十进制转任意进制与 yield

		发布于	2022-08-18 00:10
		保质期	2025-08
		新鲜度	19%

标签

算法

进位制

Python

过程描述

用除N求余法计算3500266221对应的十六进制的过程如下：

$$\begin{array}{rl}3500266221÷16& =218766638\cdots 13\\ 218766638÷16& =13672914\cdots 14\\ 13672914÷16& =854557\cdots 2\\ 854557÷16& =53409\cdots 13\\ 53409÷16& =3338\cdots 1\\ 3338÷16& =208\cdots 10\\ 208÷16& =13\cdots 0\\ 13÷16& =0\cdots 13\end{array}$$

余数倒序组成数列 [13, 0, 10, 1, 13, 2, 14, 13]，按顺序查询进制对应的字符集，得到结果 D0A1D2ED。

	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
	0	1	2	3	4	5	6	7	8	9	A	B	C	D	E	F
13														D
0	0
10											A
1		1
13														D
2			2
14															E
13														D

循环实现

def dec2n(x, charset):
    base = len(charset)
    result = ''
    quotient = x  # 商
    while quotient >= base:
        # 同时计算商和余数，并存起来：
        quotient, remainder = quotient // base, quotient % base
        result += charset[remainder]
    else:
        result += charset[quotient]
    return result[::-1]

if __name__ == '__main__':
    print(dec2n(3500266221, '0123456789ABCDEF'))
    # 输出：D0A1D2ED

递归实现

def dec2n(x, base, charset):
    if x < base:
        return charset[x]
    return dec2n(x // base, base, charset) + charset[x % base]

if __name__ == '__main__':
    BASE16 = '0123456789ABCDEF'
    print(dec2n(3500266221, len(BASE16), BASE16))
    # 输出：D0A1D2ED

迭代器实现

def dec2n(x, charset):
    # i=3500266221, base=16, charset="0123456789ABCDEF"
    # -> [13, 14, 2, 13, 1, 10, 0, 13]
    # -> ['D', 'E', '2', 'D', '1', 'A', '0', 'D']
    def dec2seq(i, base):
        while i >= base:
            yield charset[i % base]
            i //= base
        yield charset[i]

    # x=3500266221, charset="0123456789ABCDEF"
    # -> ['D', 'E', '2', 'D', '1', 'A', '0', 'D']
    # -> "DE2D1A0D"
    # -> "D0A1D2ED"
    return ''.join(dec2seq(int(x), len(charset)))[::-1]


if __name__ == '__main__':
    print(dec2n(3500266221, '0123456789ABCDEF'))
    # 输出：D0A1D2ED

yield 只在生成器函数内使用。不同于 return 的一旦返回则立即结束，yield 可以多次返回不同的值，直到函数执行结束。