【BZOJ3203】保护出题人（动态规划，斜率优化）

#include<cstdio>
using namespace std;
#define ll long long
#define RG register
#define MAX 111111
inline ll read()
{
    RG int x=0,t=1;RG char ch=getchar();
    while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
    if(ch=='-')t=-1,ch=getchar();
    while(ch<='9'&&ch>='0')x=x*10+ch-48,ch=getchar();
    return x*t;
}
struct Node{double x,y;}p[MAX];
double Slope(Node a,Node b){return (a.y-b.y)/(a.x-b.x);}
int n,Q[MAX],t;
double d,a,b,ans,s;
int main()
{
    n=read();d=read();
    for(int i=1;i<=n;++i)
    {
        a=read();b=read();p[i].x-=s;s+=a;p[i].y=-i*d;
        while(t>1&&Slope(p[i],p[Q[t]])>Slope(p[Q[t]],p[Q[t-1]]))--t;
        Q[++t]=i;p[0].x=-s;p[0].y=-i*d-b;int l=1,r=t;
        while(l<r)
        {
            int mid=(l+r)>>1;
            if(Slope(p[Q[mid]],p[Q[mid+1]])>Slope(p[Q[mid+1]],p[0]))l=mid+1;
            else r=mid;
        }
        ans+=1/Slope(p[Q[l]],p[0]);
    }
    printf("%.0lf\n",ans);
    return 0;
}