Create karatsuba_algorithm.py

The Karatsuba algorithm is a fast multiplication algorithm.It reduces the multiplication of two n-digit numbers to at most n^log2(3).

Author: STK101

Algorithms/karatsuba_algorithm.py

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+def zero(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 Multiplication(x ,y):
+ 
+ x = str(x)
+ y = str(y)
+ # recursion base case
+ if len(x) == 1 and len(y) == 1:
+ return int(x) * int(y)
+ if len(x) < len(y):
+ x = zero(x, len(y) - len(x))
+ elif len(y) < len(x):
+ y = zero(y, len(x) - len(y))
+ n = len(x)
+ j = n//2
+ 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:])
+ ac = Multiplication(a, c)
+ bd = Multiplication(b, d)
+ k = Multiplication(a + b, c + d)
+ A = int(zero(str(ac), AZeroPadding, False))
+ B = int(zero(str(k - ac - bd), BZeroPadding, False))
+ return A + B + bd