Statistics

Problem Statement

Draw a square with side length sideLength on a plane. Then, inscribe a circle in the square. Inscribe another square in that circle, and yet another circle in the second square. Continue this process until K circles appear on the plane.

For example, if K=3, the picture would look like this:

For each circle, compute the area within the circle that does not belong to any other figure inside that circle. Return the sum of those areas. In the example above, the area to compute is colored in stripes.

Definition

Class:

RecursiveFigures

Method:

getArea

Parameters:

int, int

Returns:

double

Method signature:

double getArea(int sideLength, int K)

(be sure your method is public)

Notes

• Your return value must have an absolute or relative error less than 1e-9.
• The area of square with side length A is A*A.
• The area of circle with radius R is pi*R*R.
• The length of diameter of the circle inscribed in a square is equal to the square's side length.
• The side length of the square inscribed in circle with radius R is equal to R*sqrt(2).

Constraints

• sideLength will be between 1 and 100, inclusive.
• K will be between 1 and 10, inclusive.

Examples

1. 10

   1

   Returns: 78.53981633974483

2. 10

   2

   Returns: 67.80972450961724

3. 10

   3

   Returns: 62.444678594553444

4. 1

   4

   Returns: 0.5976215563702155

5. 7

   7

   Returns: 28.133324544098755

6. 9

   6

   Returns: 46.77771336928683

7. 16

   7

   Returns: 146.9822670059037

8. 18

   4

   Returns: 193.62938426394982

9. 19

   7

   Returns: 207.26796245754392

10. 21

    5

    Returns: 257.6361432379073

11. 23

    6

    Returns: 305.4988934858362

12. 23

    9

    Returns: 302.39471145091727

13. 28

    7

    Returns: 450.1331927055801

14. 32

    2

    Returns: 694.3715789784806

15. 41

    8

    Returns: 962.3269510244776

16. 44

    2

    Returns: 1312.7962665061896

17. 44

    4

    Returns: 1156.995333132737

18. 45

    2

    Returns: 1373.1469213197493

19. 45

    7

    Returns: 1162.6526979959183

20. 47

    7

    Returns: 1268.2962024064113

21. 47

    9

    Returns: 1262.7408650190475

22. 50

    2

    Returns: 1695.2431127404311

23. 51

    2

    Returns: 1763.7309344951445

24. 52

    2

    Returns: 1833.57495074005

25. 52

    7

    Returns: 1552.5001952498578

26. 53

    1

    Returns: 2206.1834409834323

27. 53

    8

    Returns: 1608.0763863341815

28. 54

    2

    Returns: 1977.3315667004385

29. 55

    1

    Returns: 2375.8294442772813

30. 55

    6

    Returns: 1746.9454684208972

31. 63

    8

    Returns: 2272.144954560472

32. 65

    3

    Returns: 2638.2876706198836

33. 66

    5

    Returns: 2544.8141495336145

34. 67

    6

    Returns: 2592.4093248731915

35. 69

    8

    Returns: 2725.5434942460074

36. 72

    10

    Returns: 2961.1810017003445

37. 76

    4

    Returns: 3451.862109594365

38. 78

    1

    Returns: 4778.362426110075

39. 79

    8

    Returns: 3572.8033916381723

40. 80

    8

    Returns: 3663.8265833174655

41. 89

    7

    Returns: 4547.838034975638

42. 89

    8

    Returns: 4534.557869759006

43. 91

    6

    Returns: 4782.299313716843

44. 94

    10

    Returns: 5047.259901817948

45. 96

    7

    Returns: 5291.361612212533

46. 98

    10

    Returns: 5485.953383551331

47. 100

    8

    Returns: 5724.7290364335395

48. 100

    10

    Returns: 5712.154710070109

49. 99

    10

    Returns: 5598.482831339714

50. 1

    10

    Returns: 0.5712154710070109

51. 100

    1

    Returns: 7853.981633974483

52. 99

    9

    Returns: 5602.590863762646

53. 99

    5

    Returns: 5725.831836450631

54. 9

    2

    Returns: 54.92587685278996

55. 3

    1

    Returns: 7.0685834705770345

56. 1

    1

    Returns: 0.7853981633974483

57. 1

    3

    Returns: 0.6244467859455345

58. 7

    10

    Returns: 27.98955807934353

59. 20

    3

    Returns: 249.77871437821378

60. 100

    7

    Returns: 5741.494804918114

61. 9

    5

    Returns: 47.320924268187035

62. 50

    5

    Returns: 1460.5223539563901

63. 2

    10

    Returns: 2.2848618840280435

64. 27

    10

    Returns: 416.4160783641109