BZOJ1911：[Apio2010]特别行动队——题解

0.5*(f[j]+a*s[j]*s[j]-b*s[j]-f[k]-a*s[k]*s[k]+b*s[k])/(a*(s[j]-s[k]))<s[i]

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=1000010;
const ll INF=1e18;
inline int read(){
    int X=0,w=1;char ch=0;
    while(ch<‘0‘||ch>‘9‘){if(ch==‘-‘)w=-1;ch=getchar();}
    while(ch>=‘0‘&&ch<=‘9‘)X=(X<<1)+(X<<3)+ch-‘0‘,ch=getchar();
    return X*w;
}
int n,l,r;
ll a,b,c;
ll f[N],q[N],s[N];
inline double suan(int k,int j){
    return 0.5*(f[j]+a*s[j]*s[j]-b*s[j]-f[k]-a*s[k]*s[k]+b*s[k])/(a*(s[j]-s[k]));
}
int main(){
    n=read(),a=read(),b=read(),c=read();
    for(int i=1;i<=n;i++)s[i]=s[i-1]+read();
    for(int i=1;i<=n;i++){
        while(l<r&&suan(q[l],q[l+1])<(double)s[i])l++;
        ll k=s[i]-s[q[l]];
        f[i]=f[q[l]]+a*k*k+b*k+c;
        while(l<r&&suan(q[r],i)<suan(q[r-1],q[r]))r--;
        q[++r]=i;
    }
    printf("%lld\n",f[n]);
    return 0;
}