Scala algorithm: Matching parentheses algorithm with foldLeft and a state machine

Algorithm goal

Algorithm to check parentheses in a String are balanced. This problem is also known as:

  • On Codility: Stacks and Queues: Brackets - Determine whether a given string of parentheses (multiple types) is properly nested.
  • On HackerRank: Balanced Brackets - Given strings of brackets, determine whether each sequence of brackets is balanced. If a string is balanced, return YES. Otherwise, return NO.

Parentheses in a String are balanced when an opening bracket is followed by another opening bracket or by a closing bracket of the same time.

For example, ([]) is balanced, but ([) and ([)] are not.

We have a plain tail-recursive solution as well: ParenthesesTailRecursive

Test cases in Scala


Algorithm in Scala

36 lines of Scala (compatible versions 2.13 & 3.0).

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Please see the tail-recursive version for algorithm explanation: ParenthesesTailRecursive. The two are nearly equivalent, except that the folding version goes through the whole string (which may not be optimal - but there is an optimisation to make it more efficient using `.view` (View). Here is the state transition diagram of this implementation. (this is © from

    [*] --> BalancedStack
    BalancedStack --> [*]
    BalancedStack --> Stacked
    BalancedStack --> Failed
    Stacked --> BalancedStack
    Stacked --> Failed
    Failed --> [*]

Scala concepts & Hints

  1. foldLeft and foldRight

    A 'fold' allows you to perform the equivalent of a for-loop, but with a lot less code.

    def foldMutable[I, O](initialState: O)(items: List[I])(f: (O, I) => O): O =
  2. Pattern Matching

    Pattern matching in Scala lets you quickly identify what you are looking for in a data, and also extract it.

    assert("Hello World".collect {
      case character if Character.isUpperCase(character) => character.toLower
    } == "hw")
  3. Stack Safety

    Stack safety is present where a function cannot crash due to overflowing the limit of number of recursive calls.

    This function will work for n = 5, but will not work for n = 2000 (crash with java.lang.StackOverflowError) - however there is a way to fix it :-)

    In Scala Algorithms, we try to write the algorithms in a stack-safe way, where possible, so that when you use the algorithms, they will not crash on large inputs. However, stack-safe implementations are often more complex, and in some cases, overly complex, for the task at hand.

    def sum(from: Int, until: Int): Int =
      if (from == until) until else from + sum(from + 1, until)
    def thisWillSucceed: Int = sum(1, 5)
    def thisWillFail: Int = sum(1, 300)
  4. State machine

    A state machine is the use of `sealed trait` to represent all the possible states (and transitions) of a 'machine' in a hierarchical form.

  5. State machine

    A state machine is the use of `sealed trait` to represent all the possible states (and transitions) of a 'machine' in a hierarchical form.

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  13. Matching parentheses algorithm with foldLeft and a state machine
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Explore the 21 most useful Scala concepts

To save you going through various tutorials, we cherry-picked the most useful Scala concepts in a consistent form.

  1. Class Inside Class
  2. Class Inside Def
  3. Collect
  4. Def Inside Def
  5. Drop, Take, dropRight, takeRight
  6. foldLeft and foldRight
  7. For-comprehension
  8. Lazy List
  9. Option Type
  10. Ordering
  11. Partial Function
  12. Pattern Matching
  13. Range
  14. scanLeft and scanRight
  15. Sliding / Sliding Window
  16. Stack Safety
  17. State machine
  18. Tail Recursion
  19. Type Class
  20. View
  21. Zip

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