Statistics

Problem Statement for "ReProduct"

Problem Statement

Each of the digits 0 through 9 has a value that is in {0, 1, 2}. At least one of the digits has value 0. These values are given: the value of digit x is base[x].

For any bigger positive integer n, the value of n is one greater than the value of p(n), where p is the product of digits of n.

You are given the number goal. Return the smallest nonnegative integer with value goal. You may assume that for any valid input the output value exists and does not exceed 10^18.

Definition

Class:
ReProduct
Method:
minimize
Parameters:
int[], int
Returns:
long
Method signature:
long minimize(int[] base, int goal)
(be sure your method is public)

Constraints

  • base will contain exactly 10 elements.
  • Each element in base will be between 0 and 2, inclusive.
  • The smallest element in base will be 0.
  • goal will be between 0 and 11, inclusive.

Examples

  1. {0,1,1,1,1,1,1,1,1,1}

    2

    Returns: 11

    As given, the number 0 has value 0. As given, each of the numbers 1-9 has value 1. The number 10 has value 1 (because the number 1*0 = 0 has value 0). The number 11 has value 2 (because the number 1*1 = 1 has value 1). Thus, 11 is the smallest number with value 2.

  2. {0,0,0,0,0,0,0,0,0,0}

    3

    Returns: 39

    We have value(39) = 1 + value(27) = 2 + value(14) = 3 + value(4) = 3, and no smaller number has value 3.

