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Problem Statement for "RugSizes"

Problem Statement

Rugs come in various sizes. In fact, we can find a rug with any integer width and length, except that no rugs have a distinct width and length that are both even integers. For example, we can find a 4x4 rug, but not a 2x4 rug. We want to know how many different choices we have for a given area.

Create a class RugSizes the contains a method rugCount that is given the desired area and returns the number of different ways in which we can choose a rug size that will cover that exact area. Do not count the same size twice -- a 6 x 9 rug and a 9 x 6 rug should be counted as one choice.

Definition

Class:
RugSizes
Method:
rugCount
Parameters:
int
Returns:
int
Method signature:
int rugCount(int area)
(be sure your method is public)

Constraints

  • area will be between 1 and 100,000, inclusive.

Examples

  1. 4

    Returns: 2

    The choices are 1 x 4 (or equivalently 4 x 1) and 2 x 2.

  2. 8

    Returns: 1

    Only 1 x 8 is available. Note that 2 x 4 has the desired area, but is not available since its width and length differ and are both even numbers.

  3. 30

    Returns: 4

  4. 100000

    Returns: 6

  5. 98415

    Returns: 10

  6. 6241

    Returns: 2

  7. 99997

    Returns: 3

  8. 99991

    Returns: 1

  9. 64

    Returns: 2

  10. 4096

    Returns: 2

  11. 8192

    Returns: 1

  12. 8193

    Returns: 2

  13. 1

    Returns: 1

  14. 2

    Returns: 1

  15. 5

    Returns: 1

  16. 100000

    Returns: 6

  17. 1

    Returns: 1

  18. 26

    Returns: 2

  19. 16

    Returns: 2

  20. 15

    Returns: 2

  21. 30

    Returns: 4

  22. 9

    Returns: 2

  23. 21

    Returns: 2

  24. 10

    Returns: 2

  25. 99999

    Returns: 6

  26. 25

    Returns: 2

  27. 56

    Returns: 2

  28. 81

    Returns: 3

  29. 500

    Returns: 4

  30. 125

    Returns: 2

  31. 97

    Returns: 1

  32. 4

    Returns: 2

  33. 45

    Returns: 3

  34. 18

    Returns: 3

  35. 98456

    Returns: 4

  36. 32420

    Returns: 4

  37. 6

    Returns: 2

  38. 121

    Returns: 2

  39. 36

    Returns: 4

  40. 35

    Returns: 2

  41. 12

    Returns: 2

  42. 72

    Returns: 3

  43. 41472

    Returns: 5

  44. 27

    Returns: 2

  45. 20

    Returns: 2

  46. 1296

    Returns: 6

  47. 64

    Returns: 2

  48. 194

    Returns: 2

  49. 2

    Returns: 1

  50. 54

    Returns: 4

  51. 100

    Returns: 4

  52. 1365

    Returns: 8

  53. 100000

    Returns: 6

  54. 1

    Returns: 1

  55. 26

    Returns: 2

  56. 16

    Returns: 2

  57. 15

    Returns: 2

  58. 30

    Returns: 4

  59. 9

    Returns: 2

  60. 21

    Returns: 2

  61. 10

    Returns: 2

  62. 99999

    Returns: 6

  63. 25

    Returns: 2

  64. 56

    Returns: 2

  65. 81

    Returns: 3

  66. 500

    Returns: 4

  67. 125

    Returns: 2

  68. 97

    Returns: 1

  69. 4

    Returns: 2

  70. 45

    Returns: 3

  71. 18

    Returns: 3

  72. 98456

    Returns: 4

  73. 32420

    Returns: 4

  74. 6

    Returns: 2

  75. 121

    Returns: 2

  76. 36

    Returns: 4

  77. 35

    Returns: 2

  78. 12

    Returns: 2

  79. 72

    Returns: 3

  80. 41472

    Returns: 5

  81. 27

    Returns: 2

  82. 20

    Returns: 2

  83. 1296

    Returns: 6

  84. 64

    Returns: 2

  85. 194

    Returns: 2

  86. 2

    Returns: 1

  87. 54

    Returns: 4

  88. 100

    Returns: 4

  89. 1365

    Returns: 8

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