mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
44254cf112
* Rename all Project Euler directories: Reason: The change was done to maintain consistency throughout the directory and to keep all directories in sorted order. Due to the above change, some config files had to be modified: 'problem_22` -> `problem_022` * Update scripts to pad zeroes in PE directories
69 lines
1.9 KiB
Python
69 lines
1.9 KiB
Python
"""
|
|
Problem 33: https://projecteuler.net/problem=33
|
|
|
|
The fraction 49/98 is a curious fraction, as an inexperienced
|
|
mathematician in attempting to simplify it may incorrectly believe
|
|
that 49/98 = 4/8, which is correct, is obtained by cancelling the 9s.
|
|
|
|
We shall consider fractions like, 30/50 = 3/5, to be trivial examples.
|
|
|
|
There are exactly four non-trivial examples of this type of fraction,
|
|
less than one in value, and containing two digits in the numerator
|
|
and denominator.
|
|
|
|
If the product of these four fractions is given in its lowest common
|
|
terms, find the value of the denominator.
|
|
"""
|
|
from fractions import Fraction
|
|
from typing import List
|
|
|
|
|
|
def is_digit_cancelling(num: int, den: int) -> bool:
|
|
if num != den:
|
|
if num % 10 == den // 10:
|
|
if (num // 10) / (den % 10) == num / den:
|
|
return True
|
|
return False
|
|
|
|
|
|
def fraction_list(digit_len: int) -> List[str]:
|
|
"""
|
|
>>> fraction_list(2)
|
|
['16/64', '19/95', '26/65', '49/98']
|
|
>>> fraction_list(3)
|
|
['16/64', '19/95', '26/65', '49/98']
|
|
>>> fraction_list(4)
|
|
['16/64', '19/95', '26/65', '49/98']
|
|
>>> fraction_list(0)
|
|
[]
|
|
>>> fraction_list(5)
|
|
['16/64', '19/95', '26/65', '49/98']
|
|
"""
|
|
solutions = []
|
|
den = 11
|
|
last_digit = int("1" + "0" * digit_len)
|
|
for num in range(den, last_digit):
|
|
while den <= 99:
|
|
if (num != den) and (num % 10 == den // 10) and (den % 10 != 0):
|
|
if is_digit_cancelling(num, den):
|
|
solutions.append(f"{num}/{den}")
|
|
den += 1
|
|
num += 1
|
|
den = 10
|
|
return solutions
|
|
|
|
|
|
def solution(n: int = 2) -> int:
|
|
"""
|
|
Return the solution to the problem
|
|
"""
|
|
result = 1.0
|
|
for fraction in fraction_list(n):
|
|
frac = Fraction(fraction)
|
|
result *= frac.denominator / frac.numerator
|
|
return int(result)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(solution())
|