Scala algorithm: Make a queue using stacks (Lists in Scala)


Algorithm goal

Make a pure-functional queue using stacks (Lists). It would have the following methods: isEmpty: Boolean, enqueue(T), dequeue: Option[(T, Queue[T])].

Try to make it efficient, where possible.

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Algorithm in Scala

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

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The most straightforward implementation of a Queue would contain a single List, however in this case, we would have to choose between making enqueue fast, or making dequeue fast, because with a List, to get the tail element is an \(O(n)\) operation.

However, there is a more efficient way, which is to use an 'incoming' and an 'outgoing' List: so long as 'outgoing' is not empty, we can destructure it at O(1) cost, and we can enqueue to 'incoming' at O(1) cost. The only time where we would face a cost would be when 'outgoing' is empty, and 'incoming' is non-empty: then, we would have to convert the 'incoming' to 'outgoing' by reversal, which is an O(n) operation. However, amortized, it would be more efficient than the biased approach. (this is © from

Scala concepts & Hints

  1. Option Type

    The 'Option' type is used to describe a computation that either has a result or does not. In Scala, you can 'chain' Option processing, combine with lists and other data structures. For example, you can also turn a pattern-match into a function that return an Option, and vice-versa!

    assert(Option(1).flatMap(x => Option(x + 2)) == Option(3))
    assert(Option(1).flatMap(x => None) == None)
  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 = {
      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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  1. Find minimum missing positive number in a sequence
  2. Longest increasing sub-sequence length
  3. Compute the length of longest valid parentheses
  4. Check if an array is a palindrome
  5. Monitor success rate of a process that may fail
  6. Find combinations adding up to N (non-unique)
  7. Remove duplicates from an unsorted List
  8. Find combinations adding up to N (unique)
  9. Find k closest elements to a value in a sorted Array
  10. Make a queue using stacks (Lists in Scala)
  11. Single-elimination tournament tree
  12. Quick Sort sorting algorithm in pure immutable Scala
  13. Compute a Roman numeral for an Integer, and vice-versa
  14. Matching parentheses algorithm with foldLeft and a state machine
  15. Traverse a tree Breadth-First, immutably
  16. Read a matrix as a spiral
  17. Remove duplicates from a sorted list (state machine)
  18. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  19. Binary search a generic Array
  20. Merge Sort: in pure immutable Scala
  21. Make a queue using Maps
  22. Is an Array a permutation?
  23. Count number of contiguous countries by colors
  24. Add numbers without using addition (plus sign)
  25. Tic Tac Toe MinMax solve
  26. Run-length encoding (RLE) Encoder
  27. Print Alphabet Diamond
  28. Balanced parentheses algorithm with tail-call recursion optimisation
  29. Reverse a String's words efficiently
  30. Count number of changes (manipulations) needed to make an anagram with foldLeft and a MultiSet
  31. Count passing cars
  32. Counting inversions of a sequence (array) using a Merge Sort
  33. Compute nth row of Pascal's triangle
  34. Run-length encoding (RLE) Decoder
  35. Check if a number is a palindrome
  36. In a range of numbers, count the numbers divisible by a specific integer
  37. Find the index of a substring ('indexOf')
  38. Reshape a matrix
  39. Closest pair of coordinates in a 2D plane
  40. Find the contiguous slice with the minimum average
  41. Compute maximum sum of subarray (Kadane's algorithm)
  42. Binary search in a rotated sorted array
  43. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  44. Length of the longest common substring
  45. Tic Tac Toe board check
  46. Find an unpaired number in an array
  47. Check if a String is a palindrome
  48. Count binary gap size of a number using tail recursion
  49. Remove duplicates from a sorted list (Sliding)
  50. Find sub-array with the maximum sum
  51. Find the minimum absolute difference of two partitions
  52. Find maximum potential profit from an array of stock price
  53. Fibonacci in purely functional immutable Scala
  54. Fizz Buzz in purely functional immutable Scala
  55. Count factors/divisors of an integer
  56. Compute single-digit sum of digits
  57. Traverse a tree Depth-First
  58. Reverse bits of an integer
  59. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  60. 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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