Dynamic programming

Dynamic programming is the most powerful design technique for solving optimization problems. Such problems generally have many possible solutions. The basic idea of dynamic programming is based on the intuition of the divide-and-conquer technique. Here, essentially, we explore the space of all the possible solutions by decomposing the problem into a series of sub-problems and then combining the results to compute the correct solution for the large problem. The divide-and-conquer algorithm is used to solve a problem by combining the solutions of the non-overlapping (disjoint) sub-problems, whereas dynamic programming is used when the sub-problems are overlapping, meaning that the sub-problems share sub-sub-problems. The dynamic programming technique is similar to divide and conquer in that a problem is broken down into smaller problems. However, in divide and conquer, each sub-problem has to be solved before its results can be used to solve bigger problems. In contrast...