Karatsuba algorithm

The Karatsuba algorithm is a divide-and-conquer algorithm used for efficient multiplication of large integers. It was discovered by Anatolii Alexeevitch Karatsuba in 1960 and is particularly significant because it reduces the multiplication of two n-digit numbers from the traditional \(O(n^2)\) time complexity to approximately \(O(n^{\log_2 3})\), which is about \(O(n^{1.585})\).