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 = ;
 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+]-v[i]-(n-i)*(s[x+]-s[i]);
 }
 double A(int x,int y)
 {
     return f[x]+v[x+]-f[y]-v[y+];
 }
 double B(int x,int y)
 {
     return s[x+]-s[y+];
 }
 int main()
 {
     scanf("%d",&n);
     for (i=;i<=n;i++)
     scanf("%lld",&a[i]);
     for (i=;i<=n;i++)
     scanf("%lld",&s[i]);
     for (j=n;j>=;j--)
     {
         v[j]=v[j+]+s[j]*(n-j);
         s[j]+=s[j+];
     }
     l=;r=;
     for (i=;i<=n;i++)
     {
         while ((l<r)&&(A(q[l],q[l+])>=B(q[l],q[l+])*(n-i))) l++;
         f[i]=calc(q[l],i);
         while ((l<r)&&(A(q[r],i)*B(q[r-],q[r])>A(q[r-],q[r])*B(q[r],i))) r--;
         r++;q[r]=i;
     }
     printf("%lld\n",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)