
 typedef long long ll;
 using namespace std;

 const int N=;
 double ans;
 ll d,a[N],x[N],sm[N];
 int n,top;
 struct P{ double x,y; }p[N],stk[N];
 double sl(P &a,P &b){ return (b.y-a.y)/(b.x-a.x); }

 int main(){
     freopen("bzoj3203.in","r",stdin);
     freopen("bzoj3203.out","w",stdout);
     scanf("%d%lld",&n,&d);
     rep(i,,n){
         scanf("%lld%lld",&a[i],&x[i]); sm[i]=sm[i-]+a[i];
         P t=(P){.*i*d,.*sm[i-]};
         while (top> && sl(stk[top-],t)>sl(stk[top],t)) top--;
         stk[++top]=t;
         int L=,R=top;
         t=(P){.*x[i]+i*d,.*sm[i]};
         while (L<R-){
             int m1=L+(R-L)/,m2=R-(R-L)/;
             if (sl(stk[m1],t)<sl(stk[m2],t)) L=m1+; else R=m2;
         }
         double res=;
         rep(i,L,R) res=max(res,sl(stk[i],t));
         ans+=res;
     }
     printf("%.0lf\n",ans);
     return ;
 }