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Problem Statement for "LISNumberDivTwo"

Problem Statement

Let A be a sequence of integers. We want to create this sequence as a concatenation of some (one or more) strictly increasing sequences. The LISNumber of A is the smallest number of strictly increasing sequences we need.

For example, the LISNumber of the sequence A = {1, 4, 4, 2, 6, 3} is 4, since A can be created as {1, 4} + {4} + {2, 6} + {3}, and there is no way to create A by concatenating 3 (or fewer) strictly increasing sequences.

Another example: The LISNumber of the sequence B = {10, 20, 30} is 1, since B is already a strictly increasing sequence.

Note that the optimal way of writing a sequence as a concatenation of some strictly increasing sequences is always unique.

You are given a int[] seq. Return the LISNumber of the sequence seq.

Definition

Class:
LISNumberDivTwo
Method:
calculate
Parameters:
int[]
Returns:
int
Method signature:
int calculate(int[] seq)
(be sure your method is public)

Constraints

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

Examples

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

    Returns: 4

    This is the example from the problem statement.

  2. {5, 8, 9, 12, 16, 32, 50}

    Returns: 1

    In this case, seq itself is already strictly increasing. Thus, the LISNumber of this sequence is 1.

  3. {1, 1, 9, 9, 2, 2, 3, 3}

    Returns: 6

    {1, 1, 9, 9, 2, 2, 3, 3} = {1} + {1, 9} + {9} + {2} + {2, 3} + {3}

  4. {50, 40, 30, 20, 10}

    Returns: 5

  5. {42}

    Returns: 1

  6. {11,19,9,19,25,30,19,35,14,23,22,21,24,19,38,21,33,33,47,49,45,47,13,50,34,4,13,29,10,16,41,47,19,40,32,9,11}

    Returns: 17

  7. {16,43,1,43,4,8,41,8,3,47,20,49,48,12,9,1,1,30,37,49,47,47,10,47,21,10,11,15,7,2,23,45,27,4,43,47,11,13,13,19,2,34,23,48}

    Returns: 24

  8. {39,38,13,18,6,3,16,17,17,50,17,28,7,38,5,38,30,3,45,1,4,42,27,16,34,20,40,50,26,25,10,22,16,13,34,33,11}

    Returns: 22

  9. {40,7,39,44,3,19,25,5,28,2,50,3,17,38,4,24,11,43,36,13,31}

    Returns: 10

  10. {46,46,31,25,35,35,2,45,37,21,23,48,26,32,23,33,30,9,16,16,34}

    Returns: 13

  11. {13,47,28,16,32,47,18,18,3,7}

    Returns: 6

  12. {42,33,15,20,50,49,47,43,24,12,40,8,29,28,25,43}

    Returns: 11

  13. {23,46,6,43,18,15,28,45,15,23,39,3}

    Returns: 6

  14. {19,43,38,42,42,43,38,43,6,9,26,4,1,37,26,50,31,37,35,33,8,48}

    Returns: 12

  15. {9,20,22,18,31,41,13,33,4,17,41}

    Returns: 4

  16. {25,15,34,34,46,30,46,40,9,37,41,31,2,17,17,32,40,27,2,5,42,37,27,43,15,21,50,47,39,20,7,41,15,36,25,49,4,8,23,29,23,4,28,6,47,5,21,40,14,31}

    Returns: 26

  17. {11,22,18,8,6,25,2,26,10,16,8,39,30,13,47,41,19,35,11,42,14,20,10,50,7,35,25,24,8,6,40,39,23,36,45,38,6,46,26,49,31,39,50,31,11,24,35,42,2,9}

    Returns: 28

  18. {48,10,23,10,29,30,45,20,38,41,33,39,25,7,22,3,41,43,13,43,29,30,12,34,19,13,33,19,11,35,21,23,21,9,45,41,10,25,18,4,20,47,26,13,37,41,31,14,47,2}

    Returns: 27

  19. {5,32,11,7,21,50,14,25,33,18,38,13,31,49,11,8,40,46,48,38,26,11,31,7,21,27,27,18,26,9,10,32,10,7,40,12,47,24,42,7,15,16,30,32,49,26,44,46,8,36}

