LA 3485 (积分 辛普森自适应法) Bridge

 1 #include <cstdio>
 2 #include <cmath>
 3 
 4 inline double F(double a, double x)
 5 {//sqrt(a^2+x^2)的原函数
 6     double a2 = a*a, x2 = x*x;
 7     double s = sqrt(a2+x2);
 8     return (x*s + a2*log(x+s))/2;
 9 }
10 
11 double length(double w, double h)
12 {//宽为w，高为h的抛物线的长度
13     double a = 4*h/w/w;
14     double b = 0.5/a;
15     return 4*a*(F(b, w/2) - F(b, 0));
16 }
17 
18 int main()
19 {
20     //freopen("in.txt", "r", stdin);
21 
22     int T;
23     scanf("%d", &T);
24     for(int kase = 1; kase <= T; kase++)
25     {
26         int D, H, B, L;
27         scanf("%d%d%d%d", &D, &H, &B, &L);
28         int n = (B-1)/D + 1;    //间隔数
29         double d = (double)B / n; //间隔
30         double l = (double)L / n;   //每段绳长
31         double Left = 0, Right = H;
32         while(Right - Left > 1e-5)
33         {//二分求抛物线高度
34             double mid = (Right + Left) / 2;
35             if(length(d, mid) > l) Right = mid;
36             else Left = mid;
37         }
38         if(kase > 1) puts("");
39         printf("Case %d:\n%.2f\n", kase, H-Left);
40     }
41 
42     return 0;
43 }