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Add Python doctests to karatsuba.py (#161) 

* Add Python doctests to karatsuba.py

`subtract()` can give the wrong answer when `y` > `x`.  @atin Your review please.

* add() and absolute_difference()

* absolute_difference("1", "0")

* Update karatsuba.py

* Update karatsuba.py
pull/173/head
Christian Clauss 2021-04-11 23:43:57 +02:00 committed by GitHub
parent c3db2ee9f9
commit c245d22869
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1 changed files with 43 additions and 9 deletions
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52
multiplication/python/karatsuba.py
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@ -1,4 +1,18 @@
"""
https://en.wikipedia.org/wiki/Karatsuba_algorithm
"""
def equalize_strings(x, y): 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) n = len(x)
m = len(y) m = len(y)
zeros = abs(n - m) * '0' zeros = abs(n - m) * '0'
@ -8,7 +22,13 @@ def equalize_strings(x, y):
x = zeros + x x = zeros + x
return x, y, len(x) return x, y, len(x)
def sum(x, y):
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) x, y, size = equalize_strings(x, y)
carry = 0 carry = 0
result = '' result = ''
@ -25,7 +45,13 @@ def sum(x, y):
result = '1' + result result = '1' + result
return result return result
def subtract(x, y):
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) x, y, size = equalize_strings(x, y)
carry = 0 carry = 0
result = "" result = ""
@ -50,7 +76,13 @@ def subtract(x, y):
result = str(dgt3) + result result = str(dgt3) + result
return result return result
def kmul(x ,y): 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) x, y, size = equalize_strings(x, y)
if size == 1: if size == 1:
return str(int(x) * int(y)) return str(int(x) * int(y))
@ -61,15 +93,17 @@ def kmul(x ,y):
d = y[mid:] d = y[mid:]
ac = kmul(a, c) ac = kmul(a, c)
bd = kmul(b, d) bd = kmul(b, d)
ab_cd = kmul(sum(a, b), sum(c, d)) ab_cd = kmul(add(a, b), add(c, d))
ad_bc = subtract(ab_cd, sum(ac, bd)) ad_bc = absolute_difference(ab_cd, add(ac, bd))
zeros = "0" * (size - mid) zeros = "0" * (size - mid)
result = sum(ac + 2 * zeros, ad_bc + zeros) result = add(ac + 2 * zeros, ad_bc + zeros)
result = sum(result, bd) result = add(result, bd)
result = result.lstrip('0') result = result.lstrip('0')
return result return result
x = "134231412"
y = "141324" if __name__ == "__main__":
print(kmul(x, y)) x = "134231412"
y = "141324"
print(kmul(x, y))