Added Karatsuba Multiplication #2

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	'''
	karatsuba multiplication (integer-wise)
	to multiply two n-digit integers, the following formula holds:
	=> (a * c * 10^n) + (b * d) + {[(b * c) + (a * d)] * 10^(n/2)}
	where: a = first half of first integer
	b = second half of first integer
	c = first half of second integer
	d = second half of second integer
	this can further be used with recursion to implement divide-and-conquer
	wherein each product (ac, bd, bc, ad) can be calculated using the same.

	note: assuming n = even & n1 = n2
	'''
	def k_multiply(x, y):
	if len(x) > 1 and len(y) > 1: # base condition: length of integers > 1
	a, b = x[:len(x) // 2], x[len(x) // 2:] # divide first int for a, b,
	c, d = y[:len(y) // 2], y[len(y) // 2:] # divide second int for c, d

	print(a, b, c, d)
	ac = k_multiply(a, c)
	bd = k_multiply(b, d)
	bc = k_multiply(b, c)
	ad = k_multiply(a, d)
	n = len(x)
	n2 = n // 2
	prod = (ac * pow(10, n)) + (bd) + ((bc + ad) * pow(10, n2)) # prod by karatsuba

	return prod
	else:
	return (x[0] * y[0]) # return product if length <= 1

	if __name__ == '__main__':
	try:
	first_integer = [int(x) for x in input('first integer: ')]
	second_integer = [int(x) for x in input('second integer: ')]

	if (len(second_integer) != len(first_integer)):
	raise ValueError

	prod = k_multiply(first_integer, second_integer)
	print(prod)
	except ValueError:
	print('Invalid Inputs')

9 changes: 5 additions & 4 deletions readme.md

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Expand Up		@@ -35,10 +35,11 @@ All the essential resources and template code needed to understand and practice
		7. [Trees](/03.%20Data%20Structures/Trees)

		### 4. 🛠 [Algorithms](/04.%20Algorithms/)
	1. [Dynamic Programming](/04.%20Algorithms/Dynamic%20Programming/)
	2. [Recursion](/04.%20Algorithms/Recursion/)
	3. [Sorting](/04.%20Algorithms/Sorting/)
	4. [Traversals](/04.%20Algorithms/Traversals)
	1. [Divide and Conquer](/04.%20Algorithms/Divide%20and%20Conquer/)
	2. [Dynamic Programming](/04.%20Algorithms/Dynamic%20Programming/)
	3. [Recursion](/04.%20Algorithms/Recursion/)
	4. [Sorting](/04.%20Algorithms/Sorting/)
	5. [Traversals](/04.%20Algorithms/Traversals)

		### 5. 📂 [File Handling and OOPS](/05.%20File%20Handling%20and%20OOPS/)
		1. [File + Classes Demo](/05.%20File%20Handling%20and%20OOPS/file%2Bclasses.py)
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