  3. {2,0,0,0,0,0,0,0,0,0}

    2

    Returns: 0

  4. {2,2,2,2,2,2,2,2,0,2}

    1

    Returns: 18

  5. {2,1,2,2,1,1,1,0,1,0}

    6

    Returns: 268

  6. {0,0,0,0,0,0,0,0,0,0}

    2

    Returns: 25

  7. {2,1,1,1,0,1,1,1,1,1}

    1

    Returns: 1

  8. {0,1,1,1,1,1,1,1,1,1}

    6

    Returns: 679

  9. {1,1,1,1,0,1,1,1,1,1}

    7

    Returns: 6788

  10. {2,2,2,2,0,2,2,2,2,2}

    10

    Returns: 2677889

  11. {0,2,0,1,2,1,0,1,2,2}

    1

    Returns: 3

  12. {0,1,2,2,2,1,1,0,0,1}

    4

    Returns: 26

  13. {1,0,1,2,1,2,1,1,2,1}

    6

    Returns: 77

  14. {2,0,1,2,0,2,1,1,0,1}

    6

    Returns: 268

  15. {0,2,2,2,2,2,2,2,2,2}

    1

    Returns: 10

  16. {0,0,0,0,0,0,0,0,0,0}

    1

    Returns: 10

  17. {2,1,1,1,0,1,1,1,1,1}

    11

    Returns: 26888999

  18. {0,1,1,1,1,1,1,1,1,1}

    11

    Returns: 277777788888899

  19. {2,2,2,2,0,2,2,2,2,2}

    0

    Returns: 4

  20. {1,1,1,1,0,1,1,1,1,1}

    4

    Returns: 47

  21. {1,1,1,1,0,1,2,1,1,1}

    4

    Returns: 28

  22. {1,1,1,1,0,1,2,1,1,1}

    9

    Returns: 2677889

  23. {1,1,2,1,1,2,2,0,2,0}

    10

    Returns: 26888999

  24. {0,0,0,0,0,0,0,0,0,0}

    11

    Returns: 277777788888899

  25. {0,0,1,2,0,2,1,2,2,1}

    6

    Returns: 77

  26. {0,1,0,1,2,2,1,2,2,2}

    10

    Returns: 3778888999

  27. {0,2,2,2,2,2,2,2,2,2}

    4

    Returns: 26

  28. {2,1,1,1,0,1,1,1,1,1}

    6

    Returns: 268

  29. {2,1,2,1,0,2,1,1,2,2}

    0

    Returns: 4

  30. {0,1,1,1,1,1,1,1,1,1}

    8

    Returns: 2677889

  31. {2,2,2,2,0,2,2,2,2,2}

    3

    Returns: 10

  32. {1,1,1,1,0,1,1,1,1,1}

    1

    Returns: 0

  33. {1,1,1,1,0,1,2,1,1,1}

    7

    Returns: 679

  34. {0,2,2,2,2,2,2,2,2,2}

    10

    Returns: 3778888999

  35. {0,0,0,0,0,0,0,0,0,0}

    6

    Returns: 6788

  36. {0,2,2,2,2,2,2,2,2,2}

    7

    Returns: 679

  37. {2,1,1,1,0,1,1,1,1,1}

    5

    Returns: 55

  38. {0,1,1,1,1,1,1,1,1,1}

    2

    Returns: 11

  39. {0,1,1,0,0,1,0,2,1,0}

    9

    Returns: 26888999

  40. {1,1,1,1,0,1,1,1,1,1}

    11

    Returns: 3778888999

  41. {2,2,0,2,2,1,0,0,2,0}

    9

    Returns: 68889

  42. {1,0,0,0,1,0,2,1,0,2}

    11

    Returns: 3778888999

  43. {1,1,1,1,0,1,2,1,1,1}

    2

    Returns: 6

  44. {2,2,2,2,0,2,2,2,2,2}

    6

    Returns: 77

  45. {0,1,1,1,1,1,0,2,2,2}

    11

    Returns: 277777788888899

  46. {0,0,0,0,0,0,0,0,0,0}

    5

    Returns: 679

  47. {2,0,1,2,0,0,0,1,1,2}

    8

    Returns: 6788

  48. {2,1,1,1,0,1,1,1,1,1}

    0

    Returns: 4

  49. {0,1,1,1,1,1,1,1,1,1}

    7

    Returns: 68889

  50. {2,2,1,0,1,2,1,2,2,0}

    11

    Returns: 26888999

  51. {0,1,2,1,0,0,2,2,1,1}

    3

    Returns: 12

  52. {1,1,1,1,0,1,1,1,1,1}

    8

    Returns: 68889

  53. {2,2,2,2,0,2,2,2,2,2}

    9

    Returns: 68889

  54. {2,0,2,1,0,2,1,0,0,0}

    8

    Returns: 6788

  55. {0,0,0,0,2,1,1,0,1,1}

