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Problem Statement for "CorrectingParenthesization"

Problem Statement

Given a string of parentheses, we must turn it into a well formed string by changing as few characters as possible (we cannot delete or insert characters).

There are 3 kinds of parentheses: regular (), brackets [] and curly brackets {}. Each pair has an opening ('(', '[' and '{' respectively) and a closing (')', ']' and '}') character.

A well formed string of parentheses is defined by the following rules:

  • The empty string is well formed.
  • If s is a well formed string, (s), [s] and {s} are well formed strings.
  • If s and t are well formed strings, the concatenation st is a well formed string.

As examples, "([{}])", "" and "(){}[]" are well formed strings and "([}]", "([)]" and "{" are malformed strings.

Given a String s of parentheses, return the minimum number of characters that need to be changed to make it into a well formed string.

Definition

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

Notes

  • Changing a character is selecting one position in the string and changing the character in that position to any other parentheses character.

Constraints

  • s will have between 0 and 50 characters, inclusive.
  • s will have an even number of characters.
  • Each character of s will be '(', '[', '{', ')', ']' or '}'.

Examples

  1. "([{}])()[]{}"

    Returns: 0

    This is already well formed.

  2. "([)]"

    Returns: 2

    With two changes you can get "([])" (there are other ways with the same number of changes).

  3. "([{}[]"

    Returns: 1

    Simply changing the second character will give you "(){}[]".

  4. ""

    Returns: 0

  5. "]["

    Returns: 2

  6. "()[]"

    Returns: 0

  7. "[(}][{}]"

    Returns: 1

  8. "((((([[[[[{{{{{}}}}}]]]]])))))"

    Returns: 0

  9. "}}}}}]]]]])))))((((([[[[[{{{{{"

    Returns: 16

  10. ")()[]{}[]{}[]{}()["

    Returns: 2

  11. "){[}]("

    Returns: 4

  12. "}]"

    Returns: 1

  13. "([{]()"

    Returns: 2

  14. "(){}[})}){}]"

    Returns: 2

  15. "[]}({[[](([(]]})"

    Returns: 5

  16. "{})({])[]}})]{{})}{{)]"

    Returns: 6

  17. "{}({}(()[[[])}(]}}{]][[(]]"

    Returns: 6

  18. "[(]{)[}]]}})}{[[)}}]{[][[][{{[[}"

    Returns: 9

  19. ")}[(({}}}}[{)}]])]]]()[]{[}[))}{}){)"

    Returns: 11

  20. "{}}{[(][]][}[]({(]{})[]]([[(})(][])][[{]{("

    Returns: 11

  21. "(]{]]]]}]){()(]}([)[((}[]])}{{{){{]{)))}(]((]]"

    Returns: 14

  22. "([{(({[{[[[{({((({{[([{{{)}}]}})}]}]])]])}})))])}]"

    Returns: 9

  23. "({{{[({([]}]})})))"

    Returns: 4

  24. "{[[((({{{(())))]]])))]"

    Returns: 5

  25. "}])}])])})}])}]]}])}])}]]{([[[{(([{{[({(([{[({[{{["

    Returns: 26

  26. "])])}}]}))}]}[{[[(([[{({(["

    Returns: 14

  27. "})]])]}]))})}]}]}}))}[{[{[[{{([[[([[({[[({"

    Returns: 22

  28. "[((({}{})()[]("

    Returns: 2

  29. "{[[()({)}[]){}][){}][)"

    Returns: 5

  30. "[([])]{}[]"

    Returns: 0

  31. "({}{}(])"

    Returns: 1

  32. "({{}{}(({[{}]]()[{{)}]]{}}](){](])[}()"

    Returns: 7

  33. "[((()[]]}()))]"

    Returns: 1

  34. "{([(]({}[))[){{}}[]}]])]]{}]){]}"

    Returns: 5

  35. "[(}([{((([])))}]))]()]"

    Returns: 2

  36. "(({}))"

    Returns: 0

  37. "{{([{}()([[]{[]{]())()])}{]}"

    Returns: 2

  38. "][((({(()][)])(}([({{}}))]()(){}{[([))()()))][{()]"

    Returns: 10

  39. "[]"

    Returns: 0

  40. "(}}[{)({[([{[][()({)}]}][{}({[({](])"

    Returns: 9

  41. "()[()([{}(()()()[]{}[[]]{}{})}()}])[]{}]{}"

    Returns: 1

  42. "[([{(}()[)]]){"

    Returns: 4

  43. "({[{{][{{{({[{{}()}{}][]})}[]}[](){{}]}()]})"

    Returns: 2

  44. "()"

    Returns: 0

  45. "{(([]}()[{}]](){}[]){){}"

    Returns: 3

  46. "{{}{([((()))][]{])}()}"

    Returns: 1

  47. "{](()[([{))[[]{]{}{}[(([}{}{)[[[]}{}]}(){()}[("

    Returns: 9

  48. "([]{[]])({[{}[]]})"

    Returns: 1

  49. "()[]{}[]{}[]{}[]}{}[]{}[]{})"

    Returns: 1

  50. "]]]]]]]]]]]]"

    Returns: 6

  51. "{{{{{{{{{{{{{{"

    Returns: 7

  52. "))))))))))))))))))))))))))))))))))))))))))))))))))"

    Returns: 25

  53. "({[[{([[{{{{(({(({{{{[[[{({{[{[(({[{{{[[[(((((((({"

