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Problem Statement for "BComputation"

Problem Statement

You will be given B0, the first element of our sequence. The following equation must hold for all n > 0:
        0  =  B0 + n+1C1B1 + n+1C2B2 + ... + n+1CnBn 
Here aCb is the standard binomial coefficient (see the notes). Return the value Bpos in the form "p/q" (quotes for clarity) where p and q are integers with no extra leading zeros and no common factors (other than 1). The denominator q must always be positive. If the returned value is 0 then return "0/1".

Definition

Class:
BComputation
Method:
getValue
Parameters:
int, int
Returns:
String
Method signature:
String getValue(int B0, int pos)
(be sure your method is public)

Notes

  • aCb has value a!/(b!(a-b)!) where a! = a*(a-1)*...*2*1.

Constraints

  • B0 will be between -100 and 100, inclusive.
  • pos will be between 0 and 15, inclusive.

Examples

  1. 1

    0

    Returns: "1/1"

    Here we simply return B0.

  2. 1

    1

    Returns: "-1/2"

    Using the given formula, we can compute B1 = -B0/2C1.

  3. 100

    11

    Returns: "0/1"

  4. 1

    4

    Returns: "-1/30"

  5. 1

    5

    Returns: "0/1"

  6. 1

    6

    Returns: "1/42"

  7. 1

    7

    Returns: "0/1"

  8. 1

    8

    Returns: "-1/30"

  9. 1

    9

    Returns: "0/1"

  10. 1

    10

    Returns: "5/66"

  11. 1

    11

    Returns: "0/1"

  12. 1

    12

    Returns: "-691/2730"

  13. 1

    13

    Returns: "0/1"

  14. 1

    14

    Returns: "7/6"

  15. 1

    15

    Returns: "0/1"

  16. -8

    2

    Returns: "-4/3"

  17. -73

    2

    Returns: "-73/6"

  18. -70

    13

    Returns: "0/1"

  19. 65

    0

    Returns: "65/1"

  20. -12

    15

    Returns: "0/1"

  21. -31

    0

    Returns: "-31/1"

  22. -13

    2

    Returns: "-13/6"

  23. 21

    3

    Returns: "0/1"

  24. 92

    12

    Returns: "-31786/1365"

  25. -26

    10

    Returns: "-65/33"

  26. 1

    13

    Returns: "0/1"

  27. -93

    12

    Returns: "21421/910"

  28. -92

    13

    Returns: "0/1"

  29. -82

    13

    Returns: "0/1"

  30. -34

    12

    Returns: "11747/1365"

  31. 75

    4

    Returns: "-5/2"

  32. -93

    5

    Returns: "0/1"

  33. 63

    0

    Returns: "63/1"

  34. -26

    10

    Returns: "-65/33"

  35. -72

    8

    Returns: "12/5"

  36. -25

    15

    Returns: "0/1"

  37. 54

    10

    Returns: "45/11"

  38. 42

    1

    Returns: "-21/1"

  39. -52

    3

    Returns: "0/1"

  40. -54

    3

    Returns: "0/1"

  41. -9

    9

    Returns: "0/1"

  42. -20

    13

    Returns: "0/1"

  43. 42

    11

    Returns: "0/1"

  44. 77

    1

    Returns: "-77/2"

  45. 38

    2

    Returns: "19/3"

  46. -79

    12

    Returns: "54589/2730"

  47. -83

    6

    Returns: "-83/42"

  48. -31

    8

    Returns: "31/30"

  49. -49

    8

    Returns: "49/30"

  50. -12

    8

    Returns: "2/5"

  51. 72

    4

    Returns: "-12/5"

  52. -36

    4

    Returns: "6/5"

  53. -89

    12

    Returns: "61499/2730"

  54. 15

    10

    Returns: "25/22"

  55. 13

    2

    Returns: "13/6"

  56. -32

    6

    Returns: "-16/21"

  57. -19

    8

    Returns: "19/30"

  58. -27

    10

    Returns: "-45/22"

  59. -31

    8

    Returns: "31/30"

  60. 80

    14

    Returns: "280/3"

  61. -86

    14

    Returns: "-301/3"

  62. -57

    14

    Returns: "-133/2"

  63. -8

    14

    Returns: "-28/3"

  64. -58

    14

    Returns: "-203/3"

  65. -53

    14

    Returns: "-371/6"

  66. 76

    14

    Returns: "266/3"

  67. 33

    14

    Returns: "77/2"

  68. 47

    14

    Returns: "329/6"

  69. -28

    14

    Returns: "-98/3"

  70. 92

    15

    Returns: "0/1"

  71. 1

    0

    Returns: "1/1"

  72. 100

    15

    Returns: "0/1"


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