I've been diving into data structures and algorithms lately and came across a rather interesting problem/solution, one which is rather straight forward, The Karatsuba algorithm :
The Karatsuba algorithm is a fast multiplication algorithm. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It reduces the multiplication of two n-digit numbers to at most O(nlog2^3) ~ O(n^1.59) single-digit multiplications in general (and exactly n^log2^3 when n is a power of 2). It is therefore asymptotically faster than the traditional algorithm, which requires n^2 single-digit products. For example, the Karatsuba algorithm requires 310 = 59,049 single-digit multiplications to multiply two 1024-digit numbers (n = 1024 = 2^10), whereas the traditional algorithm requires (2^10)^2 = 1,048,576 (a speedup of 17.75 times).