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Problem Statement for "Drbalance"

Problem Statement

A plus/minus string is a string in which each character is either a '+' or a '-'.

The balance of a plus/minus string is computed as the number of '+' characters minus the number of '-' characters.

For example, the balance of the string "++-+" is 3-1 = 2, and the balance of the string "---" is 0-3 = -3.

The prefix of a string S is any string that can be obtained by removing some (possibly none, possibly all) characters from the end of S. For example, the prefixes of the string "++-+" are the strings "++-+", "++-", "++", "+", and "".

Given a plus/minus string, its negativity is the number of its prefixes that have a negative balance. For example, the negativity of the string "++-+" is 0, as none of its prefixes have a negative balance. The negativity of the string "---" is 3. Its three prefixes with a negative balance are "-", "--", and "---".

You are given a String s that is a plus/minus string. You are also given an int k. Your goal is to change s into a string with negativity at most k. In other words, you want to change s into a string that has at most k prefixes that have a negative balance.

In order to change s you are going to perform a sequence of zero or more steps. In each step you can change a single '-' character in s into a '+' or vice versa. Compute and return the smallest number of steps needed.

Definition

Class:
Drbalance
Method:
lesscng
Parameters:
String, int
Returns:
int
Method signature:
int lesscng(String s, int k)
(be sure your method is public)

Constraints

  • s will contain between 1 and 50 characters, inclusive.
  • k will be between 0 and the length of s, inclusive.
  • Each character in s will be either '+' or '-'.

Examples

  1. "---"

    1

    Returns: 1

    One step is sufficient. If we change character 0 of s into a '+', we will obtain the string "+--". This string has only one prefix with a negative balance - namely, the entire string "+--". As k=1, we have reached our goal.

  2. "+-+-"

    0

    Returns: 0

  3. "-+-+---"

    2

    Returns: 1

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

    3

    Returns: 3

  5. "-+--+--+--++++----+"

    3

    Returns: 2

  6. "-----+-----+--++---+---++---+--+----+-+---"

    22

    Returns: 6

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

    23

    Returns: 6

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

    21

    Returns: 6

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

    6

    Returns: 11

  10. "---++---+-"

    2

    Returns: 2

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

    13

    Returns: 9

  12. "------++++++--+--+-++--+-+----+----++-"

    1

    Returns: 4

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

    8

    Returns: 2

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

    13

    Returns: 4

  15. "--+++-+-++-----++---+----------++-+-----+-"

    8

    Returns: 6

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

    1

    Returns: 3

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

    3

    Returns: 3

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

    8

    Returns: 3

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

    22

    Returns: 1

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

    23

    Returns: 4

  21. "-+-------+--+----++------+--+-------+--+----"

    40

    Returns: 1

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

    36

    Returns: 0

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

    11

    Returns: 3

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

    7

    Returns: 5

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

    32

    Returns: 1

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

    0

    Returns: 6

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

    15

    Returns: 11

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

    2

    Returns: 5

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

    10

    Returns: 7

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

    29

    Returns: 8

  31. "-+-++-++---------+------+--------++-+-+++----+-+++"

    29

    Returns: 5

  32. "+---+--"

    4

    Returns: 1

  33. "-++++---+--+--+-+++----+-"

    2

    Returns: 1

  34. "-----+"

    3

    Returns: 2

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

    1

    Returns: 12

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

    12

    Returns: 2

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

    28

    Returns: 2

  38. "------++--+---+---+--+---+----"

    25

    Returns: 2

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

    17

    Returns: 8

  40. "+---+------++--+++-+-------++--+++-+----++"

    7

    Returns: 5

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

    12

    Returns: 7

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

    7

    Returns: 2

  43. "-----+----------+--+---+-++---+++--"

    13

    Returns: 8

  44. "---++----+--++-----++--+--------+---+----"

    17

    Returns: 5

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

    20

    Returns: 4

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

    0

    Returns: 1

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

    0

    Returns: 1

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

    6

    Returns: 6

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

    6

    Returns: 2

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

    11

    Returns: 1

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

    4

    Returns: 4

  52. "-"