    8

    Returns: 2677889

  56. {1,1,1,1,0,2,2,2,1,1}

    8

    Returns: 68889

  57. {0,2,2,2,2,2,2,2,2,2}

    0

    Returns: 0

  58. {0,0,0,0,0,0,0,0,0,0}

    0

    Returns: 0

  59. {2,1,1,1,0,1,1,1,1,1}

    10

    Returns: 2677889

  60. {1,0,0,1,0,2,1,0,1,2}

    1

    Returns: 0

  61. {0,1,1,1,1,1,1,1,1,1}

    4

    Returns: 39

  62. {1,1,1,1,0,1,1,1,1,1}

    5

    Returns: 77

  63. {2,1,2,2,0,0,0,2,0,2}

    7

    Returns: 688

  64. {1,1,1,1,0,1,2,1,1,1}

    8

    Returns: 68889

  65. {0,0,0,2,1,2,0,2,0,2}

    0

    Returns: 0

  66. {0,0,0,0,0,0,0,0,0,0}

    10

    Returns: 3778888999

  67. {0,2,1,2,2,1,2,1,2,2}

    3

    Returns: 11

  68. {0,2,2,2,2,2,2,2,2,2}

    3

    Returns: 11

  69. {0,2,0,1,2,0,1,2,0,1}

    9

    Returns: 26888999

  70. {2,1,1,1,0,1,1,1,1,1}

    9

    Returns: 68889

  71. {2,0,2,2,2,2,1,2,2,1}

    9

    Returns: 68889

  72. {0,2,0,2,1,0,1,1,2,1}

    10

    Returns: 3778888999

  73. {0,1,1,1,1,1,1,1,1,1}

    9

    Returns: 26888999

  74. {2,0,2,2,1,2,2,0,2,1}

    5

    Returns: 47

  75. {0,1,1,1,2,2,0,1,0,0}

    8

    Returns: 2677889

  76. {2,2,2,2,0,2,2,2,2,2}

    2

    Returns: 0

  77. {1,1,1,1,0,1,1,1,1,1}

    2

    Returns: 10

  78. {1,1,1,1,0,1,2,1,1,1}

    6

    Returns: 377

  79. {1,1,2,0,1,1,0,0,2,1}

    5

    Returns: 49

  80. {1,1,1,1,0,1,2,1,1,1}

    11

    Returns: 3778888999

  81. {0,2,2,2,2,2,2,2,2,2}

    9

    Returns: 26888999

  82. {0,0,0,0,0,0,0,0,0,0}

    9

    Returns: 26888999

  83. {1,2,0,2,1,0,0,1,1,2}

    1

    Returns: 0

  84. {0,2,2,2,2,2,2,2,2,2}

    6

    Returns: 77

  85. {2,1,1,1,0,1,1,1,1,1}

    4

    Returns: 25

  86. {0,1,1,1,1,1,1,1,1,1}

    3

    Returns: 26

  87. {0,2,0,1,0,1,0,1,0,0}

    2

    Returns: 1

  88. {0,2,0,0,1,1,2,0,0,1}

    3

    Returns: 11

  89. {1,1,1,1,0,1,2,1,1,1}

    1

    Returns: 0

  90. {2,2,2,2,0,2,2,2,2,2}

    5

    Returns: 47

  91. {0,0,0,0,0,0,0,0,0,0}

    4

    Returns: 77

  92. {0,2,0,2,1,0,1,2,1,1}

    1

    Returns: 4

  93. {1,0,2,0,1,0,0,2,2,1}

    0

    Returns: 1

  94. {2,1,1,1,0,1,1,1,1,1}

    3

    Returns: 10

  95. {2,2,2,0,1,1,0,2,0,1}

    5

    Returns: 55

  96. {0,1,1,1,1,1,1,1,1,1}

    0

    Returns: 0

  97. {0,2,2,2,1,1,2,1,0,0}

    0

    Returns: 0

  98. {0,0,2,0,0,0,0,0,2,0}

    11

    Returns: 277777788888899

  99. {2,0,1,2,1,1,0,1,0,1}

    10

    Returns: 2677889

  100. {0,2,0,0,1,0,1,2,1,2}

    8

    Returns: 2677889

  101. {1,1,1,1,0,1,1,1,1,1}

    9

    Returns: 2677889

  102. {2,2,2,2,0,2,2,2,2,2}

    8

    Returns: 6788

  103. {1,1,1,1,2,0,0,2,1,0}

    0

    Returns: 5

  104. {0,2,2,1,2,2,2,2,2,2}

    7

    Returns: 679

  105. {1,0,2,1,2,0,2,2,1,0}

    5

    Returns: 39

  106. {0,0,0,0,0,0,0,0,0,0}

    3

    Returns: 39

  107. {1,2,1,2,0,0,1,1,0,1}

    0

    Returns: 4

  108. {1,0,2,0,2,1,0,1,2,0}

