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Problem Statement for "ToastXRaspberry"

Problem Statement

You have some raspberry jam and a slice of plain toast. You're going to create a slice of breathtaking raspberry toast by applying some of the jam to the toast. Each application will apply L layers of raspberry jam, where L is a positive integer (chosen before the application) and L is not greater than upper_limit. A slice of breathtaking raspberry toast is a slice of plain toast that has had exactly layer_count layers of raspberry jam applied. Return the minimum number of applications required to turn a slice of plain toast into a slice of breathtaking raspberry toast.

Definition

Class:
ToastXRaspberry
Method:
apply
Parameters:
int, int
Returns:
int
Method signature:
int apply(int upper_limit, int layer_count)
(be sure your method is public)

Constraints

  • upper_limit will be between 1 and 100, inclusive.
  • layer_count will be between 1 and 1000, inclusive.

Examples

  1. 4

    13

    Returns: 4

    One possible way is to apply 4, 4, 3, then 2 layers of jam.

  2. 8

    5

    Returns: 1

    A single application is sufficient.

  3. 100

    1000

    Returns: 10

  4. 99

    1000

    Returns: 11

  5. 1

    1

    Returns: 1

  6. 73

    265

    Returns: 4

  7. 78

    56

    Returns: 1

  8. 52

    603

    Returns: 12

  9. 45

    625

    Returns: 14

  10. 37

    693

    Returns: 19

  11. 75

    444

    Returns: 6

  12. 35

    645

    Returns: 19

  13. 53

    998

    Returns: 19

  14. 78

    954

    Returns: 13

  15. 75

    105

    Returns: 2

  16. 1

    1

    Returns: 1

  17. 1

    3

    Returns: 3

  18. 1

    8

    Returns: 8

  19. 1

    21

    Returns: 21

  20. 1

    55

    Returns: 55

  21. 1

    145

    Returns: 145

  22. 1

    380

    Returns: 380

  23. 1

    996

    Returns: 996

  24. 1

    1000

    Returns: 1000

  25. 2

    1

    Returns: 1

  26. 2

    3

    Returns: 2

  27. 2

    8

    Returns: 4

  28. 2

    21

    Returns: 11

  29. 2

    55

    Returns: 28

  30. 2

    145

    Returns: 73

  31. 2

    380

    Returns: 190

  32. 2

    996

    Returns: 498

  33. 2

    1000

    Returns: 500

  34. 4

    1

    Returns: 1

  35. 4

    3

    Returns: 1

  36. 4

    8

    Returns: 2

  37. 4

    21

    Returns: 6

  38. 4

    55

    Returns: 14

  39. 4

    145

    Returns: 37

  40. 4

    380

    Returns: 95

  41. 4

    996

    Returns: 249

  42. 4

    1000

    Returns: 250

  43. 8

    1

    Returns: 1

  44. 8

    3

    Returns: 1

  45. 8

    8

    Returns: 1

  46. 8

    21

    Returns: 3

  47. 8

    55

    Returns: 7

  48. 8

    145

    Returns: 19

  49. 8

    380

    Returns: 48

  50. 8

    996

    Returns: 125

  51. 8

    1000

    Returns: 125

  52. 15

    1

    Returns: 1

  53. 15

    3

    Returns: 1

  54. 15

    8

    Returns: 1

  55. 15

    21

    Returns: 2

  56. 15

    55

    Returns: 4

  57. 15

    145

    Returns: 10

  58. 15

    380

    Returns: 26

  59. 15

    996

    Returns: 67

  60. 15

    1000

    Returns: 67

  61. 28

    1

    Returns: 1

  62. 28

    3

    Returns: 1

  63. 28

    8

    Returns: 1

  64. 28

    21

    Returns: 1

  65. 28

    55

    Returns: 2

  66. 28

    145

    Returns: 6

  67. 28

    380

    Returns: 14

  68. 28

    996

    Returns: 36

  69. 28

    1000

    Returns: 36

  70. 53

    1

    Returns: 1

  71. 53

    3

    Returns: 1

  72. 53

    8

    Returns: 1

  73. 53

    21

    Returns: 1

  74. 53

    55

    Returns: 2

  75. 53

    145

    Returns: 3

  76. 53

    380

    Returns: 8

  77. 53

    996

    Returns: 19

  78. 53

    1000

    Returns: 19

  79. 99

    1

    Returns: 1

  80. 99

    3

    Returns: 1

  81. 99

    8

    Returns: 1

  82. 99

    21

    Returns: 1

  83. 99

    55

    Returns: 1

  84. 99

    145

    Returns: 2

  85. 99

    380

    Returns: 4

  86. 99

    996

    Returns: 11

  87. 99

    1000

    Returns: 11

  88. 100

    1

    Returns: 1

  89. 100

    3

    Returns: 1

  90. 100

    8

    Returns: 1

  91. 100

    21

    Returns: 1

  92. 100

    55

    Returns: 1

  93. 100

    145

    Returns: 2

  94. 100

    380

    Returns: 4

  95. 100

    996

    Returns: 10

  96. 100

    1000

    Returns: 10

  97. 4

    16

    Returns: 4

  98. 5

    10

    Returns: 2

  99. 3

    12

    Returns: 4

  100. 3

    9

    Returns: 3

  101. 10

    10

    Returns: 1

  102. 2

    4

    Returns: 2

  103. 5

    15

    Returns: 3

  104. 5

    5

    Returns: 1

  105. 73

    292

    Returns: 4

  106. 4

    4

    Returns: 1

  107. 2

    2

    Returns: 1

  108. 1

    2

    Returns: 2

  109. 8

    16

    Returns: 2

  110. 4

    12

    Returns: 3

  111. 1

    5

    Returns: 5

  112. 3

    6

    Returns: 2

  113. 3

    3

    Returns: 1

  114. 55

    55

    Returns: 1

  115. 4

    28

    Returns: 7

  116. 2

    14

    Returns: 7

  117. 5

    25

    Returns: 5

  118. 10

    50

    Returns: 5

  119. 10

    20

    Returns: 2

  120. 2

    6

    Returns: 3

  121. 3

    54

    Returns: 18

  122. 25

    100

    Returns: 4

  123. 1

    100

    Returns: 100

  124. 5

    20

    Returns: 4

  125. 3

    10

    Returns: 4

  126. 2

    20

    Returns: 10

  127. 3

    4

    Returns: 2

  128. 1

    6

    Returns: 6

  129. 20

    20

    Returns: 1

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