Roman numerals originated from the Etruscan numerals system, which inspired the Roman numeral symbols:
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
Algorithm in Scala
56 lines of Scala (compatible versions 2.13 & 3.0).
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
Scala concepts & Hints
'collect' allows you to use Pattern Matching, to filter and map items.
Drop, Take, dropRight, takeRight
Scala's `drop` and `take` methods typically remove or select `n` items from a collection.
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!
Pattern matching in Scala lets you quickly identify what you are looking for in a data, and also extract it.
scanLeft and scanRight
Scala's `scan` functions enable you to do folds like foldLeft and foldRight, while collecting the intermediate results
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.
In Scala, tail recursion enables you to rewrite a mutable structure such as a while-loop, into an immutable algorithm.
'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.