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

Published

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.

Test cases in Scala

assert(Queue.empty.isEmpty)
assert(Queue.empty.enqueue("A").dequeue.contains("A" -> Queue.empty))
assert(
  Queue.empty.enqueue("A").enqueue("B").dequeue.map(_._1).contains("A")
)
assert(
  Queue.empty
    .enqueue("A")
    .enqueue("B")
    .dequeue
    .map(_._2)
    .flatMap(_.dequeue)
    .map(_._1)
    .contains("B")
)
assert(
  Queue.empty
    .enqueue("A")
    .enqueue("B")
    .dequeue
    .map(_._2)
    .flatMap(_.dequeue)
    .map(_._2)
    .flatMap(_.dequeue)
    .isEmpty
)
assert(
  Queue.empty
    .enqueue("A")
    .enqueue("B")
    .dequeue
    .map(_._2.enqueue("C"))
    .flatMap(_.dequeue)
    .map(_._1)
    .contains("B")
)
assert(
  Queue.empty
    .enqueue("A")
    .enqueue("B")
    .dequeue
    .map(_._2.enqueue("C"))
    .flatMap(_.dequeue)
    .map(_._2)
    .flatMap(_.dequeue)
    .map(_._1)
    .contains("C")
)
assert(
  Queue.empty
    .enqueue("A")
    .enqueue("B")
    .dequeue
    .map(_._2.enqueue("C"))
    .flatMap(_.dequeue)
    .map(_._2)
    .flatMap(_.dequeue)
    .map(_._2)
    .flatMap(_.dequeue)
    .isEmpty
)

Algorithm in Scala

20 lines of Scala (compatible versions 2.13 & 3.0), showing how concise Scala can be!

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Explanation

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 www.scala-algorithms.com)

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 = {
      @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

How our 100 algorithms look

  1. A description/goal of the algorithm.
  2. An explanation with both Scala and logical parts.
  3. A proof or a derivation, where appropriate.
  4. Links to Scala concepts used in this specific algorithm, also unit-tested.
  5. An implementation in pure-functional immutable Scala, with efficiency in mind (for most algorithms, this is for paid subscribers only).
  6. Unit tests, with a button to run them immediately in our in-browser IDE.
Screenshot of an example algorithm demonstrating the listed features

Study our 100 Scala Algorithms: 6 fully free, 94 published & 6 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. Check a binary tree is balanced
  3. Print a binary tree
  4. Remove duplicates from an unsorted List
  5. Make a queue using stacks (Lists in Scala)
  6. Find height of binary tree
  7. Single-elimination tournament tree
  8. Reverse Polish Notation calculator
  9. Quick Sort sorting algorithm in pure immutable Scala
  10. Maximum wait at a fuel station
  11. Find minimum missing positive number in a sequence
  12. Least-recently used cache (LRU)
  13. Count pairs of a given expected sum
  14. Binary heap (min-heap)
  15. Compute a Roman numeral for an Integer, and vice-versa
  16. Compute keypad possibilities
  17. Matching parentheses algorithm with foldLeft and a state machine
  18. Traverse a tree Breadth-First, immutably
  19. Read a matrix as a spiral
  20. Remove duplicates from a sorted list (state machine)
  21. Token Bucket Rate Limiter
  22. Leaky Bucket Rate Limiter
  23. Merge Sort: stack-safe, tail-recursive, in pure immutable Scala, N-way
  24. Longest increasing sub-sequence length
  25. Reverse first n elements of a queue
  26. Binary search a generic Array
  27. Game of Life
  28. Merge Sort: in pure immutable Scala
  29. Make a queue using Maps
  30. Is an Array a permutation?
  31. Count number of contiguous countries by colors
  32. Add numbers without using addition (plus sign)
  33. Tic Tac Toe MinMax solve
  34. Run-length encoding (RLE) Encoder
  35. Print Alphabet Diamond
  36. Find kth largest element in a List
  37. Balanced parentheses algorithm with tail-call recursion optimisation
  38. Reverse a String's words efficiently
  39. Count number of changes (manipulations) needed to make an anagram with an efficient foldLeft
  40. Count passing cars
  41. Count dist intersections
  42. Establish execution order from dependencies
  43. Counting inversions of a sequence (array) using a Merge Sort
  44. Longest common prefix of strings
  45. Check if an array is a palindrome
  46. Compute missing ranges
  47. Check a directed graph has a routing between two nodes (depth-first search)
  48. Compute nth row of Pascal's triangle
  49. Run-length encoding (RLE) Decoder
  50. Check if a number is a palindrome
  51. In a range of numbers, count the numbers divisible by a specific integer
  52. Compute minimum number of Fibonacci numbers to reach sum
  53. Find the longest palindrome within a string
  54. Find the index of a substring ('indexOf')
  55. Reshape a matrix
  56. Compute the steps to transform an anagram only using swaps
  57. Compute modulo of an exponent without exponentiation
  58. Closest pair of coordinates in a 2D plane
  59. Find the contiguous slice with the minimum average
  60. Compute maximum sum of subarray (Kadane's algorithm)
  61. Pure-functional double linked list
  62. Binary search in a rotated sorted array
  63. Check if a directed graph has cycles
  64. Rotate Array right in pure-functional Scala - using an unusual immutable efficient approach
  65. Check a binary tree is a search tree
  66. Length of the longest common substring
  67. Sliding Window Rate Limiter
  68. Tic Tac Toe board check
  69. Find an unpaired number in an array
  70. Check if a String is a palindrome
  71. Count binary gap size of a number using tail recursion
  72. Remove duplicates from a sorted list (Sliding)
  73. Monitor success rate of a process that may fail
  74. Least-recently used cache (MRU)
  75. Find sub-array with the maximum sum
  76. Find the minimum absolute difference of two partitions
  77. Find maximum potential profit from an array of stock price
  78. Fibonacci in purely functional immutable Scala
  79. Fizz Buzz in purely functional immutable Scala
  80. Find triplets that sum to a target ('3Sum')
  81. Find combinations adding up to N (non-unique)
  82. Find the minimum item in a rotated sorted array
  83. Make a binary search tree (Red-Black tree)
  84. Mars Rover
  85. Find combinations adding up to N (unique)
  86. Find indices of tuples that sum to a target (Two Sum)
  87. Count factors/divisors of an integer
  88. Compute single-digit sum of digits
  89. Fixed Window Rate Limiter
  90. Traverse a tree Depth-First
  91. Reverse bits of an integer
  92. Find k closest elements to a value in a sorted Array
  93. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  94. 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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