键盘系列

"""
N=7
output=9
N=3
output=3
"""


def get_a(n_num):
    def dp(n, a_num, a_copy):
        if n <= 0 : return a_num
        return max(
            dp(n-1, a_num + 1, a_copy),
            dp(n-2, a_num, a_num),
            dp(n-1, a_num+a_copy, a_copy)
        )
    return dp(n_num, 0, 0)


def get_a_1(n_num):
    memo = {}
    
    def dp(n, a_num, a_copy):
        if n <= 0 : return a_num
        if (n, a_num, a_copy) in memo: return memo[(n, a_num, a_copy)]
        memo[(n, a_num, a_copy)] = max(
            dp(n-1, a_num + 1, a_copy),
            dp(n-2, a_num, a_num),
            dp(n-1, a_num+a_copy, a_copy)
        )
        return memo[(n, a_num, a_copy)]
    return dp(n_num, 0, 0)


def get_a_2(n):
    dp = [0 for _ in range(n+1)]
    for i in range(1, n+1):
        dp[i] = dp[i - 1] + 1
        for j in range(2, i):
            dp[i] = max(dp[i], dp[j - 2] * (i - j + 1))
    return dp[n]


if __name__ == "__main__":
    N = 7
    res1 = get_a_2(N)
    print(res1)

    N = 3
    res2 = get_a_2(N)
    print(res2)