Statistics

Problem Statement for "ProdCalc"

Problem Statement

You have a calculator that can only handle numbers with up to d digits. Initially, the number shown on the screen is 1. You must perform exactly op multiplication operations. Each operation multiplies the number on the screen by a digit between 2 and 9, inclusive. The result of each operation must be a number with d or less digits. Return the largest number that can be displayed on the screen after op operations. If there is no way to perform op operations without overflowing the calculator, return -1.

Definition

Class:
ProdCalc
Method:
highest
Parameters:
int, int
Returns:
long
Method signature:
long highest(int d, int op)
(be sure your method is public)

Constraints

  • d will be between 2 and 8, inclusive.
  • op will be between 0 and 30, inclusive.

Examples

  1. 4

    3

    Returns: 729

    The calculator can store up to 4 digits. With 3 multiplications, we can obtain at most 729, by using digit 9 every time: 1 * 9 * 9 * 9 = 729.

  2. 8

    0

    Returns: 1

    No multiplications can be performed.

  3. 2

    3

    Returns: 98

    The storage is limited to 2 digits. The highest number that can be shown on screen after 3 multiplications is 98 (2 * 7 * 7).

  4. 8

    10

    Returns: 99574272

  5. 8

    20

    Returns: 99532800

  6. 8

    30

    Returns: -1

    Even if we would only use digit 2 every time, 2^30 has more than 8 digits and overflows the calculator.

  7. 2

    6

    Returns: 96

  8. 2

    0

    Returns: 1

  9. 2

    1

    Returns: 9

  10. 2

    2

    Returns: 81

  11. 3

    1

    Returns: 9

  12. 2

    4

    Returns: 96

  13. 2

    5

    Returns: 96

  14. 2

    7

    Returns: -1

  15. 2

    30

    Returns: -1

  16. 3

    0

    Returns: 1

  17. 3

    2

    Returns: 81

  18. 3

    3

    Returns: 729

  19. 3

    4

    Returns: 980

  20. 3

    5

    Returns: 980

  21. 3

    6

    Returns: 972

  22. 3

    7

    Returns: 972

  23. 3

    8

    Returns: 960

  24. 3

    9

    Returns: 768

  25. 3

    10

    Returns: -1

  26. 3

    30

    Returns: -1

  27. 4

    4

    Returns: 6561

  28. 4

    5

    Returns: 9800

  29. 4

    6

    Returns: 9800

  30. 4

    7

    Returns: 9800

  31. 4

    8

    Returns: 9720

  32. 4

    9

    Returns: 9720

  33. 4

    10

    Returns: 9600

  34. 4

    11

    Returns: 9216

  35. 4

    12

    Returns: 9216

  36. 4

    13

    Returns: 8192

  37. 4

    14

    Returns: -1

  38. 5

    17

    Returns: -1

  39. 6

    20

    Returns: -1

  40. 7

    24

    Returns: -1

  41. 8

    27

    Returns: -1

  42. 5

    5

    Returns: 59049

  43. 5

    6

    Returns: 99225

  44. 5

    7

    Returns: 99225

  45. 5

    8

    Returns: 99225

  46. 5

    9

    Returns: 98784

  47. 5

    10

    Returns: 98784

  48. 5

    11

    Returns: 98304

  49. 5

    12

    Returns: 98304

  50. 5

    13

    Returns: 98304

  51. 5

    14

    Returns: 98304

  52. 5

    15

    Returns: 98304

  53. 5

    16

    Returns: 98304

  54. 6

    6

    Returns: 531441

  55. 6

    7

    Returns: 995328

  56. 6

    8

    Returns: 995328

  57. 6

    9

    Returns: 995328

  58. 6

    10

    Returns: 995328

  59. 6

    11

    Returns: 995328

  60. 6

    12

    Returns: 995328

  61. 6

    13

    Returns: 995328

  62. 6

    14

    Returns: 995328

  63. 6

    15

    Returns: 995328

  64. 6

    16

    Returns: 995328

  65. 6

    17

    Returns: 995328

  66. 6

    18

    Returns: 983040

  67. 6

    19

    Returns: 786432

  68. 7

    7

    Returns: 4782969

  69. 7

    8

    Returns: 9953280

  70. 7

    9

    Returns: 9953280

  71. 7

    10

    Returns: 9953280

  72. 7

    11

    Returns: 9953280

  73. 7

    12

    Returns: 9953280

  74. 7

    13

    Returns: 9953280

  75. 7

    14

    Returns: 9953280

  76. 7

    15

    Returns: 9953280

  77. 7

    16

    Returns: 9953280

  78. 7

    17

    Returns: 9953280

  79. 7

    18

    Returns: 9953280

  80. 7

    19

    Returns: 9953280

  81. 7

    20

    Returns: 9830400

  82. 7

    21

    Returns: 9437184

  83. 7

    22

    Returns: 9437184

  84. 7

    23

    Returns: 8388608

  85. 8

    8

    Returns: 43046721

  86. 8

    9

    Returns: 99574272

  87. 8

    11

    Returns: 99574272

  88. 8

    12

    Returns: 99574272

  89. 8

    13

    Returns: 99574272

  90. 8

    14

    Returns: 99574272

  91. 8

    15

    Returns: 99574272

  92. 8

    16

    Returns: 99574272

  93. 8

    17

    Returns: 99574272

  94. 8

    18

    Returns: 99532800

  95. 8

    19

    Returns: 99532800

  96. 8

    21

    Returns: 99532800

  97. 8

    22

    Returns: 99090432

  98. 8

    23

    Returns: 99090432

  99. 8

    24

    Returns: 94371840

  100. 8

    25

    Returns: 83886080

  101. 8

    26

    Returns: 67108864

  102. 8

    27

    Returns: -1

  103. 8

    28

    Returns: -1

  104. 8

    29

    Returns: -1

  105. 8

    30

    Returns: -1

  106. 8

    25

    Returns: 83886080

  107. 8

    9

    Returns: 99574272

  108. 2

    2

    Returns: 81

  109. 2

    4

    Returns: 96

  110. 4

    14

    Returns: -1

  111. 8

    20

    Returns: 99532800

  112. 8

    0

    Returns: 1

  113. 8

    30

    Returns: -1

  114. 8

    26

    Returns: 67108864

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