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enh(Python): rename from karatsuba.py to karatsuba_algorithm.py (#670)

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Alim Kerem Erdoğmuş 2022-01-24 20:33:29 +03:00 committed by GitHub
parent 65caa7adf9
commit d3590720cf
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3 changed files with 114 additions and 110 deletions
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2
algorithms/Python/README.md
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@ -15,7 +15,7 @@
- [Two Sum](dictionaries/two-sum.py) - [Two Sum](dictionaries/two-sum.py)
## Multiplication ## Multiplication
- [Karatsuba](multiplication/karatsuba.py) - [Karatsuba](multiplication/karatsuba_algorithm.py)
## Recursion ## Recursion
- [Factorial](recursion/factorial.py) - [Factorial](recursion/factorial.py)

109
algorithms/Python/multiplication/karatsuba.py
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@ -1,109 +0,0 @@
"""
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))

113
algorithms/Python/multiplication/karatsuba_algorithm.py 100644
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@ -0,0 +1,113 @@
"""
https://en.wikipedia.org/wiki/Karatsuba_algorithm
"""
def equalize_strings(x_value, y_value):
"""
>>> 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_value = len(x_value)
m_value = len(y_value)
zeros = abs(n_value - m_value) * '0'
if n_value > m_value:
y_value = zeros + y_value
elif m_value > n_value:
x_value = zeros + x_value
return x_value, y_value, len(x_value)
def add_function(x_value, y_value):
"""
>>> all(add_function(str(x), str(y)) == str(x + y) for x, y
... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
True
"""
x_value, y_value, size = equalize_strings(x_value, y_value)
carry = 0
result = ''
for i in range(1, size+1):
# print(i)
dgt1 = int(x_value[size - i])
dgt2 = int(y_value[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_value, y_value):
"""
>>> 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_value, y_value, size = equalize_strings(x_value, y_value)
carry = 0
result = ""
for i in range(size):
if y_value[i] <= x_value[i]:
break
#tmp = x_value
#x_value = y_value
#y_value = tmp
x_value, y_value = y_value, x_value
break
for i in range(1, size+1):
dgt1 = int(x_value[size - i])
dgt2 = int(y_value[size - i])
dgt3 = dgt1 - dgt2 - carry
if dgt3 < 0:
dgt3 += 10
carry = 1
else:
carry = 0
result = str(dgt3) + result
return result
def kmul_function(x_value ,y_value):
"""
>>> all(kmul_function(str(x), str(y)) == str(x * y) for x, y
... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
True
"""
x_value, y_value, size = equalize_strings(x_value, y_value)
if size == 1:
return str(int(x_value) * int(y_value))
mid = int(size / 2)
a_value = x_value[:mid]
b_value = x_value[mid:]
c_value = y_value[:mid]
d_value = y_value[mid:]
ac_value = kmul_function(a_value, c_value)
bd_value = kmul_function(b_value, d_value)
ab_cd_value = kmul_function(add_function(a_value, b_value), add_function(c_value, d_value))
ad_bc_value = absolute_difference(ab_cd_value, add_function(ac_value, bd_value))
zeros = "0" * (size - mid)
result = add_function(ac_value + 2 * zeros, ad_bc_value + zeros)
result = add_function(result, bd_value)
result = result.lstrip('0')
return result
if __name__ == "__main__":
X_VAR = "134231412"
Y_VAR = "141324"
print(kmul_function(X_VAR, Y_VAR))