3437: 小P的牧场

3437: 小P的牧场

思路

　　斜率优化。

　　dp[i]表示到第i个点（第i个点按控制台）的最小代价。

代码

#include<cstdio>
#include<iostream>
 
using namespace std;
typedef long long LL;

const int N = 1000100;
LL f[N],s[N],a[N],b[N];
int q[N],L,R;

inline int read() {
    int x = 0,f = 1;char ch = getchar();
    for (; !isdigit(ch); ch=getchar()) if(ch=='-') f=-1;
    for (; isdigit(ch); ch=getchar()) x = x*10+ch-'0';
    return x * f; 
}
double Slope(int i,int j) {
    return 1.0*(f[i]+s[i]-f[j]-s[j])/(1.0*(b[i]-b[j]));
}
int main() {
    int n = read();
    for (int i=1; i<=n; ++i) a[i] = read();
    for (int i=1; i<=n; ++i) {
        b[i] = read();
        s[i] = s[i-1] + 1ll * b[i] * i;
        b[i] += b[i-1];  // 顺序不能反！ 
    }
    int L = 1,R = 1;
    q[1] = 0;
    for (int i=1; i<=n; ++i) {
        while (L<R && Slope(q[L],q[L+1]) < (double)i) L++;
        int j = q[L];
        f[i] = f[j] + i * (b[i-1] - b[j]) - (s[i-1] - s[j]) + a[i];
        while (L<R && Slope(q[R-1],q[R]) > Slope(q[R],i)) R--;
        q[++R] = i; 
    }
    cout << f[n];
    return 0;
}