3437: 小P的牧场

Posted 2020-11-02 HWIM

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

 1 #include<cstdio>
 2 #include<iostream>
 3  
 4 using namespace std;
 5 typedef long long LL;
 6 
 7 const int N = 1000100;
 8 LL f[N],s[N],a[N],b[N];
 9 int q[N],L,R;
10 
11 inline int read() {
12     int x = 0,f = 1;char ch = getchar();
13     for (; !isdigit(ch); ch=getchar()) if(ch==‘-‘) f=-1;
14     for (; isdigit(ch); ch=getchar()) x = x*10+ch-‘0‘;
15     return x * f; 
16 }
17 double Slope(int i,int j) {
18     return 1.0*(f[i]+s[i]-f[j]-s[j])/(1.0*(b[i]-b[j]));
19 }
20 int main() {
21     int n = read();
22     for (int i=1; i<=n; ++i) a[i] = read();
23     for (int i=1; i<=n; ++i) {
24         b[i] = read();
25         s[i] = s[i-1] + 1ll * b[i] * i;
26         b[i] += b[i-1];  // 顺序不能反！ 
27     }
28     int L = 1,R = 1;
29     q[1] = 0;
30     for (int i=1; i<=n; ++i) {
31         while (L<R && Slope(q[L],q[L+1]) < (double)i) L++;
32         int j = q[L];
33         f[i] = f[j] + i * (b[i-1] - b[j]) - (s[i-1] - s[j]) + a[i];
34         while (L<R && Slope(q[R-1],q[R]) > Slope(q[R],i)) R--;
35         q[++R] = i; 
36     }
37     cout << f[n];
38     return 0;
39 }