三分 HDOJ 3714 Error Curves

题目传送门

 1 /*
 2     三分：凹(凸)函数求极值
 3 */
 4 #include <cstdio>
 5 #include <algorithm>
 6 #include <cstring>
 7 #include <cmath>
 8 using namespace std;
 9
10 const int MAXN = 1e4 + 10;
11 const int INF = 0x3f3f3f3f;
12 const double EPS = 0.0000000001;
13 struct F    {
14     double a, b, c;
15 }f[MAXN];
16 int n;
17
18 double cal(double x)    {
19     double res = -INF;
20     for (int i=1; i<=n; ++i)    {
21         res = max (res, f[i].a * x * x + f[i].b * x + f[i].c);
22     }
23     return res;
24 }
25
26 int main(void)  {       //HDOJ 3714 Error Curves
27     //freopen ("HDOJ_3714.in", "r", stdin);
28
29     int T;  scanf ("%d", &T);
30     while (T--) {
31         scanf ("%d", &n);
32         for (int i=1; i<=n; ++i)    {
33             scanf ("%lf%lf%lf", &f[i].a, &f[i].b, &f[i].c);
34         }
35
36         double l = 0.0, r = 1000.0;
37         for (int i=1; i<=100; ++i)  {
38             double mid = (l + r) / 2;
39             double rmid = (mid + r) / 2;
40             if (cal (mid) < cal (rmid)) r = rmid;
41             else    l = mid;
42         }
43         printf ("%.4f\n", cal (r));
44     }
45
46     return 0;
47 }