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