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

Algorithm goal

Roman numerals became originate 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.

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

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Scala Concepts & Hints

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")

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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))

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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)

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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")

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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))

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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)

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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)

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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))

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Algorithm in Scala

60 lines of Scala (version 2.13).

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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"
)
def romanNumeral(n: Int): String = ???

def parseRomanNumeral(num: String): Option[Int] = ???