Statistics

Problem Statement for "KingdomAndDucks"

Problem Statement

King Dengklek received a container full of ducks as his birthday gift from his loyal subjects. Each duck is of a specific type, represented by an integer between 1 and 50, inclusive. He was told that the container contains the same number of ducks of each type that is present in the container.

King Dengklek wants to guess the total number of ducks in the container. He removed some of the ducks from the container and examined their types. These types are given in int[] duckTypes, where duckTypes[i] is the type of the i-th duck (0-based index) King Dengklek picked.

Compute and return the total number of ducks in the container in the beginning (before King Dengklek removed some of them). If there are multiple possibilities, return the smallest one.

Definition

Class:
KingdomAndDucks
Method:
minDucks
Parameters:
int[]
Returns:
int
Method signature:
int minDucks(int[] duckTypes)
(be sure your method is public)

Constraints

  • duckTypes will contain between 1 and 50 elements, inclusive.
  • Each element of duckTypes will be between 1 and 50, inclusive.

Examples

  1. {5, 8}

    Returns: 2

    The container might have contained one duck of each of types 5 and 8.

  2. {4, 7, 4, 7, 4}

    Returns: 6

    The container might have contained three ducks of each of types 4 and 7.

  3. {17, 17, 19, 23, 23, 19, 19, 17, 17}

    Returns: 12

  4. {50}

    Returns: 1

    The container might have contained only one duck of type 50.

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

    Returns: 5

  6. {1}

    Returns: 1

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

    Returns: 50

  8. {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50}

    Returns: 50

  9. {7, 26, 31, 35, 22, 20, 19, 49, 29, 47, 12, 1, 32, 45, 30, 23, 11, 27, 3, 2, 4, 9, 17, 24, 46, 5, 34, 14, 21, 28, 37, 39, 43, 41, 48, 38, 16, 25, 6, 8, 40, 42, 36, 18, 33, 50, 10, 44, 15, 13}

    Returns: 50

  10. {9, 3, 6, 5, 2, 1, 13, 13, 14, 1, 11, 11, 2, 12, 14, 7, 7, 8, 4, 8, 10, 12, 9, 10, 3, 5, 6, 4, 15}

    Returns: 30

  11. {4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 7, 4, 4, 4, 4, 4, 4}

    Returns: 38

  12. {45, 34, 4, 34, 45, 12, 4, 34, 12, 34, 7, 25, 45, 12, 6, 7, 7, 12, 4, 45, 4, 7, 4, 7, 34, 7, 45, 6, 12, 4, 6, 45, 25, 34, 25, 25, 25, 4, 25, 25, 7, 45, 6, 34, 12, 6, 6, 6, 12}

    Returns: 49

  13. {2, 39, 14, 6, 14, 2, 6, 2, 6, 14, 2, 39, 14, 6, 39, 14, 6, 26, 39, 6, 2, 39, 14, 26, 14, 39, 14, 26, 26, 26, 6, 39, 26, 26, 2, 26, 6, 14, 26, 26, 14, 2, 39, 2, 39, 39, 6, 6, 2, 2}

    Returns: 50

  14. {24, 27, 27, 3, 24, 22, 27, 40, 21, 3, 24, 40, 40, 22, 29, 22, 21, 3, 22, 27, 22, 22, 29, 21, 22, 40, 22, 24, 22, 21, 3, 29, 40, 22, 21, 29, 22, 29, 27, 24, 22, 40, 27, 40, 29, 21, 24, 3, 3}

    Returns: 84

  15. {27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27}

    Returns: 22

  16. {35, 8, 40, 18, 13, 8, 35, 13, 35, 13, 18, 13, 49, 35, 18, 13, 18, 35, 13, 40, 18, 35, 49, 8, 49, 40, 49, 35, 40, 40, 8, 18, 13, 35, 18, 35, 8, 49, 8, 49, 40, 18, 49, 49, 49, 40, 8}

