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Published at Jul 13 2018
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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

See also: http://www.novaroma.org/via_romana/numbers.html

For installation and learning resources, refer to the exercism help page.

For running the tests provided, you will need the Minitest gem. Open a terminal window and run the following command to install minitest:

```
gem install minitest
```

If you would like color output, you can `require 'minitest/pride'`

in
the test file, or note the alternative instruction, below, for running
the test file.

Run the tests from the exercise directory using the following command:

```
ruby roman_numerals_test.rb
```

To include color from the command line:

```
ruby -r minitest/pride roman_numerals_test.rb
```

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

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

```
require 'minitest/autorun'
require_relative 'roman_numerals'
# Common test data version: 1.0.0 070e8d5
class RomanNumeralsTest < Minitest::Test
def test_1
# skip
assert_equal 'I', 1.to_roman
end
def test_2
skip
assert_equal 'II', 2.to_roman
end
def test_3
skip
assert_equal 'III', 3.to_roman
end
def test_4
skip
assert_equal 'IV', 4.to_roman
end
def test_5
skip
assert_equal 'V', 5.to_roman
end
def test_6
skip
assert_equal 'VI', 6.to_roman
end
def test_9
skip
assert_equal 'IX', 9.to_roman
end
def test_27
skip
assert_equal 'XXVII', 27.to_roman
end
def test_48
skip
assert_equal 'XLVIII', 48.to_roman
end
def test_59
skip
assert_equal 'LIX', 59.to_roman
end
def test_93
skip
assert_equal 'XCIII', 93.to_roman
end
def test_141
skip
assert_equal 'CXLI', 141.to_roman
end
def test_163
skip
assert_equal 'CLXIII', 163.to_roman
end
def test_402
skip
assert_equal 'CDII', 402.to_roman
end
def test_575
skip
assert_equal 'DLXXV', 575.to_roman
end
def test_911
skip
assert_equal 'CMXI', 911.to_roman
end
def test_1024
skip
assert_equal 'MXXIV', 1024.to_roman
end
def test_3000
skip
assert_equal 'MMM', 3000.to_roman
end
# Problems in exercism evolve over time, as we find better ways to ask
# questions.
# The version number refers to the version of the problem you solved,
# not your solution.
#
# Define a constant named VERSION inside of the top level BookKeeping
# module, which may be placed near the end of your file.
#
# In your file, it will look like this:
#
# module BookKeeping
# VERSION = 1 # Where the version number matches the one in the test.
# end
#
# If you are curious, read more about constants on RubyDoc:
# http://ruby-doc.org/docs/ruby-doc-bundle/UsersGuide/rg/constants.html
def test_bookkeeping
skip
assert_equal 2, BookKeeping::VERSION
end
end
```

```
class Fixnum
def to_roman
RomanNumeral.to_roman(self)
end
end
module RomanNumeral
ROMAN_NUMERALS = {
1 => 'I',
5 => 'V',
10 => 'X',
50 => 'L',
100 => 'C',
500 => 'D',
1000 => 'M'
}
def self.to_roman(integer)
unless (0...4000).include? integer
raise RangeError, "#{integer}:#{integer.class} can't be written as a Roman numeral"
end
roman = ''
digits(integer).each_with_index do |digit, index|
exponent = digits(integer).length - index - 1
roman << roman_digit_notation(digit, exponent)
end
roman
end
private
def self.digits(integer)
integer.to_s.chars.map(&:to_i)
end
def self.digit?(digit)
(0..9).include? digit
end
def self.roman_digit_notation(digit, exponent)
unless digit? digit
raise RangeError, "#{digit}:#{digit.class} is not a digit"
end
case digit
when 4, 9
subtractive_roman_digit_notation(digit, exponent)
when (1..3), (5..8)
additive_roman_digit_notation(digit, exponent)
else
''
end
end
def self.additive_roman_digit_notation(digit, exponent)
augend = digit < 5 ? 1 : 5
augend_character = ROMAN_NUMERALS[augend * 10**exponent]
addend = digit - augend
addend_character = ROMAN_NUMERALS[10**exponent]
"#{ augend_character }#{ addend_character * addend }"
end
def self.subtractive_roman_digit_notation(digit, exponent)
minuend = digit > 5 ? 10 : 5
minuend_character = ROMAN_NUMERALS[minuend * 10**exponent]
subtrahend = minuend - digit
subtrahend_character = ROMAN_NUMERALS[10**exponent]
"#{ subtrahend_character * subtrahend }#{ minuend_character }"
end
end
```

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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