110 lines
2.3 KiB
Python
110 lines
2.3 KiB
Python
"""
|
|
https://en.wikipedia.org/wiki/Karatsuba_algorithm
|
|
"""
|
|
|
|
|
|
def equalize_strings(x, y):
|
|
"""
|
|
>>> def eq_str(x, y):
|
|
... max_len = max(len(x), len(y))
|
|
... return x.zfill(max_len), y.zfill(max_len), max_len
|
|
>>>
|
|
>>> all(equalize_strings(x, y) == eq_str(x, y) for x, y
|
|
... in (('x' * i, 'y' * (i // 2)) for i in range(10)))
|
|
True
|
|
"""
|
|
n = len(x)
|
|
m = len(y)
|
|
zeros = abs(n - m) * '0'
|
|
if n > m:
|
|
y = zeros + y
|
|
elif m > n:
|
|
x = zeros + x
|
|
return x, y, len(x)
|
|
|
|
|
|
def add(x, y):
|
|
"""
|
|
>>> all(add(str(x), str(y)) == str(x + y) for x, y
|
|
... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
|
|
True
|
|
"""
|
|
x, y, size = equalize_strings(x, y)
|
|
carry = 0
|
|
result = ''
|
|
for i in range(1, size+1):
|
|
# print(i)
|
|
dgt1 = int(x[size - i])
|
|
dgt2 = int(y[size - i])
|
|
dgt3 = (dgt1 + dgt2 + carry) % 10
|
|
result = str(dgt3) + result
|
|
carry = int((dgt1 + dgt2 + carry) / 10)
|
|
# print(dgt1, dgt2, dgt3, result, carry)
|
|
|
|
if carry:
|
|
result = '1' + result
|
|
return result
|
|
|
|
|
|
def absolute_difference(x, y):
|
|
"""
|
|
>>> all(absolute_difference(str(x), str(y)) == str(abs(x - y)) for x, y
|
|
... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
|
|
True
|
|
"""
|
|
x, y, size = equalize_strings(x, y)
|
|
carry = 0
|
|
result = ""
|
|
for i in range(size):
|
|
if y[i] < x[i]:
|
|
break
|
|
elif x[i] < y[i]:
|
|
tmp = x
|
|
x = y
|
|
y = tmp
|
|
break
|
|
|
|
for i in range(1, size+1):
|
|
dgt1 = int(x[size - i])
|
|
dgt2 = int(y[size - i])
|
|
dgt3 = dgt1 - dgt2 - carry
|
|
if dgt3 < 0:
|
|
dgt3 += 10
|
|
carry = 1
|
|
else:
|
|
carry = 0
|
|
result = str(dgt3) + result
|
|
return result
|
|
|
|
|
|
def kmul(x ,y):
|
|
"""
|
|
>>> all(kmul(str(x), str(y)) == str(x * y) for x, y
|
|
... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
|
|
True
|
|
"""
|
|
x, y, size = equalize_strings(x, y)
|
|
if size == 1:
|
|
return str(int(x) * int(y))
|
|
mid = int(size / 2)
|
|
a = x[:mid]
|
|
b = x[mid:]
|
|
c = y[:mid]
|
|
d = y[mid:]
|
|
ac = kmul(a, c)
|
|
bd = kmul(b, d)
|
|
ab_cd = kmul(add(a, b), add(c, d))
|
|
ad_bc = absolute_difference(ab_cd, add(ac, bd))
|
|
zeros = "0" * (size - mid)
|
|
|
|
result = add(ac + 2 * zeros, ad_bc + zeros)
|
|
result = add(result, bd)
|
|
result = result.lstrip('0')
|
|
return result
|
|
|
|
|
|
if __name__ == "__main__":
|
|
x = "134231412"
|
|
y = "141324"
|
|
print(kmul(x, y))
|