    Returns: 54

  17. {9, 17, 17, 47, 19, 22, 41, 41, 4, 41, 4, 19, 5, 9, 17, 47, 19, 4, 5, 9, 9, 22, 9, 19, 41, 41, 17, 41, 47, 47, 22, 5, 22, 4, 5, 17, 41}

    Returns: 56

  18. {32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32}

    Returns: 12

  19. {19, 17, 2, 2, 2, 17, 19, 2, 19, 19, 22, 23, 19, 17, 2, 2, 17, 22, 2, 23, 23, 17, 23, 2, 19, 2, 17, 23, 22}

    Returns: 45

  20. {15, 30, 13, 15, 13, 13, 21, 48, 21, 21, 48, 30, 30, 30, 48, 15, 21, 48, 48, 33, 21, 30, 15, 13, 15, 13, 30, 33, 15, 15, 33, 33, 21, 13, 48, 13, 33}

    Returns: 42

  21. {16, 44, 49, 44, 49, 44, 49, 44, 44, 44, 49, 16, 49, 44, 16, 16, 49, 44, 49}

    Returns: 24

  22. {1, 46, 46, 46, 1, 46, 1, 1, 46, 46, 46, 1, 1, 1, 46, 46, 1, 1, 46, 1, 1}

    Returns: 22

  23. {7, 32, 7, 20, 7, 20, 32, 32, 20, 7, 7, 7, 7, 7, 32, 20, 32, 7, 20, 32, 20}

    Returns: 27

  24. {29, 5, 29, 29, 29, 6, 34, 6, 34, 5, 5, 5, 29, 6, 34, 29, 6, 6, 34, 34, 29, 34, 6, 5, 5, 6, 5, 5, 34, 29, 5, 6, 6}

    Returns: 36

  25. {48, 48, 36, 36, 48, 36, 48, 32, 48, 21, 48, 48, 21, 48, 32, 48, 24, 24, 48, 36, 21, 21, 48, 32, 48, 32, 32, 21, 24, 48, 36, 24, 21, 48, 24, 36, 32, 24, 32, 24}

    Returns: 70

  26. {15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15}

    Returns: 17

  27. {28, 8, 36, 42, 28, 42, 28, 42, 26, 42, 26, 42, 26, 36, 26, 8, 36, 26, 8, 36, 36, 42, 36, 8, 36, 8, 28, 42, 8, 8, 28}

    Returns: 35

  28. {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: 24

  29. {30, 36, 7, 38, 21, 38, 19, 47, 47, 47, 32, 49, 29, 9, 41, 9, 9, 45, 21, 32, 28, 7, 12, 36, 31, 16, 38, 19, 39}

    Returns: 54

  30. {37, 1, 37, 46, 46, 46, 46, 46, 37, 46, 1, 46, 1, 46, 37, 37, 1, 37, 37, 1, 1, 46, 1, 37, 37, 1, 46, 1, 37, 46, 1}

    Returns: 33

  31. {50, 8, 8, 50, 50, 8, 8, 50, 50, 50, 50, 50, 8, 8, 8, 50, 50, 8, 8, 50, 8, 8, 50}

    Returns: 24

  32. {32, 3, 5, 26, 4, 29, 1, 5, 27, 33}

    Returns: 18

  33. {41, 29}

    Returns: 2

  34. {32, 39, 48, 30, 9, 50, 7, 35, 22, 6, 13, 13, 14, 34, 37, 32, 18, 31, 45, 20, 22, 7, 32, 16, 45, 43, 25, 29, 13, 46, 24, 14, 31, 17, 4, 36, 35, 37, 9, 9, 24, 8, 15, 1, 15, 14, 32}

    Returns: 120

  35. {40, 44, 18, 45, 46, 10, 50, 14, 46, 6, 48, 14, 29, 33, 2, 20, 47, 41, 27, 15, 50, 50, 26, 48, 30, 44, 19, 21, 13, 28, 44, 19, 16, 12, 3, 17, 35}

