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  1. #include <math.h>
  2. #include <stdio.h>
  3. #include <stdlib.h>
  4.  
  5. // (0, ±e, d)
  6. // (±a, ±b, c)
  7. // (±b, ±a, -c)
  8. // (±e, 0, -d)
  9.  
  10. typedef double scalar;
  11.  
  12. scalar vol(scalar a, scalar b, scalar c, scalar d) {
  13. 	scalar e = (a * c - a * d + b * c + b * d) / (2 * c);
  14. 	if (!(0. <= e && e <= b)) {
  15. 		return 0.;
  16. 	}
  17. 	scalar h4 = hypot(a, d - c);
  18. 	scalar h53 = hypot(b - e, d - c);
  19. 	scalar h54 = hypot(a - b, 2 * c);
  20.  
  21. 	scalar s0 = ( (b + e) * h4 + a * h53 + (a + b) * h54 ) * 4.;
  22. 	scalar v0 = ( a * (d - c) * (b * 2. + e) + (a * a + b * b + 4 * a * b) * c ) * ((scalar)4. / (scalar)3.);
  23.  
  24. 	scalar s0_i = 1/s0;
  25. 	scalar r_s0_i = sqrt(s0_i);
  26. 	scalar v = v0 * r_s0_i * s0_i;
  27. 	return v;
  28. }
  29.  
  30. int main() {
  31. 	scalar v_max = 0.;
  32. 	scalar a_max = .5;
  33. 	scalar b_max = .5;
  34. 	scalar c_max = .5;
  35. 	scalar d_max = .5;
  36. 	scalar r = 1.;
  37. 	for (int i = 0; i < 53; i++) {
  38. 		for (int j = 0; j < 100; j++) {
  39. 			scalar a, b, c, d;
  40. 			do {
  41. 				a = a_max + (rand() * (1. / RAND_MAX) - .5) * r;
  42. 				b = b_max + (rand() * (1. / RAND_MAX) - .5) * r;
  43. 				c = c_max + (rand() * (1. / RAND_MAX) - .5) * r;
  44. 				d = d_max + (rand() * (1. / RAND_MAX) - .5) * r;
  45. 			} while (a <= b || c >= d);
  46. 			scalar v = vol(a, b, c, d);
  47. 			if (v > v_max) {
  48. 				v_max = v;
  49. 				a_max = a;
  50. 				b_max = b;
  51. 				c_max = c;
  52. 				d_max = d;
  53. 			}
  54. 		}
  55. 		r *= .5;
  56. 	}
  57. 	printf("%.16f\r\n", vol(a_max, b_max, c_max, d_max));
  58. 	return 0;
  59. }
  60.  
Success #stdin #stdout 0s 4512KB
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0.0743448680932300
https://ideone.com/Jl6zc2
language:
C++ (gcc 8.3)
created:
3 years ago
visibility:
public

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