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