This gist contains the famous algorithm "karatsuba" in python which is used to efficiently multiply two numbers.

karatsuba.py

def multiply(x, y):
    n = len(str(x))
    if n == 1:
        return x * y

    nby2 = n // 2
    ten_to_nby2 = 10 ** nby2
    a = x // ten_to_nby2
    b = x % ten_to_nby2
    c = y // ten_to_nby2
    d = y % ten_to_nby2

    ac = multiply(a, c)
    bd = multiply(b, d)
    ad_plus_bc = multiply(a + b, c + d) - ac - bd

    product = (ac * ten_to_nby2**2) + (ad_plus_bc * ten_to_nby2) + bd
    return product


def integerInput(n):
    try:
        return int(input(f"Enter the number {n}: "))
    except:
        return 0
  
import time

a = integerInput(1)
b = integerInput(2)

start = time.time()
print(multiply(a, b))
end = time.time()
print(f"The total time taken is : {end - start} ms")