sol1.py

"""
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?
"""

frommathimportgcd


defsolution(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
fordinrange(max_d+1):
forninrange(d//3+1, (d+1) //2):
ifgcd(n, d) ==1:
fractions_number+=1
returnfractions_number


if__name__=="__main__":
print(f"{solution() =}")