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Problem Statement for "DivisibleSetDiv2"

Problem Statement

You are given a int[] b containing a sequence of n positive integers: b[0], ..., b[n-1]. We are now looking for another sequence a[0], ..., a[n-1]. This sequence should have the following properties:
  • Each a[i] should be a number of the form 2^x[i] where x[i] is some positive integer. In other words, each a[i] is one of the numbers 2, 4, 8, 16, ...
  • For each i, the value a[i]^b[i] (that is, a[i] to the power b[i]) should be divisible by P, where P is the product of all a[i].
Determine whether there is at least one sequence with the desired properties. Return "Possible" (quotes for clarity) if such a sequence exists and "Impossible" otherwise.

Definition

Class:
DivisibleSetDiv2
Method:
isPossible
Parameters:
int[]
Returns:
String
Method signature:
String isPossible(int[] b)
(be sure your method is public)

Constraints

  • b will contain between 1 and 50 elements, inclusive.
  • Each element in b will be between 1 and 10, inclusive.

Examples

  1. {3,2}

    Returns: "Possible"

    One valid sequence is the sequence {2, 2}. That is, a[0] = a[1] = 2. Clearly, each a[i] is a power of two not smaller than 2. The product of all a[i] is 2*2 = 4. Both a[0]^b[0] = 2^3 = 8 and a[1]^b[1] = 2^2 = 4 are divisible by 4.

  2. {3,3,3}

    Returns: "Possible"

    Here, one valid sequence is {2, 2, 2}.

  3. {1,10}

    Returns: "Impossible"

    Suppose that a[0] = x and a[1] = y. The value a[0]^b[0] = x^1 should be divisible by x*y. This is only possible for y = 1. However, 1 is not a positive power of two, so we cannot have a[1] = 1.

  4. {5,3,9,7}

    Returns: "Possible"

  5. {1}

    Returns: "Possible"

  6. {7,10,2,7,9}

    Returns: "Possible"

  7. {10,7,7,3,8,9}

    Returns: "Possible"

  8. {1}

    Returns: "Possible"

  9. {8,8,4,2}

    Returns: "Possible"

  10. {2,8,3}

    Returns: "Possible"

  11. {4,3,3}

    Returns: "Possible"

  12. {9,9,6,3,9,7}

    Returns: "Possible"

  13. {9,5,8,3,9,10}

    Returns: "Possible"

  14. {7,6,10,8,9,10,7,9}

    Returns: "Possible"

  15. {3,9,10,10,3}

    Returns: "Possible"

  16. {9,7,7,4,3}

    Returns: "Possible"

  17. {8,2,8,7,10}

    Returns: "Possible"

  18. {10,3,3,7}

    Returns: "Possible"

  19. {6,3,10,8,5}

    Returns: "Possible"

  20. {10,5,7,5,9,5}

    Returns: "Possible"

  21. {8,9,9,2,9}

    Returns: "Possible"

  22. {1}

    Returns: "Possible"

  23. {9,3,5,3}

    Returns: "Possible"

  24. {5,4,9,9,7,6}

    Returns: "Possible"

  25. {2,10,3}

    Returns: "Possible"

  26. {6,3,3,9}

    Returns: "Possible"

  27. {1}

    Returns: "Possible"

  28. {2, 3, 10}

    Returns: "Possible"

    One valid sequence is {8, 4, 2}.

  29. {4,8,9,3,9}

    Returns: "Possible"

  30. {9,6,6,2}

    Returns: "Possible"

  31. {8,8,9,7,3,7}

    Returns: "Possible"

  32. {7,10,4,6,3}

    Returns: "Possible"

  33. {2,2}

    Returns: "Possible"

  34. {6,9,8,9,10,8,5}

    Returns: "Possible"

  35. {10,10,10,10,10,10,10,10,10,10}

    Returns: "Possible"

  36. {10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10}

    Returns: "Impossible"

  37. {7,7,7,7,7,7,7}

    Returns: "Possible"

  38. {1}

    Returns: "Possible"

  39. {7,6}

    Returns: "Possible"

  40. {6,9,3,9}

    Returns: "Possible"

  41. {3,2,1,7,7,10}

    Returns: "Impossible"

  42. {8,3,8,6,7,5,8,1}

    Returns: "Impossible"

  43. {9,1,3,6,9,3,9,9,6,9}

    Returns: "Impossible"

  44. {2,5,6,7,8,4,7,10,5,2,2,7,9,8,3,1,9,1,8,4,3,8,4,6,4,1,8,7,7,9,9,6}

    Returns: "Impossible"

  45. {4,6,7,7,3,5,5,1,5,3,4,9,2,10,7,10,4,6,9,9,4,8,3,1,6,9,2,7,1,2,6,1,6,1,4,4}

    Returns: "Impossible"

  46. {1,1,5,7,8,4,5,2,7,1,6,9,7,9,4,3,9,3,6,6,2,7,10,5,1,4,5,6,8,3,3,9,2,6,6,2,4,10}

    Returns: "Impossible"

  47. {7,6,2,7,3,6,7,8,1,6,9,10,5,2,10,9,4,3,9,2,2,2,2,1,5,5,7,2,10,5,2,1,5,4,8,3,5,3,6,2}

    Returns: "Impossible"

  48. {3,3,9,7,3,6,9,8,5,7,2,5,5,7,10,2,5,10,3,4,7,1,4,1,1,9,3,2,7,1,5,1,9,4,3,5,2,4,1,7,10,5}

    Returns: "Impossible"

  49. {8,4,4,7,10,4,8,9,6,2,7,4,2,2,10,5,9,9,2,3,7,6,1,1,10,1,8,7,3,1,3,7,9,3,10,5,7,2,1,7,2,6,4,5}

