integer-to-roman.rb

# Seven different symbols represent Roman numerals with the following values:
# Symbol	Value
# I	1
# V	5
# X	10
# L	50
# C	100
# D	500
# M	1000

# Roman numerals are formed by appending the conversions of decimal place values from highest to lowest. Converting a decimal place value into a Roman numeral has the following rules:

#     If the value does not start with 4 or 9, select the symbol of the maximal value that can be subtracted from the input, append that symbol to the result, subtract its value, and convert the remainder to a Roman numeral.
#     If the value starts with 4 or 9 use the subtractive form representing one symbol subtracted from the following symbol, for example, 4 is 1 (I) less than 5 (V): IV and 9 is 1 (I) less than 10 (X): IX. Only the following subtractive forms are used: 4 (IV), 9 (IX), 40 (XL), 90 (XC), 400 (CD) and 900 (CM).
#     Only powers of 10 (I, X, C, M) can be appended consecutively at most 3 times to represent multiples of 10. You cannot append 5 (V), 50 (L), or 500 (D) multiple times. If you need to append a symbol 4 times use the subtractive form.

# Given an integer, convert it to a Roman numeral.

# Example 1:

# Input: num = 3749

# Output: "MMMDCCXLIX"

# Explanation:

# 3000 = MMM as 1000 (M) + 1000 (M) + 1000 (M)
#  700 = DCC as 500 (D) + 100 (C) + 100 (C)
#   40 = XL as 10 (X) less of 50 (L)
#    9 = IX as 1 (I) less of 10 (X)
# Note: 49 is not 1 (I) less of 50 (L) because the conversion is based on decimal places

# Example 2:

# Input: num = 58

# Output: "LVIII"

# Explanation:

# 50 = L
#  8 = VIII

# Example 3:

# Input: num = 1994

# Output: "MCMXCIV"

# Explanation:

# 1000 = M
#  900 = CM
#   90 = XC
#    4 = IV

# Constraints:

#     1 <= num <= 3999

# @param {Integer} num
# @return {String}
# @param {Integer} num
# @return {String}
def int_to_roman(num)
    
  magnitudes = [1000, 100, 10, 1]
  magnitude_symbols = ['M', 'C', 'X', 'I']
  half_symbols = ['', 'D', 'L', 'V']
  remainder = num
  roman = ''

  magnitudes.each_with_index do |magnitude, i|

      current_value =  remainder / magnitude

      if current_value <= 3
          current_value.times do
              roman << magnitude_symbols[i]
          end
      elsif current_value == 4
          roman << magnitude_symbols[i]
          roman << half_symbols[i]
      elsif current_value > 4 && current_value < 9
          roman << half_symbols[i]
          (current_value - 5).times do
              roman << magnitude_symbols[i]
          end
      else
          roman << magnitude_symbols[i]
          roman << magnitude_symbols[i - 1]
      end   

      remainder = remainder % magnitude 

  end  

  roman
end