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Problem Statement for "AllButOneDivisor"

Problem Statement

You are given a int[] divisors containing K elements. Find a positive integer n such that exactly K-1 elements of divisors are exact divisors of n. If there are several such numbers n, return the smallest possible one. If no such number n exists, return -1 instead.

Definition

Class:
AllButOneDivisor
Method:
getMinimum
Parameters:
int[]
Returns:
int
Method signature:
int getMinimum(int[] divisors)
(be sure your method is public)

Notes

  • A number x is an exact divisor of y if y divided by x yields an integer result.
  • If x is an exact divisor of y then we call y a multiple of x.

Constraints

  • divisors will contain between 2 and 6 elements, inclusive.
  • Each element of divisors will be distinct.
  • Each element of divisors will be between 1 and 15, inclusive.

Examples

  1. {2,3,5}

    Returns: 6

    There are many possible values for n in this case. For example: 6, 15, 75 and 12. 6 is the smallest of them.

  2. {2,4,3,9}

    Returns: 12

  3. {3,2,6}

    Returns: -1

    Every multiple of 3 and 2 is also a multiple of 6. Every multiple of 6 is also a multiple of 2 and 3. Therefore, a number that is a multiple of exactly 2 out of the three elements in this array cannot exist.

  4. {6,7,8,9,10}

    Returns: 360

  5. {10,6,15}

    Returns: -1

  6. {10,11,12,13,14,15}

    Returns: 4620

  7. {2,4,6,3}

    Returns: 6

  8. {8,9,5,7,11,13}

    Returns: 27720

  9. {14,15,6}

    Returns: 30

  10. {7,14,2}

    Returns: -1

  11. {4,3,1,12}

    Returns: -1

  12. {1,2}

    Returns: 1

  13. {1,2,3}

    Returns: 2

  14. {15,14,1}

    Returns: 14

  15. {15,14,13,1,12}

    Returns: 420

  16. {2,4,8,6,3}

    Returns: 12

  17. {2,4,11,6,3}

    Returns: 12

  18. {2,4,13,6,3}

    Returns: 12

  19. {8,9,15,7,11,13}

    Returns: 27720

  20. {2,3,5,6}

    Returns: 6

    It is best to remove 5 instead of 6 (the maximum)

