Statistics

Problem Statement for "DivisibleSetDiv1"

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 = {a[0], ..., a[n-1]}. This sequence should have the following properties:
  • The elements of the sequence a should be distinct.
  • Each a[i] should be an integer greater than 1.
  • For each i, the value a[i]^b[i] (that is, a[i] to the power b[i]) should be divisible by p[i], where p[i] is the product of all other elements of a. (I.e. p[i] = a[0]*a[1]*...*a[i-1]*a[i+1]*...*a[n-1].)
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:
DivisibleSetDiv1
Method:
isPossible
Parameters:
int[]
Returns:
String
Method signature:
String isPossible(int[] b)
(be sure your method is public)

Constraints

  • b will contain between 2 and 50 elements, inclusive.
  • Each element in b will be between 1 and 10, inclusive.

Examples

  1. {2,1}

    Returns: "Possible"

    Here, we have the following requirements: The values a[0] and a[1] should be distinct positive integers, both greater than 1. The value a[0]^2 should be divisible by a[1]. The value a[1]^1 should be divisible by a[0]. One sequence with the above properties is the sequence a = {2, 4}.

  2. {1,1}

    Returns: "Impossible"

    In this test case the requirements imply that a[0] must be divisible by a[1] and vice versa. This is possible only if a[0] = a[1]. However, the elements of a must be distinct, so there is no valid sequence.

  3. {7, 7, 7}

    Returns: "Possible"

    For example, a = {12, 54, 18}.

  4. {6,7,5,2}

    Returns: "Possible"

  5. {1,7,10,7,8}

    Returns: "Possible"

  6. {3,3,6,10}

    Returns: "Possible"

  7. {1,4,3}

    Returns: "Possible"

  8. {4,10,3,7,2}

    Returns: "Possible"

  9. {8,1,2}

    Returns: "Possible"

  10. {3,1,3}

    Returns: "Impossible"

  11. {5,8,2,10,8,7}

    Returns: "Possible"

  12. {6,8,5,9,5,4,8}

    Returns: "Possible"

  13. {9,10,10,8,7,9,8,10,8}

    Returns: "Possible"

  14. {4,1,3}

    Returns: "Possible"

  15. {5,3,8,7,9,8,7}

    Returns: "Possible"

  16. {2,7,3,8,7}

    Returns: "Possible"

  17. {2,4,7,10,3}

    Returns: "Possible"

  18. {6,7,2,10,9,4}

    Returns: "Possible"

  19. {5,9,8,4,7,9,5}

    Returns: "Possible"

  20. {7,1,8,8,9}

    Returns: "Possible"

  21. {7,1,3,10}

    Returns: "Possible"

  22. {7,10,9,1,5}

    Returns: "Possible"

  23. {7,7,1,4}

    Returns: "Possible"

  24. {9,7,10,9,2,3}

    Returns: "Possible"

  25. {5,1,10,7,9}

    Returns: "Possible"

  26. {8,1,7,9,8}

    Returns: "Possible"

  27. {10,8,8,8,1}

    Returns: "Possible"

  28. {6,4,9,1}

    Returns: "Possible"

  29. {2,7,6,6,3}

    Returns: "Possible"

  30. {7,1,8,9,7}

    Returns: "Possible"

  31. {10,3,8,5,8,7,6}

    Returns: "Possible"

  32. {10,7,3,7,2}

    Returns: "Possible"

  33. {1,3,9,8}

    Returns: "Possible"

  34. {9,9,9,9,9,9,9,9,9,9}

    Returns: "Impossible"

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

    Returns: "Impossible"

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

    Returns: "Impossible"

  38. {8,8}

    Returns: "Possible"

  39. {7,3,5,1}

    Returns: "Impossible"

  40. {9,9,9,3,6,9}

    Returns: "Possible"

  41. {4,9,6,6,9,2,6,10}

    Returns: "Impossible"

  42. {9,5,7,2,9,4,4,5,1,6}

    Returns: "Impossible"

  43. {10,4,2,4,4,2,5,10,6,4,1,9}

    Returns: "Impossible"

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

    Returns: "Impossible"

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

    Returns: "Impossible"

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

    Returns: "Impossible"

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

    Returns: "Impossible"

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

    Returns: "Impossible"

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

    Returns: "Impossible"

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

    Returns: "Impossible"

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

    Returns: "Impossible"

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

    Returns: "Impossible"

  53. {6,6,7,4,9,1,8,9,2,10,10,2,6,3,3,8,7,9,7,3,2,5,3,6,8,2,3,4,2,1,1,2}

    Returns: "Impossible"

