Which algorithm design paradigm uses the principle of using previously solved subproblems?

Dynamic programming is an algorithm design paradigm that is specifically focused on breaking down complex problems into simpler subproblems and solving each of these subproblems just once, storing their solutions. This approach is especially useful when the same subproblems are solved multiple times, which is often the case in optimization problems. By storing the results of subproblems, dynamic programming avoids the inefficiency of redundant calculations, optimizing both time and computational resources.

For example, in calculating Fibonacci numbers using dynamic programming, once the result for a particular index is computed, it is stored in an array or table. When that Fibonacci number is needed again, the algorithm can look up the pre-computed value instead of recalculating it, which significantly speeds up the process.

This two-pronged approach of overlapping subproblems and optimal substructure is what defines dynamic programming, distinguishing it from other paradigms like greedy algorithms, divide and conquer, or backtracking, which do not rely on storing previously solved subproblems in the same way.