    Returns: 87

  36. {3, 34, 15, 42, 10, 30, 21, 44, 48, 43, 21, 23, 3, 22, 22, 15, 38, 28, 20, 32, 7, 20, 36, 37, 45, 18, 48, 27, 35, 18, 25, 4, 10, 15, 30, 47, 19}

    Returns: 81

  37. {23, 24, 40, 26, 25, 13, 1, 27, 17, 18, 26, 42, 12, 24, 34, 26, 4, 38, 30, 44, 37, 30, 17, 30, 9, 6, 28, 44, 48, 34, 2, 46, 30, 10, 47, 28, 5, 9, 26, 20, 2, 26, 31}

    Returns: 145

  38. {6, 13, 17, 27, 6, 29, 49, 4, 2, 5, 10}

    Returns: 20

  39. {49, 33, 22, 50, 27, 37, 18, 5, 46, 40, 9, 5, 46, 35, 50, 5, 24, 49, 50, 4, 22, 30, 45, 44, 22, 31, 39, 18, 45, 43, 13, 44, 35, 8, 48, 44, 16, 43}

    Returns: 72

  40. {40, 47, 35, 7, 19, 24, 3, 31, 34, 9, 25, 13, 41, 49, 4, 9, 12, 29, 20, 27, 19, 4, 21, 43, 9, 26, 30, 4, 9, 22, 33, 12, 41, 14, 42, 38, 1, 5, 1, 45}

    Returns: 124

  41. {29, 6, 7, 6, 11, 18, 47, 50, 7, 26, 18, 36, 37, 6, 32, 13, 4, 11, 20}

    Returns: 42

  42. {28, 14, 5, 32, 41, 38, 11, 40, 26, 24}

    Returns: 10

  43. {27, 38, 33, 29, 24, 17, 43, 36, 46, 17, 6, 8, 39, 27, 27, 26, 32, 21, 15, 23, 43, 28, 21, 42}

    Returns: 57

  44. {14, 32, 10, 7, 35, 44, 40, 31, 22, 48, 33, 20, 7, 38, 34, 23, 7, 21, 42, 24, 50, 9, 22, 6, 9, 50, 9, 45, 41, 7}

    Returns: 92

  45. {42, 29, 26, 28, 45, 2, 46, 12, 29, 4, 12, 14, 44, 13, 25, 5, 31, 15, 8, 21, 32, 12, 5, 5, 30, 5, 24, 16, 34, 37, 50, 28, 34, 40, 45, 16}

    Returns: 104

  46. {26, 43, 1, 19, 45, 41, 19, 46, 21, 3, 28, 33, 26, 37, 36, 33, 1, 8, 6, 4}

    Returns: 32

  47. {26, 6, 33, 46, 12, 47, 20, 2}

    Returns: 8

  48. {49, 48, 31, 10, 48, 41, 25, 6, 15, 39, 5, 34, 8, 50, 10, 16, 13, 13, 40, 43, 46, 30, 34, 47, 43, 37, 5, 18, 16, 47, 10, 28}

    Returns: 69

  49. {46, 43, 36, 23, 2, 16, 43, 47, 2, 21, 7, 12, 14, 39, 18, 39, 15, 7, 16, 21, 46, 13, 8, 23, 6, 30, 34, 21, 11, 44, 8, 30, 21, 4, 25, 5, 28, 32, 13, 10, 28, 43, 30, 1, 1, 8, 29, 5}

    Returns: 116

  50. {12, 14, 17, 19, 48, 4, 15, 18, 7, 30, 14, 6, 3, 28}

    Returns: 26

  51. {42}

    Returns: 1

  52. {38, 47, 5, 50, 14, 30, 6, 11, 43, 11, 12, 4, 17, 39, 2, 49, 34, 42, 17, 39, 21, 25, 34, 30, 30, 46, 8, 1, 9, 43, 50, 20, 48, 42, 49, 13, 9, 20, 33, 39, 19, 37, 45, 48, 8, 4, 21, 40, 13}

