113 lines
3.7 KiB
Python
113 lines
3.7 KiB
Python
"""
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If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
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Not all numbers produce palindromes so quickly. For example,
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349 + 943 = 1292
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1292 + 2921 = 4213
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4213 + 3124 = 7337
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That is, 349 took three iterations to arrive at a palindrome.
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Although no one has proved it yet, it is thought that some numbers, like 196,
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never produce a palindrome. A number that never forms a palindrome through the
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reverse and add process is called a Lychrel number. Due to the theoretical nature
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of these numbers, and for the purpose of this problem, we shall assume that
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a number is Lychrel until proven otherwise. In addition you are given that for
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every number below ten-thousand, it will either (i) become a palindrome
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in less than fifty iterations, or, (ii) no one, with all the computing power that exists,
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has managed so far to map it to a palindrome. In fact, 10677 is the first number to
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be shown to require over fifty iterations before producing a palindrome:
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4668731596684224866951378664 (53 iterations, 28-digits).
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Surprisingly, there are palindromic numbers that are themselves Lychrel numbers;
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the first example is 4994.
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How many Lychrel numbers are there below ten-thousand?
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NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
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"""
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import time
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from functools import wraps
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from typing import Any, Callable, TypeVar
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from bitarray import bitarray
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F = TypeVar("F", bound=Callable[..., Any])
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def benchmark(repeat: int = 1) -> Callable[[F], F]:
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"""
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重复运行目标函数并计算平均耗时。
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平均耗时会被存储在 wrapper.avg_time 和 wrapper.total_time 中，
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同时会打印到控制台。函数的返回值不受影响。
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"""
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if repeat < 1:
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raise ValueError("repeat 必须 >= 1")
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def decorator(func: F) -> F:
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@wraps(func)
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def wrapper(*args: Any, **kwargs: Any) -> Any:
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total = 0.0
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result = None
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for _ in range(repeat):
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start = time.perf_counter()
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result = func(*args, **kwargs)
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end = time.perf_counter()
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total += end - start
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wrapper.avg_time = total / repeat # type: ignore[attr-defined]
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wrapper.total_time = total # type: ignore[attr-defined]
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print(
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f"[Benchmark] {func.__name__} | 重复 {repeat} 次 | "
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f"平均: {wrapper.avg_time:.6f}s | 总计: {wrapper.total_time:.6f}s" # type: ignore[attr-defined]
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)
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return result
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# 初始化属性，避免调用前访问报错
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wrapper.avg_time = 0.0 # type: ignore[attr-defined]
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wrapper.total_time = 0.0 # type: ignore[attr-defined]
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return wrapper # type: ignore[return-value]
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return decorator
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def reverse_int(n: int) -> int:
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return int(str(n)[::-1])
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@benchmark(repeat=15)
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def count_lychrel_numbers(limit: int = 10000, max_iter: int = 50) -> int:
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is_not_lychrel = bitarray(limit + 1)
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is_not_lychrel.setall(0)
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is_not_lychrel[0] = 1
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for i in range(1, limit + 1):
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if is_not_lychrel[i]:
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continue
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n = i
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chain = [n]
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for _ in range(max_iter):
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n += reverse_int(n)
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# 检查是否形成回文
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if n == reverse_int(n):
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for num in chain:
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if num > limit:
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break
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is_not_lychrel[num] = 1
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break
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chain.append(n)
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return is_not_lychrel.count(0)
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if __name__ == "__main__":
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result = count_lychrel_numbers(10000)
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print(f"Number of Lychrel numbers below 10,000: {result}")
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