Sidney Zhang
fbfbfd25b4
✨ feat(eular_12.py)：添加欧拉项目第12题的解决方案，计算第一个拥有超过500个因数的三角数 📝 docs(readme.md)：添加三角数的详细文档，涵盖数学概念、应用领域和博弈论中的实际例子
73 lines
1.7 KiB
Python
73 lines
1.7 KiB
Python
"""
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The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number
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would be 1+2+3+4+5+6+7=28. The first ten terms would be:
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1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
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Let us list the factors of the first seven triangle numbers:
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1 : 1
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3 : 1, 3
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6 : 1, 2, 3, 6
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10 : 1, 2, 5, 10
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15 : 1, 3, 5, 15
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21 : 1, 3, 7, 21
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28 : 1, 2, 4, 7, 14, 28
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We can see that 28 is the first triangle number to have over five divisors.
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What is the value of the first triangle number to have over five hundred divisors?
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NOTE：
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-> in Math
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解法的核心是找到所有质因数及对应的最大幂, 根据组合数学的方法估算因数数量
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-> in Coding
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循环遍历
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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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print(f"Time taken: {end_time - start_time} seconds")
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return result
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return wrapper
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def get_factors(n):
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if n == 0:
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raise ValueError("0 没有因数集合")
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n = abs(n) # 处理负数
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factors = set()
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for i in range(1, int(math.isqrt(n)) + 1):
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if n % i == 0:
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factors.add(i)
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factors.add(n // i)
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return sorted(factors)
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def get_triangle_number(n: int) -> int:
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return n * (n + 1) // 2
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@timer
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def main_coding() -> None:
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n = 1
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while True:
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triangle_number = get_triangle_number(n)
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factors = get_factors(triangle_number)
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if len(factors) > 500:
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print(triangle_number)
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break
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n += 1
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if __name__ == "__main__":
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main_coding()
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