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python 中没有 + 运算符的求和

[英]Summation without + operator in python

Need to get sum of x and y without + operator.需要在没有+运算符的情况下获得 x 和 y 的总和。

I trid to sum two number using adder.If we xor x and y ( x ^ y ), we will get summation without carry.我尝试使用加法器对两个数字求和。如果我们对 x 和 y ( x ^ y ) 进行异或运算,我们将得到不带进位的求和。 From x & y we can get carry.x & y我们可以得到进位。 To add this carry in summation, call add function again.要将此进位加到总和中,请再次调用 add function。 but its not give answer.但它没有给出答案。 where is the error in my code.我的代码中的错误在哪里。

def add(a,b):
    if a == 0:
        return b
    return add(a^b, a&b)

x = 10
y = 20
print(add(10, 20))

Error:错误:

File "main.py", line 4, in add文件“main.py”,第 4 行,添加

return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 4, in add return add(a^b, a&b) File "main.py", line 2, in add if a == 0: RuntimeError: maximum recursion depth exceeded in comparison

You also have to shift the carries:您还必须转移进位:

def add(a,b):
    if a == 0:
        return b
    if b == 0:
        return a
    return add(a^b, (a&b) << 1)

x = 3
y = 2
print(add(x, y))
# 5

This explains only why you end in an endless loop.仅解释了为什么您会陷入无限循环。 Your proposed addition algorithm is flawed, see Thierry Lathuille 's answer for a correct addition as well.您提出的加法算法存在缺陷,请参阅Thierry Lathuille的正确加法答案。


You forgot half of the base case:你忘记了一半的基本情况:

def add(a,b):
    if a == 0 or b==0:   # if either one is zero
        return a or b         # return the non-zero one (or 0 if both are 0)
    return add(a^b, a&b)

x = 10
y = 20
print(add(10, 20))

prints印刷

30     # this only works for some numbers, you algo is not correct, try add(3,2)

Debugging:调试:

def add(a,b):
    print(f"a  {bin(a):>10}")
    print(f"b  {bin(b):>10}")
    if a == 0 or b==0:
        return a or b
    return add(a^b, a&b)

a      0b1010
b     0b10100
-------------        # manually added the xor/and
xor     11110        # to show what happens:
and     00000        # b is 0       

a     0b11110
b         0b0        # now it terminates as b is 0

You missed two condition.你错过了两个条件。 If b == 0 then return a.如果 b == 0 则返回 a。 Then also shift carry.然后也转移进位。

def add(a,b):
    if a == 0:
        return b
    if b == 0:
        return a
    return add(a^b, a&b << 1)

x = 10
y = 20
print(add(10, 20))

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