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Problem Statement for "ParenthesesDiv2Medium"

Problem Statement

Correct parentheses sequences can be defined recursively as follows:
  • The empty string "" is a correct sequence.
  • If "X" and "Y" are correct sequences, then "XY" (the concatenation of X and Y) is a correct sequence.
  • If "X" is a correct sequence, then "(X)" is a correct sequence.
  • Each correct parentheses sequence can be derived using the above rules.
Examples of correct parentheses sequences include "", "()", "()()()", "(()())", and "(((())))".


You have a String s of length n, where n is even. Your task is to change it into a correct parentheses sequence. In order to do that, you are allowed to flip some parentheses. Flipping a parenthesis changes it from '(' to ')' and vice versa.


There is always a way to change s into a correct parentheses sequence by doing at most (n/2)+1 flips. Find any such sequence of flips. Return a int[] containing a sequence of 0-based indices of parentheses in s you want to flip.

Definition

Class:
ParenthesesDiv2Medium
Method:
correct
Parameters:
String
Returns:
int[]
Method signature:
int[] correct(String s)
(be sure your method is public)

Constraints

  • s will contain between 2 and 50 characters, inclusive.
  • The length of s will be even.
  • Each character in s will be '(' or ')'.

Examples

  1. ")("

    Returns: {0, 1 }

    The returned sequence represents the following sequence of changes: Start with the string ")(". Flip character 0. This produces the string "((". Flip character 1. This produces the string "()", which is a corrent parentheses sequence.

  2. ")))))((((("

    Returns: {0, 2, 4, 5, 7, 9 }

    Performing the flips described by the returned sequence changes the given string into the corrent parentheses sequence "()()()()()". The answer {2, 0, 4, 9, 7, 5} would also be valid, as the order in which we perform the flips does not matter. However, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} is not a valid answer: this sequence of flips does produce a correct parentheses sequence but the number of flips is too large. As the length of s is 10, we may only perform at most 10/2 + 1 = 6 flips.

  3. "((()"

    Returns: {1 }

  4. ")))(()(())))))"

    Returns: {0, 1, 2 }

    Here, {0, 1, 2, 3, 3} would also be a valid answer. Flipping the same parenthesis twice is allowed, even though it is clearly useless.

  5. "()()()()()()()()()()()()()"

    Returns: { }

  6. "))))))(()())(()()))))))))))())"

    Returns: {0, 2, 4, 7, 10, 13, 16, 18, 20, 22, 24, 28, 8, 27 }

  7. ")()()())()"

    Returns: {6, 0, 5 }

  8. "))))())))))()))))))))))))))))))(()(())))))))))"

    Returns: {0, 2, 6, 8, 12, 14, 16, 18, 20, 22, 24, 26, 28, 35, 36, 38, 40, 42, 44, 10, 31 }

  9. ")()()(())((())(())()"

    Returns: {11, 12, 15, 16, 0, 9 }

  10. ")(((()()(()("

    Returns: {3, 9, 0, 11 }

  11. ")()())((((()())))()))()(()))"

    Returns: {4, 7, 9, 14, 18, 26, 0, 23 }

  12. "(((((((((()((((((((((("

    Returns: {1, 3, 5, 7, 9, 13, 15, 17, 19, 21, 10, 11 }

  13. ")))((((("

    Returns: {0, 5, 7, 2, 3 }

  14. ")))()(())()(((()))))"

    Returns: {0, 13, 16, 18, 2, 11 }

  15. "))))))))))))))))()))))))))))))))))"

    Returns: {0, 2, 4, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 28, 30, 32 }

  16. ")))))))()))))))))))))))())))"

    Returns: {0, 2, 4, 8, 10, 12, 14, 16, 18, 20, 24, 26, 6, 23 }

  17. ")(((((((()((((((((((((()(((((((((("

    Returns: {3, 5, 7, 11, 13, 15, 17, 19, 21, 25, 27, 29, 31, 33, 0, 1 }

  18. "(()())))(((((()((())()"

    Returns: {1, 4, 6, 9, 11, 13, 17, 18, 2, 15 }

  19. "((((((()((((()((()(()(()(())))()()(()((()))(()(((("

    Returns: {1, 3, 5, 9, 11, 15, 19, 25, 26, 28, 35, 39, 40, 47, 49, 20, 43 }

  20. ")((((()(()(("

