"""
Consider all integer combinations of a^b for 2<=a<=5 and 2<=b<=5 :

2^2 = 4  2^3 = 8  2^4 = 16  2^5 = 32
3^2 = 9  3^3 = 27  3^4 = 81  3^5 = 243
4^2 = 16  4^3 = 64  4^4 = 256  4^5 = 1024
5^2 = 25  5^3 = 125  5^4 = 625  5^5 = 3125

If they are then placed in numerical order, with any repeats removed,
we get the following sequence of 15 distinct terms:

4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125

How many distinct terms are in the sequence generated by a^b for 2<=a<=100 and 2<=b<=100 ?
"""

import time


def timer(func):
    def wrapper(*args, **kwargs):
        start_time = time.time()
        result = func(*args, **kwargs)
        end_time = time.time()
        print(f"{func.__name__} runtime: {end_time - start_time} seconds")
        return result

    return wrapper


def count_distinct_terms_efficient(limit_a, limit_b):
    # 预计算每个 a 的最小底数表示
    base_map = {}
    power_map = {}

    for a in range(2, limit_a + 1):
        base_map[a] = a
        power_map[a] = 1

    # 找出所有可以表示为幂的数
    for power in range(2, 7):  # 2^7=128>100，所以最多到6次幂
        base = 2
        while base**power <= limit_a:
            value = base**power
            # 如果这个值还没有被更小的底数表示
            if base_map[value] == value:
                base_map[value] = base
                power_map[value] = power
            base += 1

    # 使用集合存储 (base, exponent) 对
    seen = set()

    for a in range(2, limit_a + 1):
        base = base_map[a]
        power = power_map[a]

        # 如果 a 是某个数的幂，我们需要检查 base 是否还能分解
        # 例如：16 = 4^2，但 4 = 2^2，所以 16 = 2^4
        # 我们需要找到最终的 base
        while base_map[base] != base:
            power = power * power_map[base]
            base = base_map[base]

        for b in range(2, limit_b + 1):
            seen.add((base, power * b))

    return len(seen)


def do_compute(a_top: int, b_top: int, a_down: int = 2, b_down: int = 2) -> int:
    tmp = set()
    for a in range(a_down, a_top + 1):
        for b in range(b_down, b_top + 1):
            tmp.add(a**b)
    return len(tmp)


@timer
def main():
    """not bad"""
    print(count_distinct_terms_efficient(100, 100))


@timer
def main2():
    print(do_compute(100, 100))


if __name__ == "__main__":
    main()
    main2()