What is the primary purpose of dynamic programming?

Dynamic programming is a powerful algorithmic technique primarily designed to solve problems by breaking them down into simpler subproblems and storing the results of these subproblems to avoid redundant calculations. This method is particularly effective for optimization problems where the same subproblems are solved multiple times, such as in the case of the Fibonacci sequence calculation, shortest paths in graphs, and many others.

By storing the outcomes of previously computed subproblems in a table (often referred to as memoization or tabulation), dynamic programming ensures that each subproblem is solved only once. This not only saves computational time but also enhances the efficiency of the algorithm significantly compared to naive recursive approaches that might recalculate the same values repeatedly.

Understanding this core principle of dynamic programming—that it avoids redundant work by saving previously computed results—is essential in grasping why this technique is so valuable in algorithm design.