[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\n",check(l));}return 0;
}