[APIO2010]特别行动队

link

维护一个上凸壳就行，普通的斜率优化。

若想要具体过程请参考以前博客

#include<iostream>
#include<cstring>
#include<cstdio>
#include<algorithm>
#define int long long
using namespace std;
inline int read(){
    int f=1,ans=0;char c=getchar();
    while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
    while(c>='0'&&c<='9'){ans=ans*10+c-'0';c=getchar();}
    return f*ans;
}
const int N=1000011;
int x[N],a,b,c,f[N],n,que[N],X[N],Y[N],l,r;
signed main(){
    f[0]=0;
    n=read(),a=read(),b=read(),c=read();
    for(int i=1;i<=n;i++) x[i]=x[i-1]+read();
    l=r=1,que[1]=0,X[0]=x[0],Y[0]=f[0]+x[0]*x[0]*a-b*x[0];
    for(int i=1;i<=n;i++){
        while(l<r&&(Y[que[l+1]]-Y[que[l]])>=2*a*x[i]*(X[que[l+1]]-X[que[l]])) l++;
        f[i]=f[que[l]]+(x[i]-x[que[l]])*(x[i]-x[que[l]])*a+(x[i]-x[que[l]])*b+c;
        X[i]=x[i],Y[i]=f[i]+x[i]*x[i]*a-x[i]*b;
        while(l<r&&(Y[que[r]]-Y[que[r-1]])*(X[i]-X[que[r]])<=(Y[i]-Y[que[r]])*(X[que[r]]-X[que[r-1]])) r--;
        que[++r]=i;
    }cout<<f[n];return 0;
}