bzoj3437 小P的牧场

　　斜率优化dp

　　代码

#include<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N = 1001010;
int n,i,j,l,r,q[N];
ll f[N],v[N],s[N],a[N];
ll calc(int x,int i)
{
    return f[x]+a[i]+v[x+1]-v[i]-(n-i)*(s[x+1]-s[i]);
}
double A(int x,int y)
{
    return f[x]+v[x+1]-f[y]-v[y+1];
}
double B(int x,int y)
{
    return s[x+1]-s[y+1];
}
int main()
{
    scanf("%d",&n);
    for (i=1;i<=n;i++)
    scanf("%lld",&a[i]);
    for (i=1;i<=n;i++)
    scanf("%lld",&s[i]);
    for (j=n;j>=1;j--)
    {
        v[j]=v[j+1]+s[j]*(n-j);
        s[j]+=s[j+1];
    }
    l=1;r=1;
    for (i=1;i<=n;i++)
    {
        while ((l<r)&&(A(q[l],q[l+1])>=B(q[l],q[l+1])*(n-i))) l++;
        f[i]=calc(q[l],i);
        while ((l<r)&&(A(q[r],i)*B(q[r-1],q[r])>A(q[r-1],q[r])*B(q[r],i))) r--;
        r++;q[r]=i;
    }
    printf("%lld
",f[n]);
} 
//f[x]+v[x+1]-f[y]-v[y+1]>(s[x+1]-s[y+1])*(n-i)
//A(y,z)/B(y,z)>A(x,y)/B(x,y)