mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
cecf43d648
* Pyupgrade to Python 3.9
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
142 lines
3.4 KiB
Python
142 lines
3.4 KiB
Python
"""
|
|
Project Euler Problem 89: https://projecteuler.net/problem=89
|
|
|
|
For a number written in Roman numerals to be considered valid there are basic rules
|
|
which must be followed. Even though the rules allow some numbers to be expressed in
|
|
more than one way there is always a "best" way of writing a particular number.
|
|
|
|
For example, it would appear that there are at least six ways of writing the number
|
|
sixteen:
|
|
|
|
IIIIIIIIIIIIIIII
|
|
VIIIIIIIIIII
|
|
VVIIIIII
|
|
XIIIIII
|
|
VVVI
|
|
XVI
|
|
|
|
However, according to the rules only XIIIIII and XVI are valid, and the last example
|
|
is considered to be the most efficient, as it uses the least number of numerals.
|
|
|
|
The 11K text file, roman.txt (right click and 'Save Link/Target As...'), contains one
|
|
thousand numbers written in valid, but not necessarily minimal, Roman numerals; see
|
|
About... Roman Numerals for the definitive rules for this problem.
|
|
|
|
Find the number of characters saved by writing each of these in their minimal form.
|
|
|
|
Note: You can assume that all the Roman numerals in the file contain no more than four
|
|
consecutive identical units.
|
|
"""
|
|
|
|
import os
|
|
|
|
SYMBOLS = {"I": 1, "V": 5, "X": 10, "L": 50, "C": 100, "D": 500, "M": 1000}
|
|
|
|
|
|
def parse_roman_numerals(numerals: str) -> int:
|
|
"""
|
|
Converts a string of roman numerals to an integer.
|
|
e.g.
|
|
>>> parse_roman_numerals("LXXXIX")
|
|
89
|
|
>>> parse_roman_numerals("IIII")
|
|
4
|
|
"""
|
|
|
|
total_value = 0
|
|
|
|
index = 0
|
|
while index < len(numerals) - 1:
|
|
current_value = SYMBOLS[numerals[index]]
|
|
next_value = SYMBOLS[numerals[index + 1]]
|
|
if current_value < next_value:
|
|
total_value -= current_value
|
|
else:
|
|
total_value += current_value
|
|
index += 1
|
|
total_value += SYMBOLS[numerals[index]]
|
|
|
|
return total_value
|
|
|
|
|
|
def generate_roman_numerals(num: int) -> str:
|
|
"""
|
|
Generates a string of roman numerals for a given integer.
|
|
e.g.
|
|
>>> generate_roman_numerals(89)
|
|
'LXXXIX'
|
|
>>> generate_roman_numerals(4)
|
|
'IV'
|
|
"""
|
|
|
|
numerals = ""
|
|
|
|
m_count = num // 1000
|
|
numerals += m_count * "M"
|
|
num %= 1000
|
|
|
|
c_count = num // 100
|
|
if c_count == 9:
|
|
numerals += "CM"
|
|
c_count -= 9
|
|
elif c_count == 4:
|
|
numerals += "CD"
|
|
c_count -= 4
|
|
if c_count >= 5:
|
|
numerals += "D"
|
|
c_count -= 5
|
|
numerals += c_count * "C"
|
|
num %= 100
|
|
|
|
x_count = num // 10
|
|
if x_count == 9:
|
|
numerals += "XC"
|
|
x_count -= 9
|
|
elif x_count == 4:
|
|
numerals += "XL"
|
|
x_count -= 4
|
|
if x_count >= 5:
|
|
numerals += "L"
|
|
x_count -= 5
|
|
numerals += x_count * "X"
|
|
num %= 10
|
|
|
|
if num == 9:
|
|
numerals += "IX"
|
|
num -= 9
|
|
elif num == 4:
|
|
numerals += "IV"
|
|
num -= 4
|
|
if num >= 5:
|
|
numerals += "V"
|
|
num -= 5
|
|
numerals += num * "I"
|
|
|
|
return numerals
|
|
|
|
|
|
def solution(roman_numerals_filename: str = "/p089_roman.txt") -> int:
|
|
"""
|
|
Calculates and returns the answer to project euler problem 89.
|
|
|
|
>>> solution("/numeralcleanup_test.txt")
|
|
16
|
|
"""
|
|
|
|
savings = 0
|
|
|
|
file1 = open(os.path.dirname(__file__) + roman_numerals_filename)
|
|
lines = file1.readlines()
|
|
for line in lines:
|
|
original = line.strip()
|
|
num = parse_roman_numerals(original)
|
|
shortened = generate_roman_numerals(num)
|
|
savings += len(original) - len(shortened)
|
|
|
|
return savings
|
|
|
|
|
|
if __name__ == "__main__":
|
|
|
|
print(f"{solution() = }")
|