chore: update 2026-04-22

solutions/0055.LychrelNum/euler_55_bit.py

@@ -0,0 +1,112 @@
+"""
+If we take 47, reverse and add, 47 + 74 = 121, which is palindromic.
+
+Not all numbers produce palindromes so quickly. For example,
+    349 + 943 = 1292
+    1292 + 2921 = 4213
+    4213 + 3124 = 7337
+That is, 349 took three iterations to arrive at a palindrome.
+
+Although no one has proved it yet, it is thought that some numbers, like 196,
+never produce a palindrome. A number that never forms a palindrome through the
+reverse and add process is called a Lychrel number. Due to the theoretical nature
+of these numbers, and for the purpose of this problem, we shall assume that
+a number is Lychrel until proven otherwise. In addition you are given that for
+every number below ten-thousand, it will either (i) become a palindrome
+in less than fifty iterations, or, (ii) no one, with all the computing power that exists,
+has managed so far to map it to a palindrome. In fact, 10677 is the first number to
+be shown to require over fifty iterations before producing a palindrome:
+    4668731596684224866951378664 (53 iterations, 28-digits).
+
+Surprisingly, there are palindromic numbers that are themselves Lychrel numbers;
+the first example is 4994.
+
+How many Lychrel numbers are there below ten-thousand?
+
+NOTE: Wording was modified slightly on 24 April 2007 to emphasise the theoretical nature of Lychrel numbers.
+"""
+
+import time
+from functools import wraps
+from typing import Any, Callable, TypeVar
+
+from bitarray import bitarray
+
+F = TypeVar("F", bound=Callable[..., Any])
+
+
+def benchmark(repeat: int = 1) -> Callable[[F], F]:
+    """
+    重复运行目标函数并计算平均耗时。
+
+    平均耗时会被存储在 wrapper.avg_time 和 wrapper.total_time 中，
+    同时会打印到控制台。函数的返回值不受影响。
+    """
+    if repeat < 1:
+        raise ValueError("repeat 必须 >= 1")
+
+    def decorator(func: F) -> F:
+        @wraps(func)
+        def wrapper(*args: Any, **kwargs: Any) -> Any:
+            total = 0.0
+            result = None
+
+            for _ in range(repeat):
+                start = time.perf_counter()
+                result = func(*args, **kwargs)
+                end = time.perf_counter()
+                total += end - start
+
+            wrapper.avg_time = total / repeat  # type: ignore[attr-defined]
+            wrapper.total_time = total  # type: ignore[attr-defined]
+
+            print(
+                f"[Benchmark] {func.__name__} | 重复 {repeat} 次 | "
+                f"平均: {wrapper.avg_time:.6f}s | 总计: {wrapper.total_time:.6f}s"  # type: ignore[attr-defined]
+            )
+            return result
+
+        # 初始化属性，避免调用前访问报错
+        wrapper.avg_time = 0.0  # type: ignore[attr-defined]
+        wrapper.total_time = 0.0  # type: ignore[attr-defined]
+        return wrapper  # type: ignore[return-value]
+
+    return decorator
+
+
+def reverse_int(n: int) -> int:
+    return int(str(n)[::-1])
+
+
+@benchmark(repeat=15)
+def count_lychrel_numbers(limit: int = 10000, max_iter: int = 50) -> int:
+    is_not_lychrel = bitarray(limit + 1)
+    is_not_lychrel.setall(0)
+    is_not_lychrel[0] = 1
+
+    for i in range(1, limit + 1):
+        if is_not_lychrel[i]:
+            continue
+
+        n = i
+        chain = [n]
+
+        for _ in range(max_iter):
+            n += reverse_int(n)
+
+            # 检查是否形成回文
+            if n == reverse_int(n):
+                for num in chain:
+                    if num > limit:
+                        break
+                    is_not_lychrel[num] = 1
+                break
+
+            chain.append(n)
+
+    return is_not_lychrel.count(0)
+
+
+if __name__ == "__main__":
+    result = count_lychrel_numbers(10000)
+    print(f"Number of Lychrel numbers below 10,000: {result}")