uva 1476 - Error Curves(三分)

题目链接:1476 - Error Curves

题目大意：给定n条二次曲线S(x)，定义F(x)=max(Si(x)), 求出F(x)在0~1000上的最小值。

解题思路：数值方法，三分。

#include <cstdio>
#include <cstring>
#include <algorithm>

using namespace std;
const int maxn = 10005;

int n, a[maxn], b[maxn], c[maxn];

double f (double x) {
    double ret = a[0] * x * x + b[0] * x + c[0];
    for (int i = 0; i < n; i++)
        ret = max(ret, a[i] * x * x + b[i] * x + c[i]);
    return ret;
}

double search (double l, double r) {
    for (int i = 0; i < 100; i++) {
        double p = l + (r-l) / 3;
        double q = r - (r-l) / 3;
        if (f(p) > f(q))
            l = p;
        else
            r = q;
    }
    return l;
}

int main () {
    int cas;
    scanf("%d", &cas);
    while (cas--) {
        scanf("%d", &n);
        for (int i = 0; i < n; i++)
            scanf("%d%d%d", &a[i], &b[i], &c[i]);
        double x = search(0, 1000);
        printf("%.4lf\n", f(x));
    }
    return 0;
}