mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
47 lines
1.1 KiB
Python
47 lines
1.1 KiB
Python
|
"""
|
||
|
|
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() = }")
|