#import "../helpers.typ": *
#import "../solutions/s0012.typ": *

= Integer to Roman

Roman numerals are represented by seven different symbols: `I`, `V`, `X`, `L`, `C`, `D` and `M`.

#align(center)[#table(
  columns: (auto, auto),
  align: center,
  [*Symbol*], [*Value*],
  [I], [1],
  [V], [5],
  [X], [10],
  [L], [50],
  [C], [100],
  [D], [500],
  [M], [1000],
)]

For example, `2` is written as `II` in Roman numeral, just two one's added together. `12` is written as `XII`, which is simply `X + II`. The number `27` is written as `XXVII`, which is `XX + V + II`.

Roman numerals are usually written largest to smallest from left to right. However, the numeral for four is not `IIII`. Instead, the number four is written as `IV`. Because the one is before the five we subtract it making four. The same principle applies to the number nine, which is written as `IX`. There are six instances where subtraction is used:

- `I` can be placed before `V` (5) and `X` (10) to make 4 and 9. 
- `X` can be placed before `L` (50) and `C` (100) to make 40 and 90. 
- `C` can be placed before `D` (500) and `M` (1000) to make 400 and 900.

Given an integer, convert it to a roman numeral.

#let integer-to-roman(num) = {
  // Solve the problem here
}

#testcases(
  integer-to-roman,
  integer-to-roman-ref, (
    (num: 3),
    (num: 58),
    (num: 1994)
  )
)
