Merge pull request #2 from mihirs16/master

Added Karatsuba Multiplication

Author: shushrutsharma

04. Algorithms/Divide and Conquer/karatsuba_multiplication.py

@@ -0,0 +1,44 @@
+'''
+    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')
+

readme.md

@@ -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)