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47 lines
1.1 KiB
Python
47 lines
1.1 KiB
Python
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"""
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Project Euler Problem 73: https://projecteuler.net/problem=73
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Consider the fraction, n/d, where n and d are positive integers.
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If n<d and HCF(n,d)=1, it is called a reduced proper fraction.
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If we list the set of reduced proper fractions for d ≤ 8 in ascending order of size,
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we get:
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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,
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5/7, 3/4, 4/5, 5/6, 6/7, 7/8
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It can be seen that there are 3 fractions between 1/3 and 1/2.
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How many fractions lie between 1/3 and 1/2 in the sorted set
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of reduced proper fractions for d ≤ 12,000?
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"""
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from math import gcd
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def solution(max_d: int = 12_000) -> int:
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"""
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Returns number of fractions lie between 1/3 and 1/2 in the sorted set
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of reduced proper fractions for d ≤ max_d
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>>> solution(4)
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0
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>>> solution(5)
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1
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>>> solution(8)
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3
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"""
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fractions_number = 0
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for d in range(max_d + 1):
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for n in range(d // 3 + 1, (d + 1) // 2):
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if gcd(n, d) == 1:
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fractions_number += 1
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return fractions_number
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if __name__ == "__main__":
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print(f"{solution() = }")
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