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[1000100],q[1000100],f[1000100];

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 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=1; i<=n; ++i) s[i] = read(),s[i] += s[i-1];
    
    int L = 1,R = 0;
    q[++R] = 0;
    for (int i=1; i<=n; ++i) {
        while (L<R && slope(q[L],q[L+1])>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-1],q[R])<slope(q[R],i)) R--;
        q[++R] = i;
    }
    cout << f[n];
    return 0;
}