Tail Recursion, a Scala language concept

Last updated

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)

Tail recursion always has a recursive call in a "final" position, ie you can only either return a result (exit the function), or return another call to self-function

In canonical form, the immutable form gets compiled down to the mutable form,

def evaluateGeneralImmutable[State, Result](initialParams: State)(
    iterate: State => State,
    terminate: State => Boolean,
    extractResult: State => Result
): Result = {
  @scala.annotation.tailrec
  def go(currentParams: State): Result =
    if (terminate(currentParams)) extractResult(currentParams)
    else go(currentParams = iterate(currentParams))

  go(initialParams)
}

becomes (after a stage of compilation):

def evaluateGeneralMutable[State, Result](initialParams: State)(
    iterate: State => State,
    terminate: State => Boolean,
    extractResult: State => Result
): Result = {
  var currentParams: State = initialParams
  while (!terminate(currentParams)) {
    currentParams = iterate(currentParams)
  }
  extractResult(currentParams)
}

This transformation can also be performed the other way round, as to give you a pure immutable solution

What are the benefits of tail recursion?

Tail recursion in Scala utilises a principle known as tail-call optimisation. It allows one to write iterative algorithms (that would otherwise would be complicated while-loops) in immutable form.

What are the benefits of immutability?

It becomes easier to reason about your code, and you always know that you can re-run a function as manytimes as you wish without causing unexpected side effects.

But really, can anything be written in this shape?

Anything that is iterative in nature can, so long as it can be represented in the canonical form.

Let's look at two versions of List#drop(n) - mutable and immutable (Drop, Take, dropRight, takeRight):

def dropMutable[T](list: List[T], n: Int): List[T] = {
  var remaining = n
  var returnList = list
  while (remaining > 0 && returnList.nonEmpty) {
    remaining = remaining - 1
    returnList = returnList.tail
  }
  returnList
}

def dropImmutable[T](list: List[T], n: Int): List[T] = {
  @scala.annotation.tailrec
  def go(remaining: Int, returnList: List[T]): List[T] = {
    if (remaining == 0) returnList
    else
      returnList match {
        case _ :: rest => go(remaining - 1, rest)
        case Nil       => Nil
      }
  }
  go(remaining = n, list)
}

assert(dropMutable(List(1, 2, 3), 2) == List(3))

assert(dropImmutable(List(1, 2, 3), 2) == List(3))

The key thing to notice really is that you move all the `var`s to arguments of the `go` function.

Very detailed advanced example:

Let's try to implement List#foldLeft (foldLeft and foldRight):

Example how to turn a function from mutable to immutable. Warning: a lot of boilerplate code.
def foldLeftMutable[T, S](list: List[T])(initial: S)(f: (S, T) => S): S = {
  var currentResult: S = initial
  var remaining: List[T] = list
  while (remaining.nonEmpty) {
    currentResult = f(currentResult, remaining.head)
    remaining = remaining.tail
  }
  currentResult
}

final case class CurrentState[S, T](
    currentResult: S,
    remainingItems: List[T]
)

def foldLeftMutableSimplified[T, S](
    list: List[T]
)(initial: S)(f: (S, T) => S): S = {
  var currentResult: CurrentState[S, T] =
    CurrentState(currentResult = initial, remainingItems = list)
  while (currentResult.remainingItems.nonEmpty) {
    currentResult = CurrentState(
      currentResult =
        f(currentResult.currentResult, currentResult.remainingItems.head),
      remainingItems = currentResult.remainingItems.tail
    )
  }
  currentResult.currentResult
}

def foldLeftCanonicalMutable[T, S](
    list: List[T]
)(initial: S)(f: (S, T) => S): S = {
  evaluateGeneralMutable(
    CurrentState(currentResult = initial, remainingItems = list)
  )(
    currentResult =>
      CurrentState(
        currentResult =
          f(currentResult.currentResult, currentResult.remainingItems.head),
        remainingItems = currentResult.remainingItems.tail
      ),
    _.remainingItems.isEmpty,
    _.currentResult
  )
}

def foldLeft[T, S](list: List[T])(initial: S)(f: (S, T) => S): S =
  evaluateGeneralImmutable[CurrentState[S, T], S](
    CurrentState(initial, list)
  )(
    iterate = currentState =>
      CurrentState(
        currentResult =
          f(currentState.currentResult, currentState.remainingItems.head),
        remainingItems = currentState.remainingItems.tail
      ),
    terminate = _.remainingItems.isEmpty,
    extractResult = _.currentResult
  )

def foldLeftInlined[T, S](list: List[T])(initial: S)(f: (S, T) => S): S = {
  type State = CurrentState[S, T]
  type Result = S

  val initialParams: State = CurrentState(initial, list)
  val iterate: State => State = currentState =>
    CurrentState(
      currentResult =
        f(currentState.currentResult, currentState.remainingItems.head),
      remainingItems = currentState.remainingItems.tail
    )
  val terminate: State => Boolean = _.remainingItems.isEmpty
  val extractResult: State => Result = _.currentResult
  @scala.annotation.tailrec
  def go(currentParams: State): Result =
    if (terminate(currentParams)) extractResult(currentParams)
    else go(currentParams = iterate(currentParams))

  go(initialParams)
}

def foldLeftInlinedFurther[T, S](
    list: List[T]
)(initial: S)(f: (S, T) => S): S = {
  type State = CurrentState[S, T]
  type Result = S

  @scala.annotation.tailrec
  def go(currentParams: State): Result =
    if (currentParams.remainingItems.isEmpty) currentParams.currentResult
    else
      go(currentParams = {
        val currentState = currentParams
        CurrentState(
          currentResult =
            f(currentState.currentResult, currentState.remainingItems.head),
          remainingItems = currentState.remainingItems.tail
        )
      })

  go(CurrentState(initial, list))
}

def foldLeftInlinedState[T, S](
    list: List[T]
)(initial: S)(f: (S, T) => S): S = {

  @scala.annotation.tailrec
  def go(currentResult: S, remainingItems: List[T]): S =
    if (remainingItems.isEmpty) currentResult
    else
      go(
        currentResult = f(currentResult, remainingItems.head),
        remainingItems = remainingItems.tail
      )

  go(initial, list)
}

def foldLeftCompact[T, S](list: List[T])(initial: S)(f: (S, T) => S): S = {

  @scala.annotation.tailrec
  def go(currentResult: S, remainingItems: List[T]): S =
    remainingItems match {
      case head :: tail =>
        go(currentResult = f(currentResult, head), remainingItems = tail)
      case Nil => currentResult
    }

  go(initial, list)
}

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

Think in Scala & master the highest paid programming language in the US

Scala is used at many places, such as AirBnB, Apple, Bank of America, BBC, Barclays, Capital One, Citibank, Coursera, eBay, JP Morgan, LinkedIn, Morgan Stanley, Netflix, Singapore Exchange, Twitter.

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

Register now (free)