Just a few algorithms with explanations in the comments.
- The Karatsuba algorithm is a multiplication algorithm developed by Anatolii Alexeevitch Karatsuba in 1960.
- It operates in O(n^log2(3)) time (~ O(n^1.585)), with n being the number of digits of the numbers we are multiplying together.
- Standard grade-school multiplication operates in O(n^2) time. Karatsuba's method is asymptotically much faster.
- Normally, you can choose any base you want, but we will be using base 10 in this algorithm with m varying depending on the length of the input.
- Specific details are included with an example in the comments before the actual method.