6 Advanced Dynamic Programming 6.1 Saving Space: Divide and Conquer Released under a Creative Commons Attribution-noncommercial-sharealike 3.0 License

Dynamic programming is a powerful technique for efficiently solving recursive problems, but it’s hardly the end of the story. In many cases, once we have a basic dynamic programming algorithm in place, we can make further improvements to bring down the running time or the space usage. We saw one example in the Fibonacci number algorithm. Buried inside the naïve iterative Fibonacci algorithm is a recursive problem—computing a power of a matrix—that can be solved more efficiently by dynamic programming techniques—in this case, repeated squaring.