[bzoj1597]: [Usaco2008 Mar]土地购买

传送门

斜率优化dp

从今天开始练习dp，各种dp

斜率方程：slope(a,b)=(f(a)-f(b))/(y(b+1)-y(a+1))

代码：

#include<bits/stdc++.h>
#define ll long long
using namespace std;
inline int read(){
    int x=0;char ch=' ';int f=1;
    while(ch!='-'&&(ch<'0'||ch>'9'))ch=getchar();
    if(ch=='-'){
        f=-1;ch=getchar();
    }
    while(ch>='0'&&ch<='9')x=x*10+ch-'0',ch=getchar();
    return x*f;
}
int n,tot;
ll x[50001],y[50001],f[50001];
int q[50001],l,r;
inline double slope(int a,int b){
    return (double)(f[a]-f[b])/(double)(y[b+1]-y[a+1]);
}
struct node{
    int x,y;
    inline bool operator < (const node& b) const {
        return (x==b.x)?y<b.y:x<b.x;
    }
}a[50001];
int main(){
    n=read();
    for(int i=1;i<=n;i++){
        a[i].x=read();a[i].y=read();
    }
    sort(a+1,a+n+1);
    for(int i=1;i<=n;i++){
        while(tot&&y[tot]<=a[i].y)tot--;
        x[++tot]=a[i].x;y[tot]=a[i].y;
    }
    l=0,r=0;
    for(int i=1;i<=tot;i++){
        while(l<r&&slope(q[l],q[l+1])<x[i])l++;
        f[i]=f[q[l]]+y[q[l]+1]*x[i];
        while(l<r&&slope(q[r],i)<slope(q[r-1],q[r]))r--;
        q[++r]=i;
    }
    printf("%lld",f[tot]);
    return 0;
}