Scala algorithm: Compute a Roman numeral for an Integer, and vice-versa

Published

Algorithm goal

Roman numerals originated from the Etruscan numerals system, which inspired the Roman numeral symbols:

Table of Roman numeral symbols
73868876676877
1510501005001000

In this system, 1 is 'I', 8 is 'VIII', 4 is 'IV', 199 is 'CXCIX' (\(100 + (90 + 9)\)).

Our goal is to convert between this representation and our Arabic numerical representation. Since the Roman numeral system is limited, going above 5000 is note necessary.

Test cases in Scala

assert(romanNumeral(1) == "I")
assert(romanNumeral(8) == "VIII")
assert(romanNumeral(39) == "XXXIX")
assert(romanNumeral(246) == "CCXLVI")
assert(romanNumeral(789) == "DCCLXXXIX")
assert(romanNumeral(2421) == "MMCDXXI")
assert(parseRomanNumeral("I") == Some(1))
assert(parseRomanNumeral("w") == None)
assert(parseRomanNumeral("VIII") == Some(8))
assert(parseRomanNumeral("XXXIX") == Some(39))
assert(parseRomanNumeral("CCXLVI") == Some(246))
assert(parseRomanNumeral("DCCLXXXIX") == Some(789))
assert(parseRomanNumeral("MMCDXXI") == Some(2421))
assert(
  {
    val randomNumber = scala.util.Random.nextInt(5000) + 1
    parseRomanNumeral(romanNumeral(randomNumber)).contains(randomNumber)
  },
  "A random number is checked without issue"
)

Algorithm in Scala

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

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Explanation

There are two major approaches - one which involves subtraction and another which does not. We use the approach that does not, because it is generally more readable.

For both converting to Roman, and converting from Roman, we use a Numeral table, which describes each significant fragment's value. (this is © from www.scala-algorithms.com)

How this table is used

Full explanation is available to subscribers Scala algorithms logo, maze part, which looks quirky

Scala concepts & Hints

  1. Collect

    'collect' allows you to use Pattern Matching, to filter and map items.

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

  2. Drop, Take, dropRight, takeRight

    Scala's `drop` and `take` methods typically remove or select `n` items from a collection.

    assert(List(1, 2, 3).drop(2) == List(3))

assert(List(1, 2, 3).take(2) == List(1, 2))

assert(List(1, 2, 3).dropRight(2) == List(1))

assert(List(1, 2, 3).takeRight(2) == List(2, 3))

assert((1 to 5).take(2) == (1 to 2))

  3. 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)

  4. 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")

  5. scanLeft and scanRight

    Scala's `scan` functions enable you to do folds like foldLeft and foldRight, while collecting the intermediate results

    assert(List(1, 2, 3, 4, 5).scanLeft(0)(_ + _) == List(0, 1, 3, 6, 10, 15))

  6. 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)

  7. 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)

  8. Zip

    'zip' allows you to combine two lists pair-wise (meaning turn a pair of lists, into a list of pairs)

    It can be used over Arrays, Lists, Views, Iterators and other collections.

    assert(List(1, 2, 3).zip(List(5, 6, 7)) == List(1 -> 5, 2 -> 6, 3 -> 7))

assert(List(1, 2).zip(List(5, 6, 7)) == List(1 -> 5, 2 -> 6))

assert(List(5, 6).zipWithIndex == List(5 -> 0, 6 -> 1))

assert(List(5, 6).zipAll(List('A'), 9, 'Z') == List(5 -> 'A', 6 -> 'Z'))

assert(List(5).zipAll(List('A', 'B'), 1, 'Z') == List(5 -> 'A', 1 -> 'B'))

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  1. Compute the length of longest valid parentheses
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  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. Check word in grid (depth-first search)
  11. Maximum wait at a fuel station
  12. Find minimum missing positive number in a sequence
  13. Least-recently used cache (LRU)
  14. Count pairs of a given expected sum
  15. Binary heap (min-heap)
  16. Compute a Roman numeral for an Integer, and vice-versa
  17. Compute keypad possibilities
  18. Matching parentheses algorithm with foldLeft and a state machine
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  40. Balanced parentheses algorithm with tail-call recursion optimisation
  41. Reverse a String's words efficiently
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  43. Count passing cars
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  57. Find the longest palindrome within a string
  58. Find the index of a substring ('indexOf')
  59. Reshape a matrix
  60. Compute the steps to transform an anagram only using swaps
  61. Compute modulo of an exponent without exponentiation
  62. Closest pair of coordinates in a 2D plane
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  65. Pure-functional double linked list
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  77. Monitor success rate of a process that may fail
  78. Least-recently used cache (MRU)
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  84. Find triplets that sum to a target ('3Sum')
  85. Find combinations adding up to N (non-unique)
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  90. Find indices of tuples that sum to a target (Two Sum)
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  93. Fixed Window Rate Limiter
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  96. Check Sudoku board
  97. Find k closest elements to a value in a sorted Array
  98. Print a binary tree vertically
  99. QuickSelect Selection Algorithm (kth smallest item/order statistic)
  100. Rotate a matrix by 90 degrees clockwise

Explore the 22 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. Variance
  21. View
  22. Zip

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