【bzoj1911】【APIO2010】【特别行动队】【斜率优化】

Description

Input

Output

Sample Input

4

-1 10 -20

2 2 3 4

Sample Output

9

HINT

题解：写出dp方程之后斜率优化即可。维护一个上凸壳。
代码：
#include<iostream>
#include<cstdio>
#define N 1000100
using namespace std;
int q
,n,h(1),t(1);
long long a,b,c,sum
,f
,v
;
long long pow(long long x){return x*x;}
long long G(int x,int y){return f[x]-f[y]+a*(pow(sum[x])-pow(sum[y]))+b*(sum[y]-sum[x]);}
long long S(int x,int y){return a*(sum[x]-sum[y]);}
double cal(int x,int y){return (G(x,y)*1.0)/(S(x,y)*2.0);}
int main(){
scanf("%d",&n);scanf("%lld%lld%lld",&a,&b,&c);
for (int i=1;i<=n;i++){scanf("%lld",&v[i]);sum[i]=sum[i-1]+v[i];}
for (int i=1;i<=n;i++){
while (h<t&&sum[i]>cal(q[h+1],q[h]))h++;
f[i]=f[q[h]]+a*pow(sum[i]-sum[q[h]])+b*(sum[i]-sum[q[h]])+c;
while (h<t&&cal(i,q[t])<cal(q[t],q[t-1])) t--;
q[++t]=i;
}
cout<<f
<<endl;
}