  54. {7,3,6,6,3,1,1,1,6,3,6,3,4,1,4,2,2,6,7,4,2,1,8,7,1,4,7,4,4,5,8,2,8,1}

    Returns: "Impossible"

  55. {5,7,3,1,1,9,5,2,6,3,10,10,10,6,2,9,4,6,7,9,3,2,6,8,1,1,7,6,9,9,4,5,5,6,10,2}

    Returns: "Impossible"

  56. {3,8,9,2,5,5,2,1,5,1,10,9,2,3,6,5,7,2,7,4,2,2,4,3,4,3,9,7,6,5,6,7,4,6,10,3,5,1}

    Returns: "Impossible"

  57. {9,5,3,2,2,7,2,7,7,7,4,7,2,10,1,1,2,3,4,9,3,2,5,4,7,5,9,2,2,8,1,9,3,10,5,3,6,6,1,8}

    Returns: "Impossible"

  58. {4,1,1,7,6,1,2,8,4,5,5,9,5,4,9,3,1,2,5,10,7,10,10,7,8,1,4,8,2,4,9,10,9,3,5,6,7,2,7,3,9,4}

    Returns: "Impossible"

  59. {7,9,6,1,9,2,9,3,7,2,1,5,4,3,9,1,5,4,7,2,2,3,8,7,10,8,10,2,1,5,5,3,9,3,3,7,7,6,10,1,10,10,10,9}

    Returns: "Impossible"

  60. {7,9,4,9,4,10,10,9,6,6,6,2,6,10,3,6,2,8,7,3,1,7,3,9,6,10,9,8,2,2,4,3,10,8,1,1,5,5,4,8,5,6,10,8,6,8}

    Returns: "Impossible"

  61. {3,9,5,1,6,9,8,8,6,6,8,6,3,3,4,6,8,1,1,2,4,3,3,3,2,1,7,1,3,8,9,9,7,8,6,4,7,9,9,6,2,7,1,4,7,8,9,2}

    Returns: "Impossible"

  62. {2,7,9,8,7,4,4,7,6,8,4,6,6,1,8,1,3,7,6,2,4,4,1,3,2,10,9,3,1,7,9,3,4,2,3,5,2,2,6,9,2,5,5,7,6,8,8,10,9,6}

    Returns: "Impossible"

  63. {4,4,4,4,9,9}

    Returns: "Impossible"

  64. {1,2,5}

    Returns: "Possible"

  65. {1,1}

    Returns: "Impossible"

  66. {1,2,5}

    Returns: "Possible"

  67. {1,3,3}

    Returns: "Impossible"

  68. {1,3,7,7}

    Returns: "Impossible"

  69. {1,4,4,9}

    Returns: "Impossible"

  70. {1,4,8,9,10}

    Returns: "Impossible"

  71. {1,4,9,9,9}

    Returns: "Impossible"

  72. {1,5,5,5}

    Returns: "Impossible"

  73. {1,5,6,9,10}

    Returns: "Impossible"

  74. {1,5,7,8,9}

    Returns: "Impossible"

  75. {1,5,8,8,8}

    Returns: "Impossible"

  76. {1,6,6,7,10}

    Returns: "Impossible"

  77. {1,6,6,8,9}

    Returns: "Possible"

  78. {1,7,7,7,7}

    Returns: "Impossible"

  79. {2,2,2}

    Returns: "Impossible"

  80. {2,2,5,5}

    Returns: "Impossible"

  81. {2,2,6,9,10}

    Returns: "Impossible"

  82. {2,2,7,8,9}

    Returns: "Impossible"

  83. {2,2,8,8,8}

    Returns: "Impossible"

  84. {2,3,3,5}

    Returns: "Impossible"

  85. {2,3,4,7,10}

    Returns: "Possible"

  86. {2,3,5,7,7}

    Returns: "Impossible"

  87. {2,4,4,5,9}

    Returns: "Impossible"

  88. {2,4,4,6,7}

    Returns: "Impossible"

  89. {2,5,5,5,5}

    Returns: "Impossible"

  90. {3,3,3,3}

    Returns: "Impossible"

  91. {3,3,3,7,7}

    Returns: "Impossible"

  92. {3,3,4,4,9}

    Returns: "Impossible"

  93. {3,3,5,5,5}

    Returns: "Impossible"

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

    Returns: "Impossible"

  95. {5, 10, 7, 4, 10 }

    Returns: "Possible"

  96. {1, 2, 5 }

    Returns: "Possible"

  97. {10, 10, 10, 10, 10, 10 }

    Returns: "Possible"

