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74 lines
1.9 KiB
Python
74 lines
1.9 KiB
Python
"""
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Project Euler Problem 2: https://projecteuler.net/problem=2
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Even Fibonacci Numbers
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Each new term in the Fibonacci sequence is generated by adding the previous
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two terms. By starting with 1 and 2, the first 10 terms will be:
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1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
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By considering the terms in the Fibonacci sequence whose values do not exceed
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four million, find the sum of the even-valued terms.
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References:
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- https://en.wikipedia.org/wiki/Fibonacci_number
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"""
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import math
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from decimal import Decimal, getcontext
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def solution(n: int = 4000000) -> int:
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"""
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Returns the sum of all even fibonacci sequence elements that are lower
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or equal to n.
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>>> solution(10)
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10
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>>> solution(15)
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10
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>>> solution(2)
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2
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>>> solution(1)
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0
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>>> solution(34)
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44
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>>> solution(3.4)
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2
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>>> solution(0)
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Traceback (most recent call last):
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...
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ValueError: Parameter n must be greater than or equal to one.
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>>> solution(-17)
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Traceback (most recent call last):
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...
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ValueError: Parameter n must be greater than or equal to one.
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>>> solution([])
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Traceback (most recent call last):
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...
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TypeError: Parameter n must be int or castable to int.
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>>> solution("asd")
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Traceback (most recent call last):
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...
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TypeError: Parameter n must be int or castable to int.
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"""
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try:
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n = int(n)
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except (TypeError, ValueError):
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raise TypeError("Parameter n must be int or castable to int.")
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if n <= 0:
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raise ValueError("Parameter n must be greater than or equal to one.")
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getcontext().prec = 100
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phi = (Decimal(5) ** Decimal("0.5") + 1) / Decimal(2)
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index = (math.floor(math.log(n * (phi + 2), phi) - 1) // 3) * 3 + 2
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num = Decimal(round(phi ** Decimal(index + 1))) / (phi + 2)
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total = num // 2
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return int(total)
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if __name__ == "__main__":
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print(f"{solution() = }")
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