[HNOI2008] 玩具装箱 D2 T3 斜率优化DP

#include<stdio.h>
#include<algorithm>
#define inf 1e18
using namespace std;
int n,l,sum[50100],a[500100];
int que[50100],h,t;
long long f[50100],q[50100],p[50100];
long long q1(long long x){return f[x]+q[x]*q[x];}
double count(int x,int y){return (q1(x)-q1(y))*1.0/(2.0*(q[x]-q[y]));}
int main()
{
    scanf("%d%d",&n,&l);
    for(int i=1;i<=n;++i)
        scanf("%d",&a[i]);
    for(int i=1;i<=n;i++)
        sum[i]=a[i]+sum[i-1];
    for(int i=1;i<=n;++i)
        f[i]=inf;
    for(int i=1;i<=n;++i)
        q[i]=sum[i]+i;
    for(int i=1;i<=n;++i)
        p[i]=sum[i]+i-l-1;
    for(int i=1;i<=n;++i)
    {
        while(h<t&&count(que[h],que[h+1])<=p[i]*1.0)h++;
        f[i]=f[que[h]]+(p[i]-q[que[h]])*(p[i]-q[que[h]]);
        while(h<t&&count(que[t-1],que[t])>=count(que[t],i))t--;
        que[++t]=i;
    }
    printf("%lld",f[n]);
}