Create Karatsuba_Multiplication_Algortihm.py

Author: infinitecoder1729

Karatsuba_Multiplication_Algortihm.py

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+# Karatsuba's algorithm
+# Step 1: Divide both the numbers into two halves (String wise) to form A,B,C,D
+# Step 2: Compute AxC and BxD (Recursive Multiplication)
+# Step 3: Compute (A+B)x(C+D) (Again Recursive Multiplication)
+# Step 4: Compute (A+B)x(C+D) - AxC - BxD
+# Step 5: The answer to the problem is 10^n(AxC) + 10^(n/2)(AxD+BxC)+BxD {This is a recursive approach}
+
+def KMul(x, y):
+    if len(str(x)) == 1 or len(str(y)) == 1:
+        return x * y
+    else:
+        n = max(len(str(x)), len(str(y)))
+        nby2 = n // 2
+        a = x // 10**nby2
+        b = x % 10**nby2
+        c = y // 10**nby2
+        d = y % 10**nby2
+        ac = KMul(a, c)
+        bd = KMul(b, d)
+        ad_plus_bc = KMul(a + b, c + d) - ac - bd
+        prod = ac * 10**(2 * nby2) + (ad_plus_bc * 10**nby2) + bd
+        return prod
+
+# Input
+x = int(input("Enter Number x: "))
+y = int(input("Enter Number y: "))
+
+# Output
+result = KMul(x, y)
+print("Product:", result)