Dynamic programming (DP) is a powerful optimization technique used to solve complex problems by breaking them down into simpler overlapping subproblems and storing the results of these subproblems to avoid redundant calculations. This method is particularly effective for problems that exhibit the properties of optimal substructure and overlapping subproblems, such as the Fibonacci sequence, knapsack problem, and shortest path problems. Unlike straightforward recursion, which solves each subproblem independently and may lead to exponential time complexity due to repeated calculations, dynamic programming significantly improves efficiency by caching previously computed results. This can be achieved through either a top-down approach, often called memoization, or a bottom-up approach, also known as tabulation. In memoization, the algorithm recursively solves subproblems and stores their results in a cache (usually an array or a dictionary) for future reference. This way, if the same subproblem is encountered again, the algorithm can retrieve the cached result instead of recomputing it. In contrast, tabulation builds a table iteratively, filling it in from the base cases up to the desired solution. The main difference between dynamic programming and recursion lies in the way they handle subproblem results. While recursion may lead to excessive function calls and redundant calculations, dynamic programming optimizes performance by storing and reusing results, often reducing the time complexity from exponential to polynomial. Understanding dynamic programming is crucial for tackling a wide range of algorithmic challenges and developing efficient solutions.