    Returns: "Impossible"

  50. {10,4,9,10,9,10,10,10,5,7,3,8,7,4,9,8,3,10,8,5,3,1,1,6,9,6,2,5,9,10,2,3,8,10,6,2,1,7,2,6,2,9,4,10,6,1}

    Returns: "Impossible"

  51. {3,9,9,8,7,6,9,2,8,9,9,5,6,3,2,3,3,9,1,5,4,6,3,6,3,8,3,8,8,7,7,3,4,1,7,3,6,9,8,10,4,8,9,1,6,1,2,4}

    Returns: "Impossible"

  52. {8,6,4,9,7,1,7,8,4,3,1,2,1,2,6,1,5,9,1,9,8,7,4,10,8,3,8,9,9,2,3,6,7,2,6,9,6,3,2,6,4,7,6,5,4,8,1,10,8,6}

    Returns: "Impossible"

  53. {4,4,2}

    Returns: "Possible"

  54. {2,3,6}

    Returns: "Possible"

  55. {3,3,6,6}

    Returns: "Possible"

  56. {3,6,3,6}

    Returns: "Possible"

  57. {10,5,2,5}

    Returns: "Possible"

  58. {3, 3, 3, 3}

    Returns: "Impossible"

  59. {7,7,7,7,7,7,7}

    Returns: "Possible"

  60. {9,9,9,9,9,9,9,9,9}

    Returns: "Possible"

  61. {9,3,3,9,9}

    Returns: "Possible"

  62. {1}

    Returns: "Possible"

  63. {2,2}

    Returns: "Possible"

  64. {2,3,6}

    Returns: "Possible"

  65. {2,4,4}

    Returns: "Possible"

  66. {2,4,8,8}

    Returns: "Possible"

  67. {2,5,5,10}

    Returns: "Possible"

  68. {2,5,10,10,10}

    Returns: "Possible"

  69. {2,6,6,6}

    Returns: "Possible"

  70. {2,6,8,9,10}

    Returns: "Impossible"

  71. {2,6,9,9,9}

    Returns: "Possible"

  72. {2,8,8,8,8}

    Returns: "Possible"

  73. {2,10,10,10,10,10}

    Returns: "Possible"

  74. {3,3,3}

    Returns: "Possible"

  75. {3,3,6,6}

    Returns: "Possible"

  76. {3,3,8,9,10}

    Returns: "Impossible"

  77. {3,3,9,9,9}

    Returns: "Possible"

  78. {3,4,4,6}

    Returns: "Possible"

  79. {3,4,6,8,8}

    Returns: "Possible"

  80. {3,5,5,6,10}

    Returns: "Possible"

  81. {3,5,5,7,8}

    Returns: "Impossible"

  82. {3,5,6,10,10,10}

    Returns: "Possible"

  83. {3,5,7,8,10,10}

    Returns: "Impossible"

  84. {3,5,7,9,9,10}

    Returns: "Possible"

  85. {3,6,6,6,6}

    Returns: "Possible"

  86. {3,6,6,8,9,10}

    Returns: "Impossible"

  87. {3,6,6,9,9,9}

    Returns: "Possible"

  88. {3,6,8,8,8,8}

    Returns: "Possible"

  89. {3,7,7,7,8,9}

    Returns: "Possible"

  90. {4,4,4,4}

    Returns: "Possible"

  91. {4,4,4,8,8}

    Returns: "Possible"

  92. {4,4,5,5,10}

    Returns: "Possible"

  93. {4,4,5,10,10,10}

    Returns: "Possible"

  94. {4,4,6,6,6}

    Returns: "Possible"

  95. {4,4,6,8,9,10}

    Returns: "Impossible"

  96. {4,4,6,9,9,9}

    Returns: "Possible"

  97. {4,4,8,8,8,8}

    Returns: "Possible"

  98. {4,5,5,8,8,10}

    Returns: "Possible"

  99. {4,5,5,8,9,9}

    Returns: "Possible"

  100. {4,5,6,7,7,10}

    Returns: "Impossible"

  101. {4,6,6,6,8,8}

    Returns: "Possible"

  102. {5,5,5,5,5}

    Returns: "Possible"

  103. {5,5,5,5,10,10}

    Returns: "Possible"

  104. {5,5,5,6,8,9}

    Returns: "Impossible"

  105. {5,5,6,6,6,10}

    Returns: "Possible"

  106. {5,5,6,6,7,8}

    Returns: "Impossible"

  107. {6,6,6,6,6,6}

    Returns: "Possible"

  108. {3,4,5,6,7}

    Returns: "Impossible"

  109. {3, 4, 5, 6, 7 }

    Returns: "Impossible"

  110. {2, 2 }

    Returns: "Possible"

  111. {9, 9, 9, 9, 9, 9, 9, 9, 9 }

    Returns: "Possible"

  112. {1, 10 }

    Returns: "Impossible"

  113. {1 }

    Returns: "Possible"

  114. {7, 10, 4, 6, 3 }

    Returns: "Possible"

  115. {2, 3, 10 }

    Returns: "Possible"

  116. {1, 1 }

    Returns: "Impossible"

  117. {1, 2, 2, 9 }

    Returns: "Impossible"

  118. {10, 10 }

    Returns: "Possible"

  119. {9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 }

    Returns: "Impossible"

  120. {3, 4, 5 }

    Returns: "Possible"

  121. {4, 4, 3, 3, 3 }

    Returns: "Impossible"

  122. {2, 2, 10 }

    Returns: "Impossible"

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