Dynamic Programming is a powerful algorithmic technique used to solve complex problems efficiently. It works by breaking down a large problem into smaller, overlapping subproblems, solving each subproblem once, and storing the results to avoid redundant calculations.
Dynamic Programming is built on two core principles. First, overlapping subproblems means the problem can be broken into smaller parts that are solved multiple times. Second, optimal substructure means the best solution to the whole problem comes from the best solutions to its parts. These principles allow us to store solutions and reuse them efficiently.
There are two main approaches to implementing Dynamic Programming. Top-down approach uses memoization, starting with the original problem and recursively breaking it down while caching results. Bottom-up approach uses tabulation, solving the smallest subproblems first and building up to the main problem iteratively. Both approaches avoid redundant calculations but differ in their execution strategy.