Statistics

Problem Statement for "DerivativeSequence"

Problem Statement

Given a sequence of K elements, we can calculate its difference sequence by taking the difference between each pair of adjacent elements. For instance, the difference sequence of {5,6,3,9,-1} is {6-5,3-6,9-3,-1-9} = {1,-3,6,-10}. Formally, the difference sequence of the sequence a1, a2, ... , ak is b1, b2, ... , bk-1, where bi = ai+1 - ai.

The derivative sequence of order N of a sequence A is the result of iteratively applying the above process N times. For example, if A = {5,6,3,9,-1}, the derivative sequence of order 2 is: {5,6,3,9,-1} -> {1,-3,6,-10} -> {-3-1,6-(-3),-10-6} = {-4,9,-16}.

You will be given a sequence a as a int[] and the order n. Return a int[] representing the derivative sequence of order n of a.

Definition

Class:
DerivativeSequence
Method:
derSeq
Parameters:
int[], int
Returns:
int[]
Method signature:
int[] derSeq(int[] a, int n)
(be sure your method is public)

Notes

  • The derivative sequence of order 0 is the original sequence. See example 4 for further clarification.

Constraints

  • a will contain between 1 and 20 elements, inclusive.
  • Each element of a will be between -100 and 100, inclusive.
  • n will be between 0 and K-1, inclusive, where K is the number of elements in a.

Examples

  1. {5,6,3,9,-1}

    1

    Returns: {1, -3, 6, -10 }

    The first example given in the problem statement.

  2. {5,6,3,9,-1}

    2

    Returns: {-4, 9, -16 }

    The second example given in the problem statement.

  3. {5,6,3,9,-1}

    4

    Returns: {-38 }

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

    3

    Returns: {0, 0, 0, 0, 0 }

    After 1 step, they all become 0.