    6

    Returns: 77

  109. {0,0,0,0,1,1,0,1,0,0}

    9

    Returns: 26888999

  110. {0,1,1,1,1,1,1,1,1,1}

    5

    Returns: 77

  111. {0,0,0,2,2,1,2,1,0,1}

    7

    Returns: 679

  112. {1,1,1,1,0,1,1,1,1,1}

    6

    Returns: 679

  113. {2,2,2,2,0,2,2,2,2,2}

    11

    Returns: 26888999

  114. {2,2,0,1,1,0,1,0,1,2}

    1

    Returns: 3

  115. {0,2,2,2,2,2,2,2,2,2}

    2

    Returns: 1

  116. {2,1,1,1,0,1,1,1,1,1}

    8

    Returns: 6788

  117. {1,0,1,1,0,0,1,0,1,1}

    8

    Returns: 68889

  118. {2,0,2,1,1,1,2,0,1,2}

    8

    Returns: 6788

  119. {0,1,1,1,1,1,1,1,1,1}

    10

    Returns: 3778888999

  120. {2,2,2,2,0,2,2,2,2,2}

    1

    Returns: 14

  121. {1,1,1,1,0,1,1,1,1,1}

    3

    Returns: 25

  122. {1,1,1,1,0,1,2,1,1,1}

    5

    Returns: 47

  123. {1,1,2,1,2,1,1,0,1,0}

    2

    Returns: 2

  124. {1,1,1,1,0,1,2,1,1,1}

    10

    Returns: 26888999

  125. {2,0,2,1,1,1,2,2,2,2}

    11

    Returns: 26888999

  126. {0,2,2,2,2,2,2,2,2,2}

    8

    Returns: 888899

  127. {0,0,0,0,0,0,0,0,0,0}

    8

    Returns: 2677889

  128. {0,1,1,2,0,1,0,2,1,1}

    11

    Returns: 277777788888899

  129. {0,2,2,2,2,2,2,2,2,2}

    5

    Returns: 39

  130. {2,1,1,1,0,1,1,1,1,1}

    7

    Returns: 688

  131. {2,0,2,2,0,2,1,2,1,2}

    9

    Returns: 68889

  132. {1,1,1,1,0,1,2,1,1,1}

    0

    Returns: 4

  133. {1,1,1,1,0,1,1,1,1,1}

    0

    Returns: 4

  134. {2,2,2,2,0,2,2,2,2,2}

    4

    Returns: 25

  135. {2,0,0,1,2,2,2,1,1,1}

    0

    Returns: 1

  136. {0,2,2,2,2,2,2,2,2,2}

    11

    Returns: 277777788888899

  137. {0,0,0,0,0,0,0,0,0,0}

    7

    Returns: 68889

  138. {1,1,2,0,2,2,0,0,2,1}

    6

    Returns: 77

  139. {2,1,1,1,0,1,1,1,1,1}

    2

    Returns: 0

  140. {0,1,1,1,1,1,1,1,1,1}

    1

    Returns: 1

  141. {1,1,1,1,0,1,1,1,1,1}

    10

    Returns: 26888999

  142. {2,0,0,1,1,1,1,2,1,2}

    2

    Returns: 0

  143. {1,2,1,0,0,2,2,1,1,0}

    5

    Returns: 47

  144. {1,1,1,1,0,1,2,1,1,1}

    3

    Returns: 16

  145. {2,2,2,2,0,2,2,2,2,2}

    7

    Returns: 679

  146. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    11

    Returns: 277777788888899

  147. {1, 0, 2, 2, 2, 2, 2, 2, 2, 2 }

    11

    Returns: 3778888999

  148. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    1

    Returns: 10

  149. {0, 2, 2, 2, 2, 2, 2, 2, 2, 2 }

    1

    Returns: 10

  150. {2, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    3

    Returns: 10

  151. {0, 2, 0, 0, 0, 0, 0, 0, 0, 0 }

    1

    Returns: 10

  152. {0, 0, 2, 2, 2, 2, 2, 2, 2, 2 }

    11

    Returns: 277777788888899

  153. {0, 0, 0, 0, 0, 0, 0, 0, 0, 0 }

    2

    Returns: 25

  154. {0, 2, 0, 0, 0, 1, 0, 2, 2, 1 }

    10

    Returns: 3778888999

  155. {0, 1, 0, 0, 1, 0, 1, 1, 0, 2 }

    3

    Returns: 19

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