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85 lines
2.6 KiB
Python
85 lines
2.6 KiB
Python
"""Develop a method to express Roman numerals in minimal form.
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The rules for writing Roman numerals allow for many ways of writing each number (see FAQ: Roman Numerals). However, there is always a "best" way of writing a particular number.
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For example, the following represent all of the legitimate ways of writing the number sixteen:
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IIIIIIIIIIIIIIII
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VIIIIIIIIIII
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VVIIIIII
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XIIIIII
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VVVI
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XVI
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The last example being considered the most efficient, as it uses the least number of numerals.
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The 11K text file, roman.txt (p089/roman.txt), contains one thousand numbers written in valid, but not necessarily minimal, Roman numerals; that is, they are arranged in descending units and obey the subtractive pair rule (see FAQ for the definitive rules for this problem).
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Find the number of characters saved by writing each of these in their minimal form.
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Note: You can assume that all the Roman numerals in the file contain no more than four consecutive identical units.
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"""
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ROMAN_NUMERALS = {
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'I': 1,
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'V': 5,
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'X': 10,
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'L': 50,
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'C': 100,
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'D': 500,
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'M': 1000
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}
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def roman_to_decimal(s):
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# Read in roman digits in reverse
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last = None
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total = 0
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for c in s[::-1]:
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val = ROMAN_NUMERALS[c]
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if last and val < last:
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total = total - val
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else:
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total = total + val
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last = val
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return total
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def decimal_to_roman(n):
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roman = ''
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lookup = dict([(v, k) for (k, v) in ROMAN_NUMERALS.iteritems()])
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values = sorted(ROMAN_NUMERALS.values())
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total = 0
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subtracted = False
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for i in xrange(len(values)):
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val = values[i]
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if val == max(values):
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count = n // val
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roman = (lookup[val] * count) + roman
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else:
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nn = (n - total) % values[i + 1]
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count = nn // val
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if count > 3:
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roman = lookup[val] + lookup[values[i + 2]] + roman
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subtracted = True
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else:
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if count and subtracted:
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count = count - 1
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subtracted = False
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roman = (lookup[val] * count) + roman
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total = total + nn
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return roman
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def main():
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saved = 0
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with open('p089/roman.txt', 'r') as f:
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while True:
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line = f.readline()
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if not line:
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break
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old = line.strip()
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new = decimal_to_roman(roman_to_decimal(old))
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print roman_to_decimal(old), old, new
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saved = saved + (len(old) - len(new))
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print 'Saved:', saved
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if __name__ == '__main__':
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main()
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