    Returns: {3, 5, 11, 0, 7 }

  21. "(((((((((((((((((((((((((("

    Returns: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25 }

  22. "(((()(((()(((())))((()((()(((("

    Returns: {1, 3, 7, 11, 13, 14, 16, 19, 23, 27, 29, 4, 5 }

  23. ")))))()))))))))))))))((()())))))))))())))())"

    Returns: {0, 2, 6, 8, 10, 12, 14, 16, 18, 23, 26, 28, 30, 32, 34, 38, 42, 4, 41 }

  24. ")(()))()()))())())((()())())()"

    Returns: {4, 10, 16, 19, 26, 0, 25 }

  25. "))))))))))))))))))()"

    Returns: {0, 2, 4, 6, 8, 10, 12, 14, 16 }

  26. "(((()))())((())))()))("

    Returns: {1, 3, 4, 8, 11, 14, 18, 6, 21 }

  27. "(((()((((()(()"

    Returns: {1, 3, 7, 9, 4, 11 }

  28. "))())))))()))())))()()()"

    Returns: {0, 4, 6, 10, 14, 16, 8, 13 }

  29. "()(()(())))()))))))(())(())))())(()()))))(())())))"

    Returns: {3, 8, 12, 14, 16, 26, 30, 33, 36, 38, 46, 48, 4, 45 }

  30. "))(((((((((((((((((((((()((((((((((((((((("

    Returns: {0, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, 33, 35, 37, 39, 41, 24, 25 }

  31. ")))))))))))))))))))))))))("

    Returns: {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 25 }

  32. "))))))())))))))))())))))))))))))))))))))))))"

    Returns: {0, 2, 4, 8, 10, 12, 14, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 16, 17 }

  33. ")((((((("

    Returns: {3, 5, 7, 0, 1 }

  34. "))())()(((()))))()()"

    Returns: {0, 9, 12, 14, 4, 7 }

  35. "())))))))))))))))()()))(()))))())())()))"

    Returns: {2, 4, 6, 8, 10, 12, 14, 20, 26, 28, 34, 38, 16, 33 }

  36. "(()()))())()))))))))))))))))))))))))))))(((((()((("

    Returns: {1, 4, 8, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 41, 43, 45, 49, 2, 47 }

  37. ")()()()("

    Returns: {0, 7 }

  38. ")()()()()()("

    Returns: {0, 11 }

  39. ")()()()()()()()()()()()()()()()("

    Returns: {0, 31 }

  40. ")))))))))))))))))))))))((((((((((((((((((((((("

    Returns: {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 22, 23 }

  41. ")()()("

    Returns: {0, 5 }

  42. ")()((("

    Returns: {5, 0, 3 }

  43. ")((((())))()))()(())()))))()()(((())(((((())(()((("

    Returns: {3, 5, 6, 8, 12, 17, 18, 22, 24, 31, 33, 34, 37, 39, 41, 42, 45, 49, 0, 47 }

  44. "()()()()()()(((("

    Returns: {13, 15 }

  45. ")()("

    Returns: {0, 3 }

  46. "(((((("

    Returns: {1, 3, 5 }

  47. "(((((((((((((((((((("

    Returns: {1, 3, 5, 7, 9, 11, 13, 15, 17, 19 }

  48. ")()()())"

    Returns: {6, 0, 5 }

  49. ")()()()()("

    Returns: {0, 9 }

  50. ")()()()()()()("

    Returns: {0, 13 }

  51. ")()()()()()()()("

    Returns: {0, 15 }

  52. "))(("

    Returns: {0, 3 }

  53. "(()()()())"

    Returns: {1, 8, 2, 7 }

  54. "(())"

    Returns: {1, 2 }

  55. "))))(((("

    Returns: {0, 2, 5, 7 }

  56. "(((("

    Returns: {1, 3 }

  57. ")))((("

    Returns: {0, 5, 2, 3 }

  58. ")()()()()()()()()("

    Returns: {0, 17 }

  59. ")()()()()()()()()()()()()()()("

    Returns: {0, 29 }

  60. "))"

    Returns: {0 }

  61. "(((((((((("

    Returns: {1, 3, 5, 7, 9 }

  62. ")()()()()()()()()()()()()("

    Returns: {0, 25 }

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