    Returns: 22

  20. {32,32,47,38,32,29,12,28,31,32,23,6,29,12,48,37,3,12,50,20,5,13,43,35,8,9,39,16,8,17,41,28,24,40,11,46,47,28,33,39,2,13,21,13,9,45,39,25,16,8}

    Returns: 28

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

    Returns: 1

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

    Returns: 2

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

    Returns: 4

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

    Returns: 7

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

    Returns: 7

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

    Returns: 7

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

    Returns: 12

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

    Returns: 13

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

    Returns: 12

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

    Returns: 11

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

    Returns: 50

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

    Returns: 48

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

    Returns: 46

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

    Returns: 45

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

    Returns: 44

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

    Returns: 43

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

    Returns: 42

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

    Returns: 39

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

    Returns: 38

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

    Returns: 39

  41. {14,21,20,10,5,1,12,25,4,2,3,23,13,18,16,24,26,28,8,22,19,27,11,7,6,9,15,17}

    Returns: 14

  42. {9,6,3,15,30,14,28,21,20,4,1,2,5,22,18,29,10,27,8,11,13,23,17,7,19,12,16,24,26,25}

    Returns: 15

  43. {3,4,2,1}

    Returns: 3

  44. {2,20,18,19,8,6,1,12,17,9,11,14,13,10,15,5,16,7,3,4}

    Returns: 11

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

    Returns: 4

  46. {17,20,8,25,27,22,23,28,1,19,4,5,3,12,14,13,11,2,24,10,9,7,6,16,26,15,21,18}

    Returns: 15

  47. {1,8,16,17,15,14,3,9,4,10,18,12,7,6,5,2,13,11,19}

    Returns: 11

  48. {3,17,34,11,19,8,32,6,16,15,10,9,5,4,31,13,22,21,18,28,14,36,12,20,29,25,30,35,27,26,23,7,33,2,37,38,24,1}

    Returns: 22

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

    Returns: 18

  50. {24,14,7,9,2,11,4,20,3,25,5,8,18,6,15,19,10,21,12,16,17,1,26,27,22,13,23}

    Returns: 13

  51. {1,2}

    Returns: 1

  52. {1,1}

    Returns: 2

  53. {2,1}

    Returns: 2

  54. {1,2,1}

    Returns: 2

  55. {1,1,2}

    Returns: 2

  56. {2,1,1}

    Returns: 3

  57. {2,1,2}

    Returns: 2

  58. {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

  59. {1, 4, 4, 2, 6, 3 }

    Returns: 4

  60. {1, 1 }

    Returns: 2

  61. {4, 4, 4, 4, 4, 4, 4 }

    Returns: 7

  62. {42 }

    Returns: 1

  63. {2, 1, 2, 1 }

    Returns: 3

  64. {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

  65. {14, 14, 28, 36, 36, 4 }

    Returns: 4

  66. {1, 2, 2, 3 }

    Returns: 2

  67. {1, 1, 4, 2, 6, 3 }

    Returns: 4

  68. {5, 8, 9, 12, 16, 32, 50 }

    Returns: 1

  69. {1, 2, 3, 4, 5, 6, 7, 8, 9 }

    Returns: 1

  70. {1, 4, 4, 6, 1 }

    Returns: 3

  71. {5, 4, 3, 1, 2 }

    Returns: 4

  72. {1, 2 }

    Returns: 1

  73. {5, 8, 9, 12, 16, 32, 50, 37, 45 }

    Returns: 2

  74. {4, 3, 5 }

    Returns: 2

  75. {1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3 }

    Returns: 4

  76. {2, 3, 1, 4 }

    Returns: 2

  77. {1, 2, 3, 4 }

    Returns: 1

  78. {3, 2, 4 }

    Returns: 2

  79. {1, 2, 3, 3, 3, 3 }

    Returns: 4

  80. {1, 4, 4, 2, 6, 8 }

    Returns: 3

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