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Problem Statement for "MaximumRangeDiv2"

Problem Statement

Cat Noku was given a calculator for his birthday. The calculator is very simple. It can only store a single variable. The variable is called X and its initial value is 0. The calculator has only two buttons: + and -. Pressing + increments X by 1 and pressing - decrements X by 1. For example, if X is 4 and Noku presses +, X is incremented to 5.

A string of '+' and '-' characters can be seen as a sequence of instructions to press the corresponding buttons. The range of such a sequence of instructions is the difference between the largest and the smallest value stored in X while executing that sequence of instructions, in order.

For example, the range of "+++++++" is 7: the largest value of X is 7 (at the end) and the smallest value is 0 (in the beginning). The range of "---" is 3: maximum is 0, minimum is (-3), their difference is 0 - (-3) = 3. The range of "+-+-+-" is 1. The range of an empty sequence of instructions is 0.

Noku's calculator came with a piece of paper that contained a String s. Each character of s was either '+' or '-'. Noku will choose and execute any (not necessarily contiguous) subsequence of these characters. Help him do so in a way that maximizes the range of the executed sequence.

Compute and return the maximal range of a subsequence of the String s.

Definition

Class:
MaximumRangeDiv2
Method:
findMax
Parameters:
String
Returns:
int
Method signature:
int findMax(String s)
(be sure your method is public)

Constraints

  • s will contain between 1 and 50 characters, inclusive.
  • Each element of s will be '+' or '-'.

Examples

  1. "+++++++"

    Returns: 7

    One optimal solution is to skip the fourth instruction (the '+' in the middle of s). Thus, the sequence of button presses will be "+----+". The value of X will change as follows: 0,1,0,-1,-2,-3,-2. The maximum number we see is 1 while the minimum number is -3, so the range is 1 - (-3) = 4.

  2. "+--+--+"

    Returns: 4

    One optimal solution is to skip the 4th instruction. Thus, the sequence of button presses will be "+----+". The number we see after each button press is 1,0,-1,-2,-3,-2. The maximum number we see is 1, while the minimum number is -3, so their range is 4.

  3. "++++--------"

    Returns: 8

  4. "-+-+-+-+-+-+"

    Returns: 6

  5. "+"

    Returns: 1

  6. "---"

    Returns: 3

  7. "---------+------"

    Returns: 15

  8. "--+--+-+-++-+-++---"

    Returns: 11

  9. "-----------------------------------------"

    Returns: 41

  10. "+++-++-"

    Returns: 5

  11. "++++-+-++++++-++-+++"

    Returns: 16

  12. "-----+"

    Returns: 5

  13. "-+-+----++-----+-+--+-+--------+-++---+-++-+--+"

    Returns: 31

  14. "--------------------------------+-----------+-"

    Returns: 44

  15. "-+-"

    Returns: 2

  16. "-----+--------"

    Returns: 13

  17. "----+------+-------------------+--++----+--+-"

    Returns: 38

  18. "+-+++-++++-+++-++"

    Returns: 13

  19. "-+++++-++++++--++++-++++--+-++++"

    Returns: 24

  20. "--+--++----+-+++----+++-+---+-+-+--+-----+"

    Returns: 26

  21. "----"

    Returns: 4

  22. "-+++-+++++-+++-+-++++++++-+++++++-"

    Returns: 27

  23. "--+---+-+-+++----+------+++--+----++----------+"

    Returns: 33

  24. "++++++-++--+++++----++-++-+++-"

    Returns: 20

  25. "-+--+-++-+--+---+++----++------+-"

    Returns: 21

  26. "+--++---"

    Returns: 5

  27. "---+---+--+------"

    Returns: 14

  28. "-+--+----+-----------------------+----+-+-"

    Returns: 36

  29. "---+-+-+--+---+++++-+-+-+--"

    Returns: 15

  30. "++-+++--+----+-----+-++---+++++-++++-+---+-++-++-+"

    Returns: 26

  31. "+-+++++"

    Returns: 6

  32. "++--+++++++++++-++++++++++++"

    Returns: 25

  33. "+++"

    Returns: 3

  34. "+-++-++++--+++----+--+--++--++--+++--+--+---+"

    Returns: 23

  35. "+++-+-++++++-+-+++++-+++++++-+--++-++-++-+--++++-"

    Returns: 35

  36. "++++++++++++++++++++++++++++++"

    Returns: 30

  37. "-+-++------++--++----++---"

    Returns: 17

  38. "+++"

    Returns: 3

  39. "+-++--+-+-"

    Returns: 5

  40. "+-++"

    Returns: 3

  41. "+--+++++++++-++++++"

    Returns: 16

  42. "--------"

    Returns: 8

  43. "------"

    Returns: 6

  44. "+"

    Returns: 1

  45. "-+-+------+-++-"

    Returns: 10

  46. "+-++----+--------+---+--++-----------+--+--+--+-"

    Returns: 36

  47. "++++++++++-++++++++++++++-++++++++++++++-++++++"

    Returns: 44

  48. "-++------+-+-+--+-----++-+-+-+--+-+++-++++-+"

    Returns: 24

  49. "+-+---++++-+--++---+--+++--+-------+++++++++++---+"

    Returns: 26

  50. "++--++-+++++-++-+-++---++--+----+--+"

    Returns: 19

  51. "+++-+++++++++-+++++++++-+--+++++"

    Returns: 27

  52. "++++++-++++++-+++++++++--+-++--+++++--+++++++"

    Returns: 36

  53. "+-----+---------------+-+"

    Returns: 21

  54. "++--+-+-+--+-++++-++++-+++--+++++-++-++++--+++++-+"

    Returns: 34

  55. "+++++++++-+++++++++++++++++++++++++-+++++++++++++"

    Returns: 47

  56. "+-+-+-"

    Returns: 3

  57. "-+-+-+-+-+-+"

    Returns: 6

  58. "+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-"

    Returns: 25

  59. "+-+-+-+-+"

    Returns: 5

  60. "-------"

    Returns: 7

  61. "+-++--"

    Returns: 3

  62. "++++++++++++++++++++++++++++++++++++++++++++++++++"

    Returns: 50

  63. "+--+--+"

    Returns: 4

  64. "++-+"

    Returns: 3

  65. "+++++++++-----+-+-+-+-+"

    Returns: 14

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