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def roman(number):
# define lookup table (as a tuple of tuples, in this case)
table = (
('I', 'II', 'III', 'IV', 'V', 'VI', 'VII', 'VIII', 'IX'),
('X', 'XX', 'XXX', 'XL', 'L', 'LX', 'LXX', 'LXXX', 'XC'),
('C', 'CC', 'CCC', 'CD', 'D', 'DC', 'DCC', 'DCCC', 'CM'),
('M', 'MM', 'MMM'))
# convert the input integer to a list of single digits
digits = [int(d) for d in str(number)]
# get the row in the lookup table for the most-significant decimal digit
inverter = len(digits) - 1
# translate decimal digits list to Roman numerals list
roman_digits = [table[inverter - i][d - 1] for i, d in enumerate(digits) if d != 0]
# convert the list of Roman numerals to a single string
return ''.join(roman_digits)
In this approach we loop over decimal digits, not their Roman equivalents.
The key point is to have a 2-dimensional lookup table, with each row corresponding to a separate digit: ones, tens, hundreds, thousands. Each digit can then be converted to its Roman equivalent with a single lookup.
Note that we need to compensate for Python's zero-based indexing by (in effect) subtracting 1 from each row and column.
Variation #1
In the code above, we used the inverter variable to work bottom-to-top through the lookup table.
This allows working left-to-right through the decimal digits.
Alternatively, we could reverse the digits list, go top-to-bottom through the lookup table, then reverse the roman_digits list before the final join().
def roman(number):
# define lookup table (as a tuple of tuples, in this case)
table = (
('I', 'II', 'III', 'IV', 'V', 'VI', 'VII', 'VIII', 'IX'),
('X', 'XX', 'XXX', 'XL', 'L', 'LX', 'LXX', 'LXXX', 'XC'),
('C', 'CC', 'CCC', 'CD', 'D', 'DC', 'DCC', 'DCCC', 'CM'),
('M', 'MM', 'MMM'))
# convert the input integer to a list of single digits, in reverse order
digits = [int(d) for d in str(number)][::-1]
# translate decimal digits list to Roman numerals list
roman_digits = [table[i][d - 1] for i, d in enumerate(digits) if d != 0]
# reverse the list of Roman numerals and convert to a single string
return ''.join(roman_digits[::-1])
This eliminates one line of code, at the cost of adding two list reverses.
The [::-1] indexing is idiomatic Python, but less experienced programmers may not find it very readable.
Credit
This approach was adapted from one created by @cmcaine on the Julia track.
