From 664de410d56ba3c8a6a394b240ba6668a2d99c6a Mon Sep 17 00:00:00 2001
From: Sidney Zhang <zly@lyzhang.me>
Date: Thu, 18 Jun 2026 16:50:26 +0800
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添加 `euler_56.py` 实现计算 a^b 形式自然数的最大数字和，包含基准测试装饰器和两种算法实现
---
 solutions/0056.PowerfulDigitSum/euler_56.py | 77 +++++++++++++++++++++
 1 file changed, 77 insertions(+)
 create mode 100644 solutions/0056.PowerfulDigitSum/euler_56.py

diff --git a/solutions/0056.PowerfulDigitSum/euler_56.py b/solutions/0056.PowerfulDigitSum/euler_56.py
new file mode 100644
index 0000000..ef30316
--- /dev/null
+++ b/solutions/0056.PowerfulDigitSum/euler_56.py
@@ -0,0 +1,77 @@
+"""
+A googol (10^100) is a massive number: one followed by one-hundred zeros;
+100^100 is almost unimaginably large: one followed by two-hundred zeros.
+Despite their size, the sum of the digits in each number is only 1 .
+
+Considering natural numbers of the form, a^b , where a,b < 100 , what is the maximum digital sum?
+"""
+
+import time
+from decimal import MAX_EMAX
+from functools import wraps
+from typing import Any, Callable, TypeVar
+
+F = TypeVar("F", bound=Callable[..., Any])
+
+
+def benchmark(repeat: int = 1) -> Callable[[F], F]:
+    if repeat < 1:
+        raise ValueError("repeat must >= 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__} | repeated {repeat} times | "
+                f"average: {wrapper.avg_time:.6f}s | total: {wrapper.total_time:.6f}s"  # type: ignore[attr-defined]
+            )
+            return result
+
+        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 powtodigit(a: int, b: int) -> tuple[int, str]:
+    res = pow(a, b)
+    return res, str(res)
+
+
+@benchmark(repeat=15)
+def main() -> None:
+    max_digit_sum = 0
+    for a in range(2, 101):
+        for b in range(2, 101):
+            digit_sum = sum(int(d) for d in powtodigit(a, b)[1])
+            max_digit_sum = max(max_digit_sum, digit_sum)
+    print(f"Maximum digit sum: {max_digit_sum}")
+
+
+@benchmark(repeat=15)
+def main_inone() -> None:
+    max_digit_sum = 0
+    abp = 1
+    a = 99
+    for b in range(100, 2, -1):
+        abp = abp * a
+        max_digit_sum = max(max_digit_sum, sum(int(d) for d in str(abp)))
+    print(f"Maximum digit sum: {max_digit_sum}")
+
+
+if __name__ == "__main__":
+    main()
+    main_inone()