Python/project_euler/problem_071/sol1.py
Dhruv 44254cf112
Rename Project Euler directories and other dependent changes (#3300)
* 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
2020-10-15 12:43:28 +05:30

49 lines
1.5 KiB
Python

"""
Ordered fractions
Problem 71
https://projecteuler.net/problem=71
Consider the fraction n/d, where n and d are positive
integers. If n<d and HCF(n,d)=1, it is called a reduced proper fraction.
If we list the set of reduced proper fractions for d ≤ 8
in ascending order of size, we get:
1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7,
1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
It can be seen that 2/5 is the fraction immediately to the left of 3/7.
By listing the set of reduced proper fractions for d ≤ 1,000,000
in ascending order of size, find the numerator of the fraction
immediately to the left of 3/7.
"""
def solution(numerator: int = 3, denominator: int = 7, limit: int = 1000000) -> int:
"""
Returns the closest numerator of the fraction immediately to the
left of given fraction (numerator/denominator) from a list of reduced
proper fractions.
>>> solution()
428570
>>> solution(3, 7, 8)
2
>>> solution(6, 7, 60)
47
"""
max_numerator = 0
max_denominator = 1
for current_denominator in range(1, limit + 1):
current_numerator = current_denominator * numerator // denominator
if current_denominator % denominator == 0:
current_numerator -= 1
if current_numerator * max_denominator > current_denominator * max_numerator:
max_numerator = current_numerator
max_denominator = current_denominator
return max_numerator
if __name__ == "__main__":
print(solution(numerator=3, denominator=7, limit=1000000))