三分/函数

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题目看上去挺吓人的,尤其是这个F(x),乍一看F(x)是一个相当复杂的函数, 但实际上我们拿笔画一下会发现这个函数是一个先减后增的函数,类似于一个大的凹二次函数

那么这题就好些多了

#include<bits/stdc++.h>
using namespace std;
double f(double a[], double x) {
	double res = 0;
	for (int i = 0;i <3;i++) {
		res = res * x + a[i];
	}
	return res;
}
struct coefficient {
	double a[3];
};
double max_x(double x, vector<coefficient>& coe) {
	double m = f(coe[0].a, x);
	for (int i = 0;i < coe.size();i++) {
		m = max(f(coe[i].a, x), m);
	}
	return m;
}

int main() {
	int T;
	cin >> T;
	cout << fixed << setprecision(4);
	while (T--) {
		int n;
		cin >> n;
		vector<coefficient> coe(n);
		for (int i = 0;i < n;i++) {
			cin >> coe[i].a[0] >> coe[i].a[1] >> coe[i].a[2];
		}
		double l = 0, r = 1000,ans=0;
		int count = 100;
		while (count--) {
			double mid_l = (2 * l + r) / 3;
			double mid_r = (l + 2 * r) / 3;
			double left = max_x(mid_l, coe), right = max_x(mid_r, coe);
			if (left>right) {
				l = mid_l;
				
			}
			else {
				r = mid_r;
				
			}
			ans = max_x((l + r) / 2, coe);
		}
		cout << ans << endl;
	}
}