  5. {0,3,9,18}

    3

    Returns: {0 }

  6. {-100,100}

    0

    Returns: {-100, 100 }

  7. {-100,100}

    1

    Returns: {200 }

  8. {100,-100}

    1

    Returns: {-200 }

  9. {-100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100 }

    19

    Returns: {52428800 }

  10. {-100}

    0

    Returns: {-100 }

  11. {-100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100 }

    15

    Returns: {3276800, -3276800, 3276800, -3276800, 3276800 }

  12. {100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100 }

    18

    Returns: {26214400, -26214400 }

  13. {-94,83,-100,-90,-99,3,-97,7,-15,-30,74}

    10

    Returns: {-37681 }

  14. {51,-86,-15,-24,69,-72,-22,16,55,-55,-88,46,15,-53,-60,-40,-82,7,-36,31}

    19

    Returns: {1074506 }

  15. {-21,75,67,80,66,50,70,-13,-47,-44,7,71,6,45,16,70,-23,-68,-84,-17}

    19

    Returns: {3062329 }

  16. {87,54,15,70,-20,-26,-58,-83,97,-23,9,16,92,-40}

    13

    Returns: {-186443 }

  17. {71,96,-32,-12,-11,51,-62,92,-95,-89,-57,44,45,5,-83,-6,70,-45,73,78}

    19

    Returns: {13232177 }

  18. {6,79,96,50,94,-56,-13,65,-54,-72,72,-100,28,-33,21,32,-57,46,-7,-11}

    19

    Returns: {-16496406 }

  19. {-8,-19,35,-16,8,10,71,-9,-38,-70,60,79,-74,-5,-95,65,-84,-75,1,0}

    13

    Returns: {-148860, 143067, -113928, 38763, 86614, -230187, 346834 }

  20. {-84,49,-13,44,99,25,97,-66,-53,82,75,-34,-4,-24}

    13

    Returns: {-201232 }

  21. {-54,14,-51,77,-95,-73,-72,-27,-87,-3,-62,-72,-52,-81,-25,37,15,-43,74,48}

    12

    Returns: {-100566, 99399, -100788, 84901, -48983, 8048, 18673, -23704 }

  22. {-34,37,-92,-3,-65,0,59,23,-62,53,-31,32,59}

    12

    Returns: {-46486 }

  23. {-4,68,-27,88,37,2,69,8,-69,-77,-63,46,73,-24,8,-76,-96,-42,-12,77}

    18

    Returns: {-817623, 452095 }

  24. {-79,-85,51,-16,-12,-50}

    5

    Returns: {-1006 }

  25. {-55,-60,-31,-12,-3,-8,-55,-92,61,-87,45,-35,32,-97,-46,-49}

    15

    Returns: {-1374708 }

  26. {-45,-81,-27,23,65,-48,-47,81}

    7

    Returns: {-2023 }

  27. {-75,20,-29,-82,76,79,-11,-43,-40,51,-7,47,-15,-18,0,-2,-26,69,65,-3}

    17

    Returns: {2536680, -2841097, 2691891 }

  28. {-33,-69,-94,-60,51,-25,-42,59,13,39,-41,-98,13,-18,-25,-98,-93}

    2

    Returns: {11, 59, 77, -187, 59, 118, -147, 72, -106, 23, 168, -142, 24, -66, 78 }

  29. {-68,87,65,63,75,64,13}

    6

    Returns: {-121 }

  30. {-41,58,-28,-100,10,10,-38,14,-74,80,-24,-8,-20,-18}

    13

    Returns: {228251 }

  31. {-56,-9,-63,-11,46,-22,61,-20,86,-13,58,-26,57,46,-78,-6,57,7,85,97}

    19

    Returns: {-18916817 }

  32. {-4,73,22,-39,18,-21,60,-83,-81,61,23,92,-63,-98,-22,-12,53}

    11

    Returns: {-61031, 41675, -3640, -36921, 62637, -65772 }

  33. {11,92,12}

    1

    Returns: {81, -80 }

  34. {37,60}

    1

    Returns: {23 }

  35. {92,-90,17,7,-84,-56,78,-41,-44,-42,-1,-59,83,59,48,-88,-49,89,-57,39}

    18

    Returns: {6169523, -6674245 }

  36. {11,26,20,81,-85,78,89}

    6

    Returns: {-3119 }

  37. {-45,-41,-90,92,-23,75,51,79,16,16,29,19}

    10

    Returns: {-36636, 25776 }

  38. {10,25,-31,-20,-88,-42,-89,-7,-26,86,-5,-61,18,-63,-43,-39,-46,-51}

    9

    Returns: {12991, -14025, 15087, -15967, 14437, -7861, -2302, 10260, -11779 }

  39. {4,71,10,9,62,-42,-95,-82,-60,6,-23,8,64,-35,-80,-18,82,89,11,-60}

    0

    Returns: {4, 71, 10, 9, 62, -42, -95, -82, -60, 6, -23, 8, 64, -35, -80, -18, 82, 89, 11, -60 }

  40. {-8,13}

    0

    Returns: {-8, 13 }

  41. {14,-17,94,-34,-14,36,47,-50,61,48,-82,89,-93,96,-15}

    0

    Returns: {14, -17, 94, -34, -14, 36, 47, -50, 61, 48, -82, 89, -93, 96, -15 }

  42. {92,78,51,24,-99,-2,-11,-94,30,-46,-1,31,11,35,-87,36,63,43,51,-47}

    0

    Returns: {92, 78, 51, 24, -99, -2, -11, -94, 30, -46, -1, 31, 11, 35, -87, 36, 63, 43, 51, -47 }

  43. {100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100, 100, -100 }

    19

    Returns: {-52428800 }

  44. {5, 6, 3, 9, -1 }

    2

    Returns: {-4, 9, -16 }

  45. {4, 4, 4, 4, 4, 4, 4, 4 }

    3

    Returns: {0, 0, 0, 0, 0 }

  46. {5, 6, 3, 9, -1 }

    4

    Returns: {-38 }

  47. {39, 29, 1, -23, 12, 4, -29, 39, 10, -19, 99, 12, -39, -16, 2 }

    10

    Returns: {-5965, 10849, -6951, -5769, 18632 }

  48. {4, 4, 4, 4, 4, 4, 4, 4 }

    6

    Returns: {0, 0 }

  49. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 }

    19

    Returns: {0 }

  50. {-100, 100 }

    0

    Returns: {-100, 100 }

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