    1

    Returns: 0

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

    9

    Returns: 5

  54. "+---++"

    1

    Returns: 1

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

    3

    Returns: 5

  56. "---+-+-++-++-+-+----+-+--+-++-+-+-+-+---+---+-++++"

    48

    Returns: 0

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

    22

    Returns: 3

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

    3

    Returns: 9

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

    10

    Returns: 1

  60. "------"

    1

    Returns: 3

  61. "---+---+--++-+-+----+--+---------+--++-+-"

    30

    Returns: 3

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

    2

    Returns: 0

  63. "+-+---+-----+---+++-------"

    3

    Returns: 5

  64. "------+-++-------+-----+-+---+--+----+---+----"

    41

    Returns: 2

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

    3

    Returns: 4

  66. "+++++++-+--+--+++--++---+----+"

    0

    Returns: 0

  67. "---------+-+----+----++-+-+--+---+"

    6

    Returns: 7

  68. "---+-----+-----+--------+--+-+-+---+++-+----++"

    1

    Returns: 11

  69. "+----+-+------+-++---+----++++----"

    11

    Returns: 5

  70. "+----++--------+---------++----++--+---+------"

    42

    Returns: 1

  71. "+-++---++--+----+-+-++--++---+-"

    11

    Returns: 2

  72. "----+--+--+-++-++------+-+++--+-"

    32

    Returns: 0

  73. "-+----+---+-----++---++++++-"

    3

    Returns: 5

  74. "---------+-+-+--++---+-+--+----------+-"

    33

    Returns: 3

  75. "---+-+--++-+----++--+------+--+-----++------+-"

    8

    Returns: 8

  76. "+++--"

    0

    Returns: 0

  77. "+----+-+----+++-+--++++-+-+--+---+-+--++"

    2

    Returns: 3

  78. "---+----+--+-----++-++--+-"

    7

    Returns: 5

  79. "-+---+----------++-++-+++-+---+"

    18

    Returns: 4

  80. "-++--+-----++-+-----++---++------+-"

    1

    Returns: 7

  81. "---+---------+----+--+-+-+--+-+-+--+-----++-+-+-+-"

    50

    Returns: 0

  82. "+---++----+-------++----+-+-+---+-+-----------+-+"

    37

    Returns: 2

  83. "---++--+---------+---+--+--+----++-+-+--+------"

    19

    Returns: 8

  84. "--++-+-+--+-----++-----+-+--+---+---+-++---"

    28

    Returns: 2

  85. "---------++------------+---+-----++---+-+----++-+"

    39

    Returns: 4

  86. "+-------++-+----+---++"

    14

    Returns: 2

  87. "+++---+-++++----+---+-------------+-------+------+"

    3

    Returns: 12

  88. "++++"

    0

    Returns: 0

  89. "---"

    0

    Returns: 2

  90. "--"

    0

    Returns: 1

  91. "-++++++"

    1

    Returns: 0

  92. "+--++-+--------+++--+"

    4

    Returns: 3

  93. "++--+++"

    3

    Returns: 0

  94. "--------------------------------------------------"

    0

    Returns: 25

  95. "-+-----"

    3

    Returns: 1

  96. "++++"

    2

    Returns: 0

  97. "+-+"

    3

    Returns: 0

  98. "-------------------+"

    1

    Returns: 9

  99. "-"

    0

    Returns: 1

  100. "+++++++"

    1

    Returns: 0

  101. "+-"

    0

    Returns: 0

  102. "-++"

    1

    Returns: 0

  103. "+++---"

    3

    Returns: 0

  104. "++++++++++++"

    3

    Returns: 0

  105. "++"

    1

    Returns: 0

  106. "+++++++++++"

    6

    Returns: 0

  107. "----------------+"

    1

    Returns: 8

  108. "-----"

    0

    Returns: 3

  109. "----"

    1

    Returns: 2

  110. "------------"

    0

    Returns: 6

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