Python/project_euler/problem_073/sol1.py

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"""
Project Euler Problem 73: https://projecteuler.net/problem=73
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 there are 3 fractions between 1/3 and 1/2.
How many fractions lie between 1/3 and 1/2 in the sorted set
of reduced proper fractions for d 12,000?
"""
from math import gcd
def solution(max_d: int = 12_000) -> int:
"""
Returns number of fractions lie between 1/3 and 1/2 in the sorted set
of reduced proper fractions for d max_d
>>> solution(4)
0
>>> solution(5)
1
>>> solution(8)
3
"""
fractions_number = 0
for d in range(max_d + 1):
for n in range(d // 3 + 1, (d + 1) // 2):
if gcd(n, d) == 1:
fractions_number += 1
return fractions_number
if __name__ == "__main__":
print(f"{solution() = }")