[暑假集训Day4T3]曲线

三分模板。

三分法求单峰函数最优值,之后每次取所有二次函数最优值即可

#pragma GCC optimize(3,"Ofast","inline")
#include<iostream>
#include<cstdio>
#define N 100005
#define eps 1e-9
using namespace std;
int read()
{
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-48;ch=getchar();}
    return x*f;
}
int t,n;
double ans,a[N],b[N],c[N];
double check(double x)
{
    double r=-21374404;
    for(int i=1;i<=n;i++)
    {
        r=max(r,double(a[i]*x*x+b[i]*x+c[i]));
    }
    return r;
}
signed main()
{
    //freopen("1.in","r",stdin);
    t=read();
    while(t--)
    {
        n=read();
        for(int i=1;i<=n;i++)
        {
            a[i]=read();
            b[i]=read();
            c[i]=read();
        }
        double l=0,r=1000,lmid,rmid;
        while(l+eps<r)
        {
            rmid=r-(r-l)/3.0;
            lmid=l+(r-l)/3.0;
            if(check(lmid)<=check(rmid))r=rmid;
            else l=lmid;
        }
        printf("%.4lf
",check(l));
    }
    return 0;
}