Do not pour out HDU - 5954 数学积分

Posted 2021-01-10 fan-jiaming

题目：题目链接

思路：纯高等数学问题，不过不是很好积分，具体积分思路及过程参考大佬博客——https://blog.csdn.net/danliwoo/article/details/53002695

AC代码：

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <algorithm>
 4 #include <cmath>
 5 #include <iomanip>
 6 
 7 using namespace std;
 8 
 9 #define pi acos(-1.0)
10 
11 double h;
12 
13 double cal(double a) {
14     return pi * cos(a) - a * cos(a) + sin(a) - pow(sin(a), 3) / 3;
15 }
16 
17 double calV(double b) {
18     double a = acos(2 * tan(b) - 1.0);
19     return (cal(a) - cal(pi)) / tan(b);
20 }
21 
22 int main()
23 {
24     int T;
25     scanf("%d", &T);
26     while(T--) {
27         scanf("%lf", &h);
28         double v = pi * h;
29         if(h < 1e-10)
30             printf("0.00000
");
31         else if(h >= 1.0) {
32             double a = atan(2.0 - h);
33             printf("%.5f
", pi / cos(a));
34         }
35         else {
36             double l = 0, r = pi / 4;
37             while(r - l > 1e-9) {
38                 double m = (l + r) / 2;
39                 if(calV(m) < v) 
40                     l = m;
41                 else
42                     r = m;
43             }
44             double x = 2 * tan(r);
45             double a = acos(x - 1);
46             double s = (pi - a + sin(a) * cos(a)) / sin(r);
47             printf("%.5f
", s);
48         }
49     }
50     return 0;
51 }