    Returns: 93

  53. {7, 10, 18, 30, 3, 43, 45, 48, 15, 48, 3, 49, 27, 49, 30, 18, 8, 22, 50, 33, 41, 28, 12, 39, 38, 20, 50, 36, 41, 6, 35}

    Returns: 48

  54. {19, 50, 13, 48, 30, 33, 8, 42, 36, 22, 35, 13, 7, 7, 13, 50, 10, 32, 40, 13, 4, 18, 33, 32, 48, 25, 35, 12, 17, 34, 44, 10, 27, 14, 11, 24, 34, 16, 11, 43, 45, 32, 13, 46, 30, 37, 24, 49}

    Returns: 160

  55. {34, 23, 35, 19}

    Returns: 4

  56. {23, 8, 19, 37, 6, 20, 33, 6, 17, 9, 47, 18, 29, 46, 46, 3, 37, 43, 40, 5, 2, 8, 3, 25, 12, 14, 42, 31, 13, 20}

    Returns: 48

  57. {1, 37}

    Returns: 2

  58. {47, 34, 18, 34, 25, 36, 39, 48, 38, 8, 43, 16}

    Returns: 22

  59. {48, 10, 6, 41, 21, 21, 18, 9, 12}

    Returns: 16

  60. {45, 1, 4, 40, 20, 10, 15, 27, 50, 20, 45, 33, 3, 34, 17, 36, 16, 6, 44, 26, 17, 19, 36, 30, 43, 46, 33, 17, 48, 34, 45, 33, 9, 23, 15, 6}

    Returns: 75

  61. {8, 24, 42, 31, 17, 34, 28, 8, 47, 20, 14, 21, 48, 46, 16, 40, 41, 42, 13, 39, 11, 15, 25, 34, 14, 44, 50, 18, 49, 4, 45, 11, 48, 6, 43, 37, 37, 29, 16, 27, 37, 27, 28, 13, 6, 41, 38, 45, 12, 27}

    Returns: 102

  62. {47, 9, 7, 44, 42, 43, 33, 35, 50, 4, 40, 41, 36, 20, 18, 48, 6, 2, 41, 7, 35, 4, 40, 33, 5, 41, 50, 10, 27, 39, 9, 37, 9, 26, 13, 10, 8, 38, 29, 49, 34}

    Returns: 90

  63. {32, 16, 45, 9, 50, 38, 11, 11, 29, 34, 30, 30, 36, 26, 35, 4, 18, 18, 14, 34, 47, 13, 20, 37, 26, 26, 6, 50, 6, 35, 18, 11, 12, 24, 39, 21, 9, 9, 48, 6, 8}

    Returns: 81

  64. {31, 46, 2, 41, 48, 7, 13, 5, 12, 16, 9, 29, 40, 13, 4, 2, 4, 34, 50, 35, 43, 12, 36, 44, 10, 30, 34, 35, 6, 24, 17, 33, 8, 37, 12, 15, 7}

    Returns: 87

  65. {21, 4, 33, 4, 32, 12, 34, 15, 43, 37, 12, 43, 42, 20, 21, 39, 43, 39, 49, 42, 25, 14, 50, 43, 9, 42, 9, 19, 15, 44, 13, 43, 30, 33}

    Returns: 105

  66. {42, 29, 37, 46, 28, 24, 50, 22, 22, 37, 39, 39, 15, 48, 31, 28, 44, 43, 13, 37, 36, 35, 45, 48, 36, 36, 43, 24, 33, 10, 47, 2, 43, 21, 25, 10, 2, 13, 32, 22, 29, 8, 7, 5}

    Returns: 84

  67. {23, 37, 33, 6, 33, 3, 23, 19, 7, 38, 30, 12, 9, 15, 8, 1, 39, 37, 20, 13, 28, 28, 23, 24, 14, 4, 12, 44, 20, 50, 16, 28, 10, 33, 13}

    Returns: 75

  68. {47, 21, 26, 3, 40, 21, 35, 26, 17, 23, 38, 7, 31, 35, 30, 46, 28, 22, 14, 2, 19, 23, 47, 14, 44, 48, 10, 6, 26, 6, 20, 38}