  21. {1,3,2,5,4}

    Returns: 12

  22. {4,1,5,3,2}

    Returns: 12

  23. {3,4,2,5,1}

    Returns: 12

  24. {2,4,3,1,5}

    Returns: 12

  25. {2,5,6,4,1,3}

    Returns: 12

  26. {3,1,2,4}

    Returns: 4

  27. {8,11,5}

    Returns: 40

  28. {14,1,6,10,5,9}

    Returns: 90

  29. {8,14,5,11,7}

    Returns: 280

  30. {13,7,14,15,6,9}

    Returns: 630

  31. {9,3,4,1,5}

    Returns: 36

  32. {11,1}

    Returns: 1

  33. {1,4,12,3,13}

    Returns: 12

  34. {4,2}

    Returns: 2

  35. {5,8,14,4}

    Returns: 40

  36. {7,13,14}

    Returns: 14

  37. {14,15}

    Returns: 14

  38. {5,13,10,9,7,2}

    Returns: 630

  39. {1,2,12,13,11}

    Returns: 132

  40. {2,3,11,12,14,1}

    Returns: 84

  41. {9,14,5}

    Returns: 45

  42. {11,1,9,2}

    Returns: 18

  43. {9,8,5,2}

    Returns: 40

  44. {4,6}

    Returns: 4

  45. {14,6}

    Returns: 6

  46. {13,1,5,9,7,4}

    Returns: 1260

  47. {11,8,15,6,4}

    Returns: 120

  48. {4,12,11}

    Returns: 12

  49. {7,5,9,1,11,6}

    Returns: 630

  50. {4,9,10,3,12}

    Returns: 36

  51. {4,10,13,12,9}

    Returns: 180

  52. {14,4,12,13,2}

    Returns: 84

  53. {9,2,14}

    Returns: 14

  54. {6,3,13,7}

    Returns: 42

  55. {2,14,4}

    Returns: 4

  56. {5,3,7,13,4,9}

    Returns: 1260

  57. {7,8,11,4}

    Returns: 56

  58. {8,10}

    Returns: 8

  59. {4,15,12,3}

    Returns: 12

  60. {4,11,10,9}

    Returns: 180

  61. {7,6,8}

    Returns: 24

  62. {2,7,11,4}

    Returns: 28

  63. {7,1,10,15,13}

    Returns: 210

  64. {4,10,14,6,9}

    Returns: 180

  65. {11,10,13,9,3,5}

    Returns: 990

  66. {2,15,12}

    Returns: 12

  67. {10,1,2,3}

    Returns: 6

  68. {2,3,6,11}

    Returns: 6

  69. {2,10,12,9,8}

    Returns: 72

  70. {2,11,15,5}

    Returns: 30

  71. {11,10,14,4,2}

    Returns: 140

  72. {2,8,10,3,13,7}

    Returns: 840

  73. {9,7,3,11,14}

    Returns: 126

  74. {6,10,5,3,1}

    Returns: -1

  75. {3,9,5,4}

    Returns: 36

  76. {14,2,4,11,7,6}

    Returns: 84

  77. {12,9,4,5}

    Returns: 36

  78. {15,2,9,5}

    Returns: 30

  79. {8,11,7,10,1}

    Returns: 280

  80. {12,14,13,4}

    Returns: 84

  81. {8,7,2,3,1,10}

    Returns: 120

  82. {10,12,7,14,9,5}

    Returns: 420

  83. {14,7,9,11,8}

    Returns: 504

  84. {1,9,7,4,2,14}

    Returns: 28

  85. {1,15,9,5,3,11}

    Returns: 45

  86. {11,6,13,1}

    Returns: 66

  87. {10,11,14,12}

    Returns: 420

  88. {9,7,12,14,10}

    Returns: 252

  89. {15,7,12,10,11,14}

    Returns: 420

  90. {9,15,13,11,12,10}

    Returns: 1980

  91. {15,11,8,14}

    Returns: 616

  92. {14,8,9,7,13}

    Returns: 504

  93. {13,7,12,9,15,14}

    Returns: 1260

  94. {11,7,13,14,12,15}

    Returns: 4620

  95. {12,7,15,9,13,8}

    Returns: 2520

  96. {11,13,15,14}

    Returns: 2002

  97. {11,14,13,9,12,10}

    Returns: 13860

  98. {9,15,12,13,11,8}

    Returns: 3960

  99. {12,8,11,9,13,15}

    Returns: 3960

  100. {8,10,14,11,12}

    Returns: 840

  101. {10,15,14,8}

    Returns: 120

  102. {15,13,9,11}

    Returns: 495

  103. {10,14,8,11}

    Returns: 280

  104. {14,11,9,13}

    Returns: 1287

  105. {7,9,13,11}

    Returns: 693

  106. {12,8,11,14,13,15}

    Returns: 9240

  107. {7, 13, 11, 14, 9 }

    Returns: 1386

  108. {1, 2 }

    Returns: 1

  109. {1, 3, 4 }

    Returns: 3

  110. {2, 3, 7 }

    Returns: 6

  111. {2, 4 }

    Returns: 2

  112. {2, 3, 5, 15 }

    Returns: 15

  113. {5, 10, 13 }

    Returns: 10

  114. {3, 2, 6 }

    Returns: -1

  115. {10, 2, 3 }

    Returns: 6

  116. {5, 7, 8, 9, 11, 13 }

    Returns: 27720

  117. {2, 3, 4, 6, 7 }

    Returns: 12

  118. {5, 7 }

    Returns: 5

  119. {6, 7, 15 }

    Returns: 30

  120. {4, 5, 6 }

    Returns: 12

  121. {3, 6, 13 }

    Returns: 6

  122. {1, 2, 4, 8 }

    Returns: 4

  123. {13, 11, 9, 8, 7, 5 }

    Returns: 27720

  124. {1, 5 }

    Returns: 1

  125. {2, 4, 8 }

    Returns: 4

  126. {2, 3 }

    Returns: 2

  127. {6, 7, 8, 9, 10 }

    Returns: 360

  128. {13, 11, 7, 5, 9, 4 }

    Returns: 13860

  129. {6, 10, 15, 14 }

    Returns: 30

  130. {3, 5, 7, 11, 13 }

    Returns: 1155

  131. {3, 13, 2 }

    Returns: 6

  132. {2, 1 }

    Returns: 1

  133. {7, 10, 15 }

    Returns: 30

  134. {15, 14, 13, 12, 11, 10 }

    Returns: 4620

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