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142 lines
3.4 KiB
Python
142 lines
3.4 KiB
Python
"""
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Project Euler Problem 89: https://projecteuler.net/problem=89
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For a number written in Roman numerals to be considered valid there are basic rules
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which must be followed. Even though the rules allow some numbers to be expressed in
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more than one way there is always a "best" way of writing a particular number.
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For example, it would appear that there are at least six ways of writing the number
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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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However, according to the rules only XIIIIII and XVI are valid, and the last example
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is considered to be the most efficient, as it uses the least number of numerals.
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The 11K text file, roman.txt (right click and 'Save Link/Target As...'), contains one
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thousand numbers written in valid, but not necessarily minimal, Roman numerals; see
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About... Roman Numerals 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
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consecutive identical units.
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"""
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import os
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SYMBOLS = {"I": 1, "V": 5, "X": 10, "L": 50, "C": 100, "D": 500, "M": 1000}
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def parse_roman_numerals(numerals: str) -> int:
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"""
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Converts a string of roman numerals to an integer.
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e.g.
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>>> parse_roman_numerals("LXXXIX")
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89
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>>> parse_roman_numerals("IIII")
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4
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"""
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total_value = 0
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index = 0
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while index < len(numerals) - 1:
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current_value = SYMBOLS[numerals[index]]
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next_value = SYMBOLS[numerals[index + 1]]
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if current_value < next_value:
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total_value -= current_value
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else:
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total_value += current_value
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index += 1
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total_value += SYMBOLS[numerals[index]]
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return total_value
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def generate_roman_numerals(num: int) -> str:
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"""
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Generates a string of roman numerals for a given integer.
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e.g.
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>>> generate_roman_numerals(89)
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'LXXXIX'
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>>> generate_roman_numerals(4)
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'IV'
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"""
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numerals = ""
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m_count = num // 1000
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numerals += m_count * "M"
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num %= 1000
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c_count = num // 100
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if c_count == 9:
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numerals += "CM"
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c_count -= 9
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elif c_count == 4:
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numerals += "CD"
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c_count -= 4
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if c_count >= 5:
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numerals += "D"
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c_count -= 5
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numerals += c_count * "C"
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num %= 100
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x_count = num // 10
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if x_count == 9:
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numerals += "XC"
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x_count -= 9
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elif x_count == 4:
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numerals += "XL"
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x_count -= 4
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if x_count >= 5:
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numerals += "L"
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x_count -= 5
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numerals += x_count * "X"
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num %= 10
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if num == 9:
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numerals += "IX"
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num -= 9
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elif num == 4:
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numerals += "IV"
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num -= 4
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if num >= 5:
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numerals += "V"
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num -= 5
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numerals += num * "I"
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return numerals
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def solution(roman_numerals_filename: str = "/p089_roman.txt") -> int:
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"""
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Calculates and returns the answer to project euler problem 89.
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>>> solution("/numeralcleanup_test.txt")
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16
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"""
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savings = 0
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file1 = open(os.path.dirname(__file__) + roman_numerals_filename)
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lines = file1.readlines()
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for line in lines:
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original = line.strip()
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num = parse_roman_numerals(original)
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shortened = generate_roman_numerals(num)
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savings += len(original) - len(shortened)
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return savings
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if __name__ == "__main__":
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print(f"{solution() = }")
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