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

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