1911: [Apio2010]特别行动队（斜率优化）

链接

思路

　　斜率优化dp。

代码

 #include<cstdio>
 #include<algorithm>
 #include<cstring>
 #include<iostream>
 #include<cmath>

 using namespace std;
 typedef long long LL;
 int n,L,R;
 LL A,B,C,s[],q[],f[];

 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 Y(int x) {
     return double(f[x]+A*s[x]*s[x]-B*s[x]);
 }
 double slope(int i,int j) {
     return (Y(i)-Y(j))/double(s[i]-s[j]);
 }
 int main() {
     n = read(),A = read(),B = read(),C = read();
     for (int i=; i<=n; ++i) s[i] = read(),s[i] += s[i-];

     int L = ,R = ;
     q[++R] = ;
     for (int i=; i<=n; ++i) {
         while (L<R && slope(q[L],q[L+])>2.0*A*s[i]) L++;
         int j = q[L];
         f[i] = f[j]+A*(s[i]-s[j])*(s[i]-s[j])+B*(s[i]-s[j])+C;
         while (L<R && slope(q[R-],q[R])<slope(q[R],i)) R--;
         q[++R] = i;
     }
     cout << f[n];
     return ;
 }