How to resolve the algorithm Roman numerals/Decode step by step in the Python programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Roman numerals/Decode step by step in the Python programming language

Table of Contents

Problem Statement

Create a function that takes a Roman numeral as its argument and returns its value as a numeric decimal integer. You don't need to validate the form of the Roman numeral. Modern Roman numerals are written by expressing each decimal digit of the number to be encoded separately, starting with the leftmost decimal digit and skipping any 0s   (zeroes). 1990 is rendered as   MCMXC     (1000 = M,   900 = CM,   90 = XC)     and 2008 is rendered as   MMVIII       (2000 = MM,   8 = VIII). The Roman numeral for 1666,   MDCLXVI,   uses each letter in descending order.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Roman numerals/Decode step by step in the Python programming language

1. First implementation:

  • This function decodes a Roman numeral string into an integer. It uses a dictionary to map Roman numeral symbols to their corresponding integer values and then iterates through the input string, calculating the value of the numeral.
  • It handles special cases where a symbol with a lower value precedes a symbol with a higher value (e.g., "IV" represents 4 instead of 6).
  • The function returns the decoded integer value.

2. Second implementation:

  • This function decodes a Roman numeral string into an integer. It uses a list of tuples, each containing a Roman numeral symbol and its corresponding integer value.
  • It iterates through the list, matching the input string to the symbols and adding the corresponding integer values.
  • It returns the decoded integer value.

3. Third implementation:

  • This function decodes a Roman numeral string into an integer. It uses a dictionary to map Roman numeral symbols to their corresponding integer values.
  • It reduces a list of integer values, starting from 0, by adding or subtracting the value of each symbol in the input string.
  • It returns the decoded integer value.

4. Fourth implementation (functional):

  • This function decodes a Roman numeral string into an integer using a functional approach.
  • It uses a defaultdict to map Roman numeral symbols to their corresponding integer values.
  • It reduces a list of integer values, starting from 0, by adding or subtracting the value of each symbol in the input string.
  • It returns the decoded integer value, if the input string is valid (i.e., contains only valid Roman numeral symbols).

5. Test Code:

  • The test code executes each of the implementations with sample Roman numeral strings and prints the decoded integer values.

Source code in the python programming language

_rdecode = dict(zip('MDCLXVI', (1000, 500, 100, 50, 10, 5, 1)))

def decode( roman ):
    result = 0
    for r, r1 in zip(roman, roman[1:]):
        rd, rd1 = _rdecode[r], _rdecode[r1]
        result += -rd if rd < rd1 else rd
    return result + _rdecode[roman[-1]]

if __name__ == '__main__':
    for r in 'MCMXC MMVIII MDCLXVI'.split():
        print( r, decode(r) )


roman_values = (('I',1), ('IV',4), ('V',5), ('IX',9),('X',10),('XL',40),('L',50),('XC',90),('C',100),
                    ('CD', 400), ('D', 500), ('CM', 900), ('M',1000))

def roman_value(roman):
    total=0
    for symbol,value in reversed(roman_values):
        while roman.startswith(symbol):
            total += value
            roman = roman[len(symbol):]
    return total

if __name__=='__main__':
    for value in "MCMXC", "MMVIII", "MDCLXVI":
        print('%s = %i' % (value, roman_value(value)))


numerals = { 'M' : 1000, 'D' : 500, 'C' : 100, 'L' : 50, 'X' : 10, 'V' : 5, 'I' : 1 }
def romannumeral2number(s):
        return reduce(lambda x, y: -x + y if x < y else x + y, map(lambda x: numerals.get(x, 0), s.upper()))


'''Roman numerals decoded'''

from operator import mul
from functools import reduce
from collections import defaultdict
from itertools import accumulate, chain, cycle


# intFromRoman :: String -> Maybe Int
def intFromRoman(s):
    '''Just the integer represented by a Roman
       numeral string, or Nothing if any
       characters are unrecognised.
    '''
    dct = defaultdict(
        lambda: None,
        zip(
            'IVXLCDM',
            accumulate(chain([1], cycle([5, 2])), mul)
        )
    )

    def go(mb, x):
        '''Just a letter value added to or
           subtracted from a total, or Nothing
           if no letter value is defined.
        '''
        if None in (mb, x):
            return None
        else:
            r, total = mb
            return x, total + (-x if x < r else x)

    return bindMay(reduce(
        go,
        [dct[k.upper()] for k in reversed(list(s))],
        (0, 0)
    ))(snd)


# ------------------------- TEST -------------------------
def main():
    '''Testing a sample of dates.'''

    print(
        fTable(__doc__ + ':\n')(str)(
            maybe('(Contains unknown character)')(str)
        )(
            intFromRoman
        )([
            "MDCLXVI", "MCMXC", "MMVIII",
            "MMXVI", "MMXVIII", "MMZZIII"
        ])
    )


# ----------------------- GENERIC ------------------------

# bindMay (>>=) :: Maybe a -> (a -> Maybe b) -> Maybe b
def bindMay(m):
    '''Injection operator for the Maybe monad.
       If m is Nothing, it is passed straight through.
       If m is Just(x), the result is an application
       of the (a -> Maybe b) function (mf) to x.'''
    return lambda mf: (
        m if None is m else mf(m)
    )


# maybe :: b -> (a -> b) -> Maybe a -> b
def maybe(v):
    '''Either the default value v, if m is Nothing,
       or the application of f to x,
       where m is Just(x).
    '''
    return lambda f: lambda m: v if None is m else (
        f(m)
    )


# snd :: (a, b) -> b
def snd(ab):
    '''Second member of a pair.'''
    return ab[1]


# ---------------------- FORMATTING ----------------------

# fTable :: String -> (a -> String) ->
# (b -> String) -> (a -> b) -> [a] -> String
def fTable(s):
    '''Heading -> x display function ->
       fx display function -> f -> xs -> tabular string.
    '''
    def go(xShow, fxShow, f, xs):
        ys = [xShow(x) for x in xs]
        w = max(map(len, ys))
        return s + '\n' + '\n'.join(map(
            lambda x, y: (
                f'{y.rjust(w, " ")} -> {fxShow(f(x))}'
            ),
            xs, ys
        ))
    return lambda xShow: lambda fxShow: lambda f: (
        lambda xs: go(xShow, fxShow, f, xs)
    )


# MAIN ---
if __name__ == '__main__':
    main()


  

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