Scala algorithm: Balanced parentheses algorithm with tail-call recursion optimisation

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.

Algorithm in Scala

29 lines of Scala (version 2.13), showing how concise Scala can be!

val OpenToClose: Map[Char, Char] = Map('{' -> '}', '[' -> ']', '(' -> ')')

val CloseToOpen: Map[Char, Char] = OpenToClose.map(_.swap)

def parenthesesAreBalanced(s: String): Boolean = {
  if (s.isEmpty) true
  else {
    @scala.annotation.tailrec
    def go(position: Int, stack: List[Char]): Boolean = {
      if (position == s.length) stack.isEmpty
      else {
        val char = s(position)
        val isOpening = OpenToClose.contains(char)
        val isClosing = CloseToOpen.contains(char)
        if (isOpening) go(position + 1, char :: stack)
        else if (isClosing) {
          val expectedCharForMatching = CloseToOpen(char)
          stack match {
            case `expectedCharForMatching` :: rest =>
              go(position + 1, rest)
            case _ =>
              false
          }
        } else false
      }
    }
    go(position = 0, stack = List.empty)
  }
}

Test cases in Scala

assert(parenthesesAreBalanced("()"))
assert(parenthesesAreBalanced("[()]"))
assert(parenthesesAreBalanced("{[()]}"))
assert(parenthesesAreBalanced("([{{[(())]}}])"))
assert(!parenthesesAreBalanced("{{[]()}}}}"))
assert(!parenthesesAreBalanced("{{[](A}}}}"))
assert(!parenthesesAreBalanced("{[(])}"))

Explanation

Also please find an alternative solution using a foldLeft state machine ParenthesesFoldingStateMachine which makes an advanced streamed implementation possible.

By definition, we need to keep track of the most recent opening bracket, and if the next bracket we approach is a closing bracket that is not the latest bracket, we terminate with a failure, whereas if it is another opening bracket, this is the bracket we consider as the latest, and if it is another closing bracket that matches the latest opening bracket, the new latest opening bracket is 'popped'. This description is enough to suggest to us that we should use a 'stack' structure, and implement our logic as described. (this is © from www.scala-algorithms.com)

In Scala, a List is equivalent to a stack, it is a structure in the form List[T] = ::(head: T, tail: List[T]) | Nil

We could solve this problem in a standard mutable style, but this would not be the immutable Scala way of doing things.

Scala concepts & Hints

  1. Def Inside Def

    A great aspect of Scala is being able to declare functions inside functions, making it possible to reduce repetition.

    def exampleDef(input: String): String = {
      def surroundInputWith(char: Char): String = s"$char$input$char"
      surroundInputWith('-')
    }
    
    assert(exampleDef("test") == "-test-")
    

    It is also frequently used in combination with Tail Recursion.

  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. Tail Recursion

    In Scala, tail recursion enables you to rewrite a mutable structure such as a while-loop, into an immutable algorithm.

    def fibonacci(n: Int): Int = {
      @scala.annotation.tailrec
      def go(i: Int, previous: Int, beforePrevious: Int): Int =
        if (i >= n) previous else go(i + 1, previous + beforePrevious, previous)
    
      go(i = 1, previous = 1, beforePrevious = 0)
    }
    
    assert(fibonacci(8) == 21)
    

Scala Algorithms: The most comprehensive library of algorithms in standard pure-functional Scala

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Study our 104 Scala Algorithms: 6 fully free, 59 published & 45 upcoming

Fully unit-tested, with explanations and relevant concepts; new algorithms published about once a week.

  1. Find minimum missing positive number in a sequence
  2. Longest increasing sub-sequence length
  3. Compute the length of longest valid parentheses
  4. Counting inversions of a sequence (array) using a Merge Sort
  5. Check if an array is a palindrome
  6. Monitor success rate of a process that may fail
  7. Find combinations adding up to N (non-unique)
  8. Remove duplicates from an unsorted List
  9. Find combinations adding up to N (unique)
  10. Find k closest elements to a value in a sorted Array
  11. Make a queue using stacks (Lists in Scala)
  12. Single-elimination tournament tree
  13. Quick Sort sorting algorithm in pure immutable Scala
  14. Compute a Roman numeral for an Integer, and vice-versa
  15. Matching parentheses algorithm with foldLeft and a state machine
  16. Traverse a tree Breadth-First, immutably
  17. Read a matrix as a spiral
  18. Remove duplicates from a sorted list (state machine)
  19. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  20. Binary search a generic Array
  21. Merge Sort: in pure immutable Scala
  22. Make a queue using Maps
  23. Is an Array a permutation?
  24. Count number of contiguous countries by colors
  25. Add numbers without using addition (plus sign)
  26. Tic Tac Toe MinMax solve
  27. Run-length encoding (RLE) Encoder
  28. Print Alphabet Diamond
  29. Balanced parentheses algorithm with tail-call recursion optimisation
  30. Reverse a String's words efficiently
  31. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  32. Compute nth row of Pascal's triangle
  33. Run-length encoding (RLE) Decoder
  34. Check if a number is a palindrome
  35. In a range of numbers, count the numbers divisible by a specific integer
  36. Find the index of a substring ('indexOf')
  37. Reshape a matrix
  38. Closest pair of coordinates in a 2D plane
  39. Find the contiguous slice with the minimum average
  40. Compute maximum sum of subarray (Kadane's algorithm)
  41. Binary search in a rotated sorted array
  42. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  43. Length of the longest common substring
  44. Tic Tac Toe board check
  45. Find an unpaired number in an array
  46. Check if a String is a palindrome
  47. Count binary gap size of a number using tail recursion
  48. Remove duplicates from a sorted list (Sliding)
  49. Find sub-array with the maximum sum
  50. Find the minimum absolute difference of two partitions
  51. Find maximum potential profit from an array of stock price
  52. Fibonacci in purely functional immutable Scala
  53. Fizz Buzz in purely functional immutable Scala
  54. Count factors/divisors of an integer
  55. Compute single-digit sum of digits
  56. Traverse a tree Depth-First
  57. Reverse bits of an integer
  58. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  59. Rotate a matrix by 90 degrees clockwise

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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