呃，老规矩，方程、转化神马的都在代码注释里面。

不会斜率优化的移步这篇：http://blog.csdn.net/vmurder/article/details/41648159

没事闲的想看点经验的来“前一篇”http://blog.csdn.net/vmurder/article/details/41682901

代码：

#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
#define N 1001000
#define inf 0x3f3f3f3f
#define INF 0x3f3f3f3f3f3f3f3fll
/*
	f[i]=f[j]+sum[i]-sum[j]-b[j]*i+b[j]*j+a[i]
	
	f[j]-sum[j]+b[j]*j=i*b[j]+f[i]-sum[i]-a[i]
	y=f[j]-sum[j]+b[j]*j
	x=b[j]
	k=i
	b=f[i]-sum[i]-a[i]
*/
using namespace std;
int n,a[N];
struct Point
{
	long long x,y;
	int id;
	Point(long long _x,long long _y,int _id):x(_x),y(_y),id(_id){}
	Point(){}
}now,q[N];
int l,r;
long long f[N],b[N],sum[N];
inline long long xmul(Point i,Point j,Point k){return (j.y-k.y)*(i.x-k.x)-(i.y-k.y)*(j.x-k.x);}
int main()
{
//	freopen("test.in","r",stdin);
//	freopen("my.out","w",stdout);
	int i,j;
	scanf("%d",&n);
	memset(f,0x3f,sizeof(f)),f[0]=0;
	for(i=1;i<=n;i++)scanf("%d",&a[i]);
	for(i=1;i<=n;i++)scanf("%I64d",&b[i]),b[i]+=b[i-1],sum[i]=sum[i-1]+b[i-1];
	for(i=1;i<=n;i++)
	{
		now=Point(b[i-1],f[i-1]-sum[i-1]+b[i-1]*i-b[i-1],i-1);
		while(l<r&&xmul(now,q[r],q[r-1])>=0)r--; //斜(j,k)>=斜(i,k) 弹
		q[++r]=now;

		long long K=i;
		while(l<r&&q[l+1].y-q[l].y<=(q[l+1].x-q[l].x)*K)l++;
		j=q[l].id;
		f[i]=f[j]+sum[i]-sum[j]-(long long)b[j]*i+(long long)b[j]*j+a[i];
	}
	cout<<f[n]<<endl;
	return 0;
}

【BZOJ3437】小P的牧场 斜率优化 动态规划