    Returns: 25

  54. "{}{[(}}]()))[)(["

    Returns: 5

  55. ")([}}{([{(({})}()(({}{)]}))}}]({]}"

    Returns: 7

  56. "}[[{{{][}(){}[][]}"

    Returns: 4

  57. "{[{({}{]]}{{}{}][(]{}])}]}[("

    Returns: 4

  58. "]}{][]{}][{[}][({{[{(}[})}()]{)}]}}["

    Returns: 10

  59. "})([)]()[}[](])]"

    Returns: 5

  60. "{}"

    Returns: 0

  61. "{{(()({](([((({({][]{[]]]){}}})[]{"

    Returns: 8

  62. "[]{[]{}([[]()[){}()}{}"

    Returns: 1

  63. "[{]]([]]}[[[[{[(]{{{[]]}[){[{())(]]{]]([)(}("

    Returns: 13

  64. "({}){{"

    Returns: 1

  65. "[[][][]((([]()())))(){}]"

    Returns: 0

  66. "{}({}]}){}()"

    Returns: 1

  67. "{]()"

    Returns: 1

  68. ")()](][]()(()()]{()[))"

    Returns: 4

  69. ")]({{}})})"

    Returns: 2

  70. "{{[{[[{}[][]}}"

    Returns: 2

  71. "({(([[[()(}]]]})()"

    Returns: 2

  72. "[{(([[}[([][]({{}{}{{({[[]}(](]}]{}}))}}}])(){})}]"

    Returns: 7

  73. "({}{[[]{}[][]}]]{}))()"

    Returns: 2

  74. "[]"

    Returns: 0

  75. "{[({}}[{{{}}}]]{}[])[}(["

    Returns: 3

  76. "[)"

    Returns: 1

  77. "{{)(}()}{}{((())({([)[{{}[}[)}]}]]([))}}"

    Returns: 8

  78. "()({}{}{"

    Returns: 1

  79. "}[}(][(){)}{]})}{}{}())]"

    Returns: 6

  80. "[[]([{}()][]"

    Returns: 1

  81. "[]))[]"

    Returns: 1

  82. "{{{[[{{}{}[{}}"

    Returns: 3

  83. ")][(][]]()"

    Returns: 2

  84. ")))(({}{}}{{{}}}})({}{}}}}}}{{{{)}())}{]}{(]))(((("

    Returns: 13

  85. "({[}[)]]({[}[)]]({[}[)]]({[}[)]]({[}[)]]({[}[)]]"

    Returns: 15

  86. ")))((("

    Returns: 4

  87. ")[]]{(()))){}}}{{[[]]]}([{]}{}}]][[(()[]])))}}}["

    Returns: 9

  88. "]]]]"

    Returns: 2

  89. "(((((]]]{]}{{]]]]{{{{))[[{{{))(({]"

    Returns: 13

  90. "([{}])()[]{}(((}}}}}}][]{])((}}}{}][][()()}}))))"

    Returns: 9

  91. "{([}"

    Returns: 1

  92. "[{}]}}}}}}"

    Returns: 3

  93. "][{{"

    Returns: 3

  94. "(}){(}({))(}{(){(}(([][][(][])((()[][][](((}"

    Returns: 11

  95. ")[{{))]("

    Returns: 4

  96. "([{}[]([{}[]([{}[]([{}[]([{}[]([{}[]([{}[]([{}[]]]"

    Returns: 8

  97. "((({[{]}}]]]"

    Returns: 4

  98. "}}}}}}])])}])])}])])}])])}])])}])])}])])}])])}]}"

    Returns: 24

  99. "(((((]]]{]}{{]]]]{{{{))[[{{{))(({](((]]{"

    Returns: 16

  100. "(}{([]){][){()[]]}})({}[]]])(][{}}{{})({}){[])[](]"

    Returns: 10

  101. "((((((((((([})))))))))))([[[[[[[[[]]]]]]]]]}"

    Returns: 2

  102. "({(((((((((((((((((}}}}}}}}}}}}}}}}}[[[[}(}((}"

    Returns: 22

  103. "((({[[]})[{]]}"

    Returns: 4

  104. "())){[[[[}()))((({][[[[]"

    Returns: 8

  105. "[({]})"

    Returns: 2

  106. ")("

    Returns: 2

  107. "]]][[["

    Returns: 4

  108. "([{}[])))))]"

    Returns: 3

  109. "]["

    Returns: 2

  110. "([{}])()[]{}([{}])()[]{}([{}])()[]{}[}[](}{}{]}]"

    Returns: 3

  111. "}}}}"

    Returns: 2

  112. "(({[))}]"

    Returns: 2

  113. "][][(((((((()))))}}}}}[[[[[[[}}}]]]]]]]]]]}}{{{{"

    Returns: 10

  114. "))}})}[[}())]{])]({[{[({}}{(())[)[{})]][){({{({]"

    Returns: 14

  115. "{{{{"

    Returns: 2

  116. "([{}[()]{(}){}[[))}}{{"

    Returns: 5

  117. "{}({[[}){(][({}{))({[}{)"

    Returns: 6

  118. "{)})"

    Returns: 2

  119. "((]))()(([))"

    Returns: 2

  120. ")}[](){{{]])(){{}))))]"

    Returns: 7

  121. "[{](})"

    Returns: 3

  122. "[([{]})]"

    Returns: 2

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