    Returns: 69

  69. {43, 24, 34, 37, 3, 15, 4, 19, 27, 28, 27, 24, 41, 26, 16, 16, 26}

    Returns: 26

  70. {12, 31, 13, 38, 36, 45, 3, 46, 12, 8, 37, 38}

    Returns: 20

  71. {8, 13, 2, 23, 13, 49, 12, 4, 8, 46, 43, 1, 15, 2, 13}

    Returns: 33

  72. {6, 41, 39, 37, 7, 6, 22, 5, 41, 46, 44, 19, 2, 41, 18, 42, 34, 17, 6, 1, 35, 8, 37, 13, 50, 5, 28, 24, 30, 20, 46, 42, 49, 50, 34, 13}

    Returns: 75

  73. {21, 18, 43, 45, 30, 22, 16, 23, 24, 25, 44, 7, 42, 41, 33, 2, 7, 1, 28, 13, 37, 19, 37, 3, 47, 37, 7, 38, 37, 27, 7, 18, 12, 3, 22, 33, 36, 12, 4, 2}

    Returns: 112

  74. {11, 1, 42, 16, 36, 9, 3, 32, 11, 50, 6, 36, 6, 5, 3}

    Returns: 22

  75. {47, 44, 25, 36, 28, 14, 27, 17, 36, 10, 38, 1, 40, 34, 27, 40}

    Returns: 26

  76. {18, 33, 32, 17, 9, 41, 5, 39}

    Returns: 8

  77. {7, 1, 1, 3, 21, 18, 35, 7, 50, 26, 26, 29, 24, 50, 50, 23, 18, 13, 17, 32, 9, 18, 7, 7, 11, 13, 26, 39}

    Returns: 68

  78. {43, 7}

    Returns: 2

  79. {38, 27, 38, 44, 40, 45, 1, 42, 38, 35, 5, 45, 45, 39, 11, 47, 6, 39, 44, 1, 25, 35, 49, 19, 13, 12, 25, 44, 50, 28, 46, 37, 18, 25, 29, 50, 38, 42, 26, 37, 28, 39, 2}

    Returns: 104

  80. {23, 9, 46, 6, 47, 24, 33, 41, 43, 38, 16, 39, 31, 13, 46, 6, 26, 48, 36, 12, 14, 42, 40, 14, 36, 31, 15, 7, 14, 10, 33, 18}

    Returns: 75

  81. {6, 50, 4, 49, 42, 25, 11, 10, 26, 23, 6, 38, 45, 40, 33, 12, 7, 11, 39, 21, 1, 31, 14, 32, 42, 29, 49, 39, 2, 8, 8, 1, 42, 21, 8, 48, 1}

    Returns: 78

  82. {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25, 50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50}

    Returns: 650

  83. {49, 50, 1, 50, 2, 3, 4, 49, 50 }

    Returns: 18

  84. {17, 17, 19, 23, 23, 19, 50, 17, 17, 50, 37, 50 }

    Returns: 20

  85. {50 }

    Returns: 1

  86. {1, 2, 2 }

    Returns: 4

  87. {3, 4, 4, 4, 4 }

    Returns: 8

  88. {1, 1, 3, 1, 3, 3, 3, 3 }

    Returns: 10

  89. {1, 1, 1, 1, 1, 1 }

    Returns: 6

  90. {50, 50 }

    Returns: 2

  91. {4, 7, 4, 7, 4 }

    Returns: 6

  92. {1, 2, 3, 2, 1 }

    Returns: 6

  93. {5, 8, 50, 50, 50 }

    Returns: 9

  94. {4, 7, 4, 7, 8 }

    Returns: 6

  95. {1, 3 }

    Returns: 2

  96. {3, 3, 4, 4 }

    Returns: 4

  97. {50, 50, 2, 50 }

    Returns: 6

  98. {5, 8, 8, 9 }

    Returns: 6

  99. {1, 1, 1, 2, 2, 3, 3, 17 }

    Returns: 12

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