mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-21 02:30:15 +00:00
9701e459e8
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
49 lines
1.2 KiB
Python
49 lines
1.2 KiB
Python
"""
|
|
Project Euler Problem 100: https://projecteuler.net/problem=100
|
|
|
|
If a box contains twenty-one coloured discs, composed of fifteen blue discs and
|
|
six red discs, and two discs were taken at random, it can be seen that
|
|
the probability of taking two blue discs, P(BB) = (15/21) x (14/20) = 1/2.
|
|
|
|
The next such arrangement, for which there is exactly 50% chance of taking two blue
|
|
discs at random, is a box containing eighty-five blue discs and thirty-five red discs.
|
|
|
|
By finding the first arrangement to contain over 10^12 = 1,000,000,000,000 discs
|
|
in total, determine the number of blue discs that the box would contain.
|
|
"""
|
|
|
|
|
|
def solution(min_total: int = 10**12) -> int:
|
|
"""
|
|
Returns the number of blue discs for the first arrangement to contain
|
|
over min_total discs in total
|
|
|
|
>>> solution(2)
|
|
3
|
|
|
|
>>> solution(4)
|
|
15
|
|
|
|
>>> solution(21)
|
|
85
|
|
"""
|
|
|
|
prev_numerator = 1
|
|
prev_denominator = 0
|
|
|
|
numerator = 1
|
|
denominator = 1
|
|
|
|
while numerator <= 2 * min_total - 1:
|
|
prev_numerator += 2 * numerator
|
|
numerator += 2 * prev_numerator
|
|
|
|
prev_denominator += 2 * denominator
|
|
denominator += 2 * prev_denominator
|
|
|
|
return (denominator + 1) // 2
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(f"{solution() = }")
|