  98. {2, 3, 3, 4 }

    Returns: "Impossible"

  99. {5, 4, 3, 2 }

    Returns: "Possible"

  100. {2, 3, 4, 5, 6 }

    Returns: "Impossible"

  101. {2, 2 }

    Returns: "Possible"

  102. {1, 2, 3, 4, 5, 6, 7, 8, 9, 9, 9, 9, 9, 9 }

    Returns: "Impossible"

  103. {3, 3, 2, 1 }

    Returns: "Impossible"

  104. {1, 2, 3 }

    Returns: "Impossible"

  105. {2, 2, 2, 2 }

    Returns: "Impossible"

  106. {2, 3, 4 }

    Returns: "Possible"

  107. {1, 2, 4 }

    Returns: "Impossible"

  108. {2, 2, 2 }

    Returns: "Impossible"

  109. {2, 2, 2, 2, 2, 2, 2, 2, 2 }

    Returns: "Impossible"

  110. {7, 8, 9, 9, 9, 9, 10, 10, 10, 10 }

    Returns: "Possible"

  111. {2, 2, 2, 2, 2 }

    Returns: "Impossible"

  112. {1, 3, 4 }

    Returns: "Possible"

  113. {4, 4, 4 }

    Returns: "Possible"

  114. {2, 2, 3 }

    Returns: "Possible"

  115. {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

    Returns: "Impossible"

  116. {4, 2, 1 }

    Returns: "Impossible"

  117. {5, 5, 5, 5 }

    Returns: "Possible"

  118. {1, 2, 6 }

    Returns: "Possible"

  119. {3, 3, 3 }

    Returns: "Possible"

  120. {2, 3, 2 }

    Returns: "Possible"

  121. {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10 }

    Returns: "Impossible"

  122. {3, 1, 3 }

    Returns: "Impossible"

  123. {3, 2, 1 }

    Returns: "Impossible"

  124. {1, 1, 10 }

    Returns: "Impossible"

  125. {2, 1, 3 }

    Returns: "Impossible"

  126. {1, 2, 2 }

    Returns: "Impossible"

  127. {2, 3, 4, 5, 6, 7, 8, 9, 10 }

    Returns: "Impossible"

  128. {3, 10, 10, 2, 8 }

    Returns: "Possible"

  129. {10, 10, 10, 10, 10 }

    Returns: "Possible"

  130. {10, 10 }

    Returns: "Possible"

  131. {6, 9, 9, 9, 9, 9, 10, 10, 10, 10 }

    Returns: "Impossible"

  132. {1, 10, 3, 10 }

    Returns: "Possible"

  133. {1, 4, 7 }

    Returns: "Possible"

  134. {7, 8, 10, 1 }

    Returns: "Possible"

  135. {1, 5, 8 }

    Returns: "Possible"

  136. {1, 3, 3 }

    Returns: "Impossible"

  137. {10, 10, 10, 10, 10, 10, 10, 10, 10 }

    Returns: "Possible"

  138. {7, 7, 7, 7 }

    Returns: "Possible"

  139. {2, 10, 10 }

    Returns: "Possible"

  140. {1, 2, 3, 4, 5, 6 }

    Returns: "Impossible"

  141. {10, 1, 1, 1 }

    Returns: "Impossible"

  142. {2, 10, 10, 10 }

    Returns: "Possible"

  143. {1, 1 }

    Returns: "Impossible"

  144. {3, 2, 2 }

    Returns: "Possible"

  145. {3, 4, 4, 5, 5 }

    Returns: "Possible"

  146. {2, 5, 5, 5 }

    Returns: "Possible"

  147. {9, 9, 9, 9, 9, 9, 4 }

    Returns: "Possible"

  148. {9, 9, 9, 9, 9, 9, 9, 9, 9 }

    Returns: "Possible"

  149. {4, 4, 3, 3 }

    Returns: "Possible"

  150. {6, 4, 1 }

    Returns: "Possible"

  151. {4, 2, 3 }

    Returns: "Possible"

  152. {9, 3, 3, 2 }

    Returns: "Possible"

  153. {6, 8, 9, 9, 10, 10, 10, 10, 10, 10 }

    Returns: "Possible"

  154. {5, 1, 2 }

    Returns: "Possible"

  155. {1, 3, 6, 9 }

    Returns: "Possible"

  156. {2, 2, 3, 3, 3 }

    Returns: "Impossible"

  157. {2, 2, 4, 7 }

    Returns: "Possible"

  158. {1, 10, 10, 10 }

    Returns: "Possible"

  159. {2, 2, 3, 4 }

    Returns: "Impossible"

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