Sidney Zhang
accc74ff43
📝 docs(solutions)：添加排列问题README文档说明欧拉数算法 ♻️ refactor(solutions)：重构排列问题代码，添加数学计算方法 ✨ feat(solutions)：新增斐波那契问题解决方案，支持大数计算和Binet公式 🔧 chore(solutions)：为两个解决方案添加性能计时器装饰器
78 lines
2.0 KiB
Python
78 lines
2.0 KiB
Python
"""
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The Fibonacci sequence is defined by the recurrence relation:
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F_n = F_{n-1} + F_{n-2}, where F_1 = 1 and F_2 = 1.
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Hence the first 12 terms will be: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
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The 12th term, F_12, is the first term to contain three digits.
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What is the index of the first term in the Fibonacci sequence to contain 1000-digits?
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"""
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import math
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import time
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def timer(func):
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def wrapper(*args, **kwargs):
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start_time = time.time()
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result = func(*args, **kwargs)
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end_time = time.time()
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during = end_time - start_time
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if during > 1:
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print(f"function {func.__name__} taken: {during:.6f} seconds")
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elif during > 0.001:
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print(f"function {func.__name__} taken: {during * 1000:.3f} milliseconds")
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else:
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print(
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f"function {func.__name__} taken: {during * 1000000:.3f} microseconds"
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)
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return result
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return wrapper
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def big_sum(a: str, b: str) -> str:
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length = max(len(a), len(b))
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carry = 0
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result = []
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for i in range(length):
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digit_a = int(a[-i - 1]) if i < len(a) else 0
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digit_b = int(b[-i - 1]) if i < len(b) else 0
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sum_digit = digit_a + digit_b + carry
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result.append(str(sum_digit % 10))
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carry = sum_digit // 10
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if carry:
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result.append(str(carry))
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return "".join(result[::-1])
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def find_fibonacci_index(digits: int) -> int:
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a, b = "1", "1"
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index = 1
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while len(a) < digits:
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a, b = b, big_sum(a, b)
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index += 1
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return index
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@timer
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def main_in_bigint():
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print(find_fibonacci_index(1000))
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def binet(n: int) -> int:
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index = math.ceil(
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(math.log10(math.sqrt(5)) + (n - 1)) / math.log10(0.5 * (1 + math.sqrt(5)))
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)
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return index
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@timer
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def main_use_binet():
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print(f"{binet(1000)}")
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if __name__ == "__main__":
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main_in_bigint()
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main_use_binet()
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