之前我发布了一个关于这个主题的问题，答案很好。 Implementing merge sort function in python class, errors然而，在课堂上递归时仍然有一些东西让我感到厌烦。在上面的链接问题中，如果我在递归子例程中添加了前缀self.，我会得到下面在类输出中生成的完全相同的错误（本文中的第三个代码块）。我明白为什么会这样; object.karatsuba()只接受self作为输入，但编码的方法除了要求2之外，因此错误。
请查看下面的代码，然后看看我对第3代码块之后的解决方案的直觉。
例如：我有一个karatsuba乘法的工作实现，不想在一个类中工作。标准的课堂乘法在课堂上工作得很好，但是......
这是一个类之外的工作代码：
def zeroPad(numberString, zeros, left = True):
"""Return the string with zeros added to the left or right."""
for i in range(zeros):
if left:
numberString = '0' + numberString
else:
numberString = numberString + '0'
return numberString
def karatsubaMultiplication(x ,y):
"""Multiply two integers using Karatsuba's algorithm."""
#convert to strings for easy access to digits
x = str(x)
y = str(y)
#base case for recursion
if len(x) == 1 and len(y) == 1:
return int(x) * int(y)
if len(x) < len(y):
x = zeroPad(x, len(y) - len(x))
elif len(y) < len(x):
y = zeroPad(y, len(x) - len(y))
n = len(x)
j = n//2
#for odd digit integers
if (n % 2) != 0:
j += 1
BZeroPadding = n - j
AZeroPadding = BZeroPadding * 2
a = int(x[:j])
b = int(x[j:])
c = int(y[:j])
d = int(y[j:])
#recursively calculate
ac = karatsubaMultiplication(a, c)
bd = karatsubaMultiplication(b, d)
k = karatsubaMultiplication(a + b, c + d)
A = int(zeroPad(str(ac), AZeroPadding, False))
B = int(zeroPad(str(k - ac - bd), BZeroPadding, False))
return A + B + bd
这是第39行失败的类中的代码：
class Karatsuba(object):
def __init__(self, x, y):
self.x = x
self.y = y
def zeroPad(self, numberString, zeros, left = True):
"""Return the string with zeros added to the left or right."""
for i in range(zeros):
if left:
numberString = '0' + numberString
else:
numberString = numberString + '0'
return numberString
def karatsuba(self):
"""Multiply two integers using Karatsuba's algorithm."""
#convert to strings for easy access to digits
self.x = str(self.x)
self.y = str(self.y)
#base case for recursion
if len(self.x) == 1 and len(self.y) == 1:
return int(self.x) * int(self.y)
if len(self.x) < len(self.y):
self.x = self.zeroPad(self.x, len(self.y) - len(self.x))
elif len(self.y) < len(self.x):
self.y = self.zeroPad(self.y, len(self.x) - len(self.y))
n = len(self.x)
j = n//2
#for odd digit integers
if (n % 2) != 0:
j += 1
BZeroPadding = n - j
AZeroPadding = BZeroPadding * 2
a = int(self.x[:j])
b = int(self.x[j:])
c = int(self.y[:j])
d = int(self.y[j:])
#recursively calculate
ac = self.karatsuba(a, c)
bd = self.karatsuba(b, d)
k = self.karatsuba(a + b, c + d)
A = int(self.zeroPad(str(ac), AZeroPadding, False))
B = int(self.zeroPad(str(k - ac - bd), BZeroPadding, False))
return A + B + bd
错误的类版本生成以下输出：
x = 234523546643636
y = 325352354534656
x = Karatsuba(x,y)
x.karatsuba()
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-5-aa1c267478ee> in <module>()
4 x = Karatsuba(x,y)
5
----> 6 x.karatsuba()
<ipython-input-1-1d1e9825dcc5> in karatsuba(self)
37 d = int(self.y[j:])
38 #recursively calculate
---> 39 ac = self.karatsuba(a, c)
40 bd = self.karatsuba(b, d)
41 k = self.karatsuba(a + b, c + d)
TypeError: karatsuba() takes 1 positional argument but 3 were given
我最初的直觉是遵循顶部段落链接问题中概述的解决方案：
class Karatsuba(object):
def __init__(self, x, y):
self.x = x
self.y = y
def zeroPad(self, numberString, zeros, left = True):
"""Return the string with zeros added to the left or right."""
for i in range(zeros):
if left:
numberString = '0' + numberString
else:
numberString = numberString + '0'
return numberString
def karatsuba(self):
"""Multiply two integers using Karatsuba's algorithm."""
