递归程序设计（2-16进制转换）

作业题目

题目1：将非负十进制整数n转换成b进制。（其中b=2~16）

算法构造

递归公式：y = a(n) % b

a(n+1) = a(n) // b

y为余数，b为目标进制

递归出口：a(n+1) != 0

初始条件：输入的数与目标进制

递归栈调用过程：

以5的2进制转化为例

递归运行层次

运行语句行号

递归工作栈状态

说明

9,10,11,12,13,14

由主函数进入第一层递归后，运行至语句（行）14，递归调用下一层

9,10,11,12,13,14

由第一层的语句（行）14进入第二层递归，运行至语句（行）14，递归调用第三层

9,10,11,12,13,14

第三层递归执行知语句（行）11，求出值为0，从语句（行）13退出第三层，返回至第二层的语句（行）14

执行第二层的语句（行）14，从语句（行）14退出第二层，返回至第一层的语句（行）14

执行第一层的语句（行）14，

然后继续进行后续处理

栈空

继续运行主函数

程序

"""
@文件:进制转化
@说明:进制转化
@时间:2019.6.6
"""

# 进制转化(递归)
def Change(remainder_gather,binary,number):    # 余数:remainder 进制:binary 集合:gather
    binary_number = ""
    remainder = number % binary
    number = number // binary
    remainder_gather.append(str(remainder))
    if number != 0:                                      # 递归出口
        Change(remainder_gather, binary, number)         # 递归函数
    else:
        for x in range(0, len(remainder_gather)):
            if remainder_gather[x] == "10":
                remainder_gather[x] = "A"
            elif remainder_gather[x] == "11":
                remainder_gather[x] = "B"
            elif remainder_gather[x] == "12":
                remainder_gather[x] = "C"
            elif remainder_gather[x] == "13":
                remainder_gather[x] = "D"
            elif remainder_gather[x] == "14":
                remainder_gather[x] = "E"
            elif remainder_gather[x] == "15":
                remainder_gather[x] = "F"
        for y in range(0, len(remainder_gather)):
            binary_number = binary_number + remainder_gather[y]
        binary_number = binary_number[::-1]
        print("递归转化结果:" + binary_number)

# 进制转化(非递归)
def Another_Change(number, binary):
    binary_number = ""
    while number != 0:                     # 直到 商=0
        remainder = number % binary
        number = number // binary
        if str(remainder) == "10":
            remainder = "A"
        elif str(remainder) == "11":
            remainder = "B"
        elif str(remainder) == "12":
            remainder = "C"
        elif str(remainder) == "13":
            remainder = "D"
        elif str(remainder) == "14":
            remainder = "E"
        elif str(remainder) == "15":
            remainder = "F"
        binary_number = binary_number + str(remainder)
    binary_number = binary_number[::-1]
    print("非递归转化结果:" + binary_number)

if __name__ == "__main__":
    number = int(input("请输入一个数:"))
    binary = int(input("请输入目标进制(2-16):"))
    remainder_gather = []
    Change(remainder_gather, binary, number)
    Another_Change(number, binary)