romannumerals.py

#    This program is free software: you can redistribute it and/or modify
#    it under the terms of the GNU General Public License as published by
#    the Free Software Foundation, either version 3 of the License, or
#    (at your option) any later version.

#    This program is distributed in the hope that it will be useful,
#    but WITHOUT ANY WARRANTY; without even the implied warranty of
#    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
#    GNU General Public License for more details.

#    You should have received a copy of the GNU General Public License
#    along with this program.  If not, see <http://www.gnu.org/licenses/>.

# Global dictionary entry
NUMERALS = {'I':1,
            'V':5,
            'X':10,
            'L':50,
            'C':100,
            'D':500,
            'M':1000}

def verify_combo(numeral, first, second):
    """Compares two values for a ratio. The maximal ratio between two numbers in
    the Roman numeral system, it turns out, is 0.1. If this condition is not
    met, throw an exception.
    """

    if first / second >= 0.1:
        pass
    else:
        raise ValueError("{} is not a valid Roman numeral.".format(numeral))

def is_combo(first, second):
    """In case of Roman numeral combos (e.g., IV), the second value is always
    bigger than the first. This function tests against that.
    """

    if first < second:
        return True
    else:
        return False

def compare(numeral, index):
    """Compares preceeding, current and succeeding numeral digits.
    Returns current digit if no combo is present.
    Returns combo value of current digit and succeeding digit are a combo.
    Returns 0 if current digit and preceeding digit are a combo.
    """

    # Initialise integer values.
    try:
        previous = NUMERALS[numeral[index-1]]
        current = NUMERALS[numeral[index]]
        next = NUMERALS[numeral[index+1]]
    except IndexError:
        pass

    if index != len(numeral)-1 and is_combo(current, next):
        verify_combo(numeral, current, next)
        return next - current
    elif index > 0 and is_combo(previous, current):
        return 0
    else:
        return current

def numeral_to_decimal(numeral):
    """Converts a numeral string value to a decimal int value."""
    decimal = 0

    # Loop through every possible letter in the numeral value.
    # Add returned value from compare() to decimal.
    for letter in range(len(numeral)):
        decimal += compare(numeral, letter)

    return decimal

def decimal_to_numeral(decimal):
    """Converts a decimal int value to a numeral string value."""
    numeral = ""
    numeral_tuples = []

    # Generate a tuple of tuples that is ordered (numeral digit, decimal value).
    for letter in sorted(NUMERALS, key=NUMERALS.get, reverse=True):
        numeral_tuples.append((letter, NUMERALS[letter]))

    # For every possible numeral digit.
    for i in range(len(NUMERALS)):
        # Perform below operations until decimal is smaler than the
        # corresponding value of the letter.
        while decimal >= numeral_tuples[i][1]:
            # The magic happens below. Undocumentable.
            if str(decimal).startswith('9')\
            and str(numeral_tuples[i][1]).startswith('5'):
                break
            elif str(decimal).startswith('4'):
                decimal -= numeral_tuples[i-1][1] * 0.8
                numeral += numeral_tuples[i][0] + numeral_tuples[i-1][0]
            elif str(decimal).startswith('9'):
                decimal -= numeral_tuples[i-2][1] * 0.9
                numeral += numeral_tuples[i][0] + numeral_tuples[i-2][0]
            else:
                decimal -= numeral_tuples[i][1]
                numeral += numeral_tuples[i][0]

    return numeral

def main():
    # Test results.
    print(numeral_to_decimal("MCMLIV"))
    print()
    print(numeral_to_decimal("MMVIII"))
    print()
    print(numeral_to_decimal("MCMXC"))
    print()
    print(numeral_to_decimal("MCDIV"))
    #print()
    #print(numeral_to_decimal("IM"))
    print()
    print(numeral_to_decimal(decimal_to_numeral(114)))
    print()
    print(decimal_to_numeral(numeral_to_decimal("MCMLIV")))
    print()
    print(decimal_to_numeral(numeral_to_decimal("MMVIII")))
    print()
    print(numeral_to_decimal(decimal_to_numeral(444)))

if __name__ == "__main__":
    main()