enh(Python): rename from karatsuba.py to karatsuba_algorithm.py (#670)
Alim Kerem Erdoğmuş
GitHub
parent
65caa7adf9
commit
d3590720cf
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@ -15,7 +15,7 @@
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- [Two Sum](dictionaries/two-sum.py)
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## Multiplication
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- [Karatsuba](multiplication/karatsuba.py)
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- [Karatsuba](multiplication/karatsuba_algorithm.py)
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## Recursion
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- [Factorial](recursion/factorial.py)
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@ -1,109 +0,0 @@
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"""
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https://en.wikipedia.org/wiki/Karatsuba_algorithm
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"""
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def equalize_strings(x, y):
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"""
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>>> def eq_str(x, y):
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... max_len = max(len(x), len(y))
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... return x.zfill(max_len), y.zfill(max_len), max_len
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>>>
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>>> all(equalize_strings(x, y) == eq_str(x, y) for x, y
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... in (('x' * i, 'y' * (i // 2)) for i in range(10)))
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True
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"""
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n = len(x)
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m = len(y)
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zeros = abs(n - m) * '0'
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if n > m:
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y = zeros + y
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elif m > n:
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x = zeros + x
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return x, y, len(x)
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def add(x, y):
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"""
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>>> all(add(str(x), str(y)) == str(x + y) for x, y
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... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
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True
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"""
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x, y, size = equalize_strings(x, y)
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carry = 0
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result = ''
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for i in range(1, size+1):
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# print(i)
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dgt1 = int(x[size - i])
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dgt2 = int(y[size - i])
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dgt3 = (dgt1 + dgt2 + carry) % 10
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result = str(dgt3) + result
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carry = int((dgt1 + dgt2 + carry) / 10)
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# print(dgt1, dgt2, dgt3, result, carry)
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if carry:
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result = '1' + result
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return result
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def absolute_difference(x, y):
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"""
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>>> all(absolute_difference(str(x), str(y)) == str(abs(x - y)) for x, y
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... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
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True
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"""
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x, y, size = equalize_strings(x, y)
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carry = 0
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result = ""
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for i in range(size):
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if y[i] < x[i]:
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break
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elif x[i] < y[i]:
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tmp = x
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x = y
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y = tmp
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break
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for i in range(1, size+1):
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dgt1 = int(x[size - i])
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dgt2 = int(y[size - i])
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dgt3 = dgt1 - dgt2 - carry
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if dgt3 < 0:
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dgt3 += 10
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carry = 1
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else:
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carry = 0
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result = str(dgt3) + result
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return result
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def kmul(x ,y):
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"""
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>>> all(kmul(str(x), str(y)) == str(x * y) for x, y
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... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
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True
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"""
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x, y, size = equalize_strings(x, y)
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if size == 1:
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return str(int(x) * int(y))
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mid = int(size / 2)
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a = x[:mid]
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b = x[mid:]
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c = y[:mid]
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d = y[mid:]
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ac = kmul(a, c)
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bd = kmul(b, d)
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ab_cd = kmul(add(a, b), add(c, d))
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ad_bc = absolute_difference(ab_cd, add(ac, bd))
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zeros = "0" * (size - mid)
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result = add(ac + 2 * zeros, ad_bc + zeros)
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result = add(result, bd)
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result = result.lstrip('0')
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return result
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if __name__ == "__main__":
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x = "134231412"
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y = "141324"
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print(kmul(x, y))
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@ -0,0 +1,113 @@
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"""
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https://en.wikipedia.org/wiki/Karatsuba_algorithm
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"""
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def equalize_strings(x_value, y_value):
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"""
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>>> def eq_str(x, y):
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... max_len = max(len(x), len(y))
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... return x.zfill(max_len), y.zfill(max_len), max_len
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>>>
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>>> all(equalize_strings(x, y) == eq_str(x, y) for x, y
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... in (('x' * i, 'y' * (i // 2)) for i in range(10)))
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True
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"""
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n_value = len(x_value)
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m_value = len(y_value)
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zeros = abs(n_value - m_value) * '0'
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if n_value > m_value:
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y_value = zeros + y_value
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elif m_value > n_value:
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x_value = zeros + x_value
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return x_value, y_value, len(x_value)
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def add_function(x_value, y_value):
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"""
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>>> all(add_function(str(x), str(y)) == str(x + y) for x, y
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... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
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True
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"""
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x_value, y_value, size = equalize_strings(x_value, y_value)
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carry = 0
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result = ''
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for i in range(1, size+1):
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# print(i)
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dgt1 = int(x_value[size - i])
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dgt2 = int(y_value[size - i])
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dgt3 = (dgt1 + dgt2 + carry) % 10
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result = str(dgt3) + result
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carry = int((dgt1 + dgt2 + carry) / 10)
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# print(dgt1, dgt2, dgt3, result, carry)
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if carry:
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result = '1' + result
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return result
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def absolute_difference(x_value, y_value):
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"""
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>>> all(absolute_difference(str(x), str(y)) == str(abs(x - y)) for x, y
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... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
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True
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"""
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x_value, y_value, size = equalize_strings(x_value, y_value)
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carry = 0
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result = ""
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for i in range(size):
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if y_value[i] <= x_value[i]:
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break
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#tmp = x_value
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#x_value = y_value
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#y_value = tmp
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x_value, y_value = y_value, x_value
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break
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for i in range(1, size+1):
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dgt1 = int(x_value[size - i])
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dgt2 = int(y_value[size - i])
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dgt3 = dgt1 - dgt2 - carry
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if dgt3 < 0:
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dgt3 += 10
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carry = 1
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else:
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carry = 0
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result = str(dgt3) + result
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return result
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def kmul_function(x_value ,y_value):
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"""
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>>> all(kmul_function(str(x), str(y)) == str(x * y) for x, y
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... in ((0, 0), (0, 1), (1, 0), (1, 1234567890), (543210, 9876543)))
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True
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"""
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x_value, y_value, size = equalize_strings(x_value, y_value)
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if size == 1:
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return str(int(x_value) * int(y_value))
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mid = int(size / 2)
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a_value = x_value[:mid]
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b_value = x_value[mid:]
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c_value = y_value[:mid]
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d_value = y_value[mid:]
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ac_value = kmul_function(a_value, c_value)
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bd_value = kmul_function(b_value, d_value)
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ab_cd_value = kmul_function(add_function(a_value, b_value), add_function(c_value, d_value))
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ad_bc_value = absolute_difference(ab_cd_value, add_function(ac_value, bd_value))
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zeros = "0" * (size - mid)
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result = add_function(ac_value + 2 * zeros, ad_bc_value + zeros)
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result = add_function(result, bd_value)
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result = result.lstrip('0')
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return result
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if __name__ == "__main__":
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X_VAR = "134231412"
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Y_VAR = "141324"
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print(kmul_function(X_VAR, Y_VAR))
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