 # PercyGrunwald's solution

## to Roman Numerals in the Elixir Track

Published at Jan 03 2019 · 0 comments
Instructions
Test suite
Solution

Write a function to convert from normal numbers to Roman Numerals.

The Romans were a clever bunch. They conquered most of Europe and ruled it for hundreds of years. They invented concrete and straight roads and even bikinis. One thing they never discovered though was the number zero. This made writing and dating extensive histories of their exploits slightly more challenging, but the system of numbers they came up with is still in use today. For example the BBC uses Roman numerals to date their programmes.

The Romans wrote numbers using letters - I, V, X, L, C, D, M. (notice these letters have lots of straight lines and are hence easy to hack into stone tablets).

`````` 1  => I
10  => X
7  => VII
``````

There is no need to be able to convert numbers larger than about 3000. (The Romans themselves didn't tend to go any higher)

Wikipedia says: Modern Roman numerals ... are written by expressing each digit separately starting with the left most digit and skipping any digit with a value of zero.

To see this in practice, consider the example of 1990.

In Roman numerals 1990 is MCMXC:

1000=M 900=CM 90=XC

2008 is written as MMVIII:

2000=MM 8=VIII

## Running tests

Execute the tests with:

``````\$ elixir roman_numerals_test.exs
``````

### Pending tests

In the test suites, all but the first test have been skipped.

Once you get a test passing, you can unskip the next one by commenting out the relevant `@tag :pending` with a `#` symbol.

For example:

``````# @tag :pending
test "shouting" do
assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
``````

Or, you can enable all the tests by commenting out the `ExUnit.configure` line in the test suite.

``````# ExUnit.configure exclude: :pending, trace: true
``````

If you're stuck on something, it may help to look at some of the available resources out there where answers might be found.

## Source

The Roman Numeral Kata http://codingdojo.org/cgi-bin/index.pl?KataRomanNumerals

## Submitting Incomplete Solutions

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

### roman_numerals_test.exs

``````if !System.get_env("EXERCISM_TEST_EXAMPLES") do
end

ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)

defmodule RomanTest do
use ExUnit.Case

# @tag :pending
test "1" do
assert Roman.numerals(1) == "I"
end

@tag :pending
test "2" do
assert Roman.numerals(2) == "II"
end

@tag :pending
test "3" do
assert Roman.numerals(3) == "III"
end

@tag :pending
test "4" do
assert Roman.numerals(4) == "IV"
end

@tag :pending
test "5" do
assert Roman.numerals(5) == "V"
end

@tag :pending
test "6" do
assert Roman.numerals(6) == "VI"
end

@tag :pending
test "9" do
assert Roman.numerals(9) == "IX"
end

@tag :pending
test "27" do
assert Roman.numerals(27) == "XXVII"
end

@tag :pending
test "48" do
assert Roman.numerals(48) == "XLVIII"
end

@tag :pending
test "59" do
assert Roman.numerals(59) == "LIX"
end

@tag :pending
test "93" do
assert Roman.numerals(93) == "XCIII"
end

@tag :pending
test "141" do
assert Roman.numerals(141) == "CXLI"
end

@tag :pending
test "163" do
assert Roman.numerals(163) == "CLXIII"
end

@tag :pending
test "402" do
assert Roman.numerals(402) == "CDII"
end

@tag :pending
test "575" do
assert Roman.numerals(575) == "DLXXV"
end

@tag :pending
test "911" do
assert Roman.numerals(911) == "CMXI"
end

@tag :pending
test "1024" do
assert Roman.numerals(1024) == "MXXIV"
end

@tag :pending
test "3000" do
assert Roman.numerals(3000) == "MMM"
end
end``````
``````defmodule Roman do
@int_to_roman_numeral_map %{
1 => "I",
5 => "V",
10 => "X",
50 => "L",
100 => "C",
500 => "D",
1000 => "M"
}

@doc """
Convert the number to a roman number.
"""
@spec numerals(pos_integer) :: String.t()
def numerals(number) do
number
|> split_integer()
|> multiply_by_ten_power()
|> Enum.reject(fn int -> int == 0 end)
|> Enum.map(&get_combined_numbers/1)
|> List.flatten()
|> Enum.map(&Map.get(@int_to_roman_numeral_map, &1, ""))
|> Enum.join()
end

defp split_integer(int) do
int
|> Kernel.to_string()
|> String.split("", trim: true)
|> Enum.map(fn int_string ->
Integer.parse(int_string)
|> case do
{int, _} ->
int

_ ->
0
end
end)
end

defp multiply_by_ten_power(int_list) do
int_list
|> Enum.with_index(1)
|> Enum.map(fn {int, index} ->
ten_factor = :math.pow(10, length(int_list) - index) |> :erlang.floor()

int * ten_factor
end)
end

defp get_combined_numbers(int, acc \\ {[], 0}) do
is_negative? = int < 0
abs_int = :erlang.abs(int)
number_pool = Map.keys(@int_to_roman_numeral_map)
{acc_list, last_index_inserted} = acc
{difference, closest_int} = get_difference_and_closest_int(abs_int, number_pool)

index_to_insert =
if is_negative? do
last_index_inserted - 1
else
last_index_inserted + 1
end

acc_list = List.insert_at(acc_list, index_to_insert, closest_int)

if difference == 0 do
acc_list
else
get_combined_numbers(difference, {acc_list, index_to_insert})
end
end

defp get_difference_and_closest_int(abs_int, number_pool) do
number_pool_with_differences =
number_pool
|> Enum.map(fn int_to_compare ->
{abs_int - int_to_compare, int_to_compare}
end)

{{difference, closest_int}, index} =
number_pool_with_differences
|> Enum.with_index()
|> Enum.min_by(fn {{difference, _int_to_compare}, _index} ->
:erlang.abs(difference)
end)

cond do
difference == 0 ->
{difference, closest_int}

difference > 0 ->
{difference, closest_int}

difference < 0 ->
# 85 => LXXXV
# 85 => ... ___{35, 50}___, {-15, 100} ...
#
# 90 => XVC
# 90 => ... {40, 50}, ___{-10, 100}___ ...
abs_difference = :erlang.abs(difference)

exact_match = Enum.find(number_pool, fn number -> number == abs_difference end)

if not is_nil(exact_match) do
{difference, closest_int}
else
Enum.at(number_pool_with_differences, index - 1)
end
end
end
end``````