BZOJ 1911 [Apio2010]特别行动队

Posted 2020-10-24 ws_zzy

题解：裸的斜率优化

少了一个括号WA了几发QWQ

总结：以后不能写这么长的式子

问题：我还不会决策单调性QWQ

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
typedef long long Lint;
const int maxn=1000009;

int n;
Lint A,B,C;
Lint s[maxn];
Lint f[maxn];

Lint Getk(int x){
	return f[x]+A*s[x]*s[x]-B*s[x];
}

int q[maxn],h,t;

int main(){
	scanf("%d",&n);
	scanf("%lld%lld%lld",&A,&B,&C);
	for(int i=1;i<=n;++i){
		int x;scanf("%d",&x);
		s[i]=s[i-1]+x;
	}
	
	q[h=t=1]=0;
	for(int i=1;i<=n;++i){
		while((h<t)&&((Getk(q[h+1])-Getk(q[h]))>2*A*(s[q[h+1]]-s[q[h]])*s[i]))++h;
		int j=q[h];
		f[i]=f[j]+A*(s[i]-s[j])*(s[i]-s[j])+B*(s[i]-s[j])+C;
		while((h<t)&&((Getk(q[t])-Getk(q[t-1]))*(s[i]-s[q[t]])<(Getk(i)-Getk(q[t]))*(s[q[t]]-s[q[t-1]])))--t;
		q[++t]=i;
	}
	
	printf("%lld\n",f[n]);
	return 0;
}