#convert to strings for easy access to digits
self.x = str(self.x)
self.y = str(self.y)
#base case for recursion
if len(self.x) == 1 and len(self.y) == 1:
return int(self.x) * int(self.y)
if len(self.x) < len(self.y):
self.x = self.zeroPad(self.x, len(self.y) - len(self.x))
elif len(self.y) < len(self.x):
self.y = self.zeroPad(self.y, len(self.x) - len(self.y))
n = len(self.x)
j = n//2
#for odd digit integers
if (n % 2) != 0:
j += 1
BZeroPadding = n - j
AZeroPadding = BZeroPadding * 2
self.a = int(self.x[:j])
self.b = int(self.x[j:])
self.c = int(self.y[:j])
self.d = int(self.y[j:])
#recursively calculate
# ac = self.karatsuba(self.a, self.c)
# bd = self.karatsuba(self.b, self.d)
ac = Karatsuba(self.a, self.c)
ac.karatsuba()
bd = Karatsuba(self.b, self.d)
bd.karatsuba()
k = Karatsuba(self.a + self.b, self.c + self.d)
k.karatsuba()
# k = self.karatsuba(self.a + self.b, self.c + self.d)
A = int(self.zeroPad(str(ac), AZeroPadding, False))
B = int(self.zeroPad(str(k - ac - bd), BZeroPadding, False))
return A + B + bd
x = 234523546643636
y = 325352354534656
x = Karatsuba(x,y)
x.karatsuba()
这超出了位置参数错误，但后来我遇到了一个新问题：
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-34-a862504dede9> in <module>()
59
60 x = Karatsuba(x,y)
---> 61 x.karatsuba()
<ipython-input-34-a862504dede9> in karatsuba(self)
44 # bd = self.karatsuba(self.b, self.d)
45 ac = Karatsuba(self.a, self.c)
---> 46 ac.karatsuba()
47 bd = Karatsuba(self.b, self.d)
48 bd.karatsuba()
<ipython-input-34-a862504dede9> in karatsuba(self)
44 # bd = self.karatsuba(self.b, self.d)
45 ac = Karatsuba(self.a, self.c)
---> 46 ac.karatsuba()
47 bd = Karatsuba(self.b, self.d)
48 bd.karatsuba()
<ipython-input-34-a862504dede9> in karatsuba(self)
44 # bd = self.karatsuba(self.b, self.d)
45 ac = Karatsuba(self.a, self.c)
---> 46 ac.karatsuba()
47 bd = Karatsuba(self.b, self.d)
48 bd.karatsuba()
<ipython-input-34-a862504dede9> in karatsuba(self)
51 # k = self.karatsuba(self.a + self.b, self.c + self.d)
52
---> 53 A = int(self.zeroPad(str(ac), AZeroPadding, False))
54 B = int(self.zeroPad(str(k - ac - bd), BZeroPadding, False))
55 return A + B + bd
ValueError: invalid literal for int() with base 10: '<__main__.Karatsuba object at 0x108142ba8>00'
此时我被困住了。
答案 0 :(得分：1)
在我输入这个问题时，我发现自己以不同的方式查看我的代码，即考虑如何最好地清楚地解释我的问题， 并且考虑了ValueError ，我发现了这个问题。
我遵循abarnert在之前关联的问题中提供的直觉是正确的。问题在于函数的其余部分如何需要递归子例程中的值;正如您在ValueError中看到的那样，递归子例程的内存位置正在传递，而不是子例程生成的值。然后解决方案很简单：将ac.karatsuba()修改为ac = ac.karatsuba(), etc...并瞧！
我认为这个（以及之前链接的问题）对于那些试图理解如何在python类中实现递归的人来说是一个很好的教程。
我希望你同意并给我好票！
这是工人阶级代码：
class Karatsuba(object):
def __init__(self, x, y):
self.x = x
self.y = y
def zeroPad(self, numberString, zeros, left = True):
"""Return the string with zeros added to the left or right."""
for i in range(zeros):
if left:
numberString = '0' + numberString
else:
numberString = numberString + '0'
return numberString
def karatsuba(self):
"""Multiply two integers using Karatsuba's algorithm."""
#convert to strings for easy access to digits
self.x = str(self.x)
self.y = str(self.y)
#base case for recursion
if len(self.x) == 1 and len(self.y) == 1:
return int(self.x) * int(self.y)
if len(self.x) < len(self.y):
self.x = self.zeroPad(self.x, len(self.y) - len(self.x))
elif len(self.y) < len(self.x):
self.y = self.zeroPad(self.y, len(self.x) - len(self.y))
n = len(self.x)
j = n//2
#for odd digit integers
if (n % 2) != 0:
j += 1
BZeroPadding = n - j
AZeroPadding = BZeroPadding * 2
self.a = int(self.x[:j])
self.b = int(self.x[j:])
self.c = int(self.y[:j])
self.d = int(self.y[j:])
#recursively calculate
# ac = self.karatsuba(self.a, self.c)
# bd = self.karatsuba(self.b, self.d)
ac = Karatsuba(self.a, self.c)
ac = ac.karatsuba()
bd = Karatsuba(self.b, self.d)
bd = bd.karatsuba()
k = Karatsuba(self.a + self.b, self.c + self.d)
k = k.karatsuba()
# k = self.karatsuba(self.a + self.b, self.c + self.d)
A = int(self.zeroPad(str(ac), AZeroPadding, False))
B = int(self.zeroPad(str(k - ac - bd), BZeroPadding, False))
return A + B + bd