Exploring dynamic programming

One question that arises when we identify overlapping subproblems is: how can we store these solutions to avoid redundant computations? This is where dynamic programming introduces the concept of memoization. It involves storing the results of subproblems in a data structure, such as an array or a dictionary, so that when the same subproblem arises again, the stored result can be used immediately, eliminating the need for recalculation.

Before we begin, it’s important to clarify that “memoization” is not a misspelling of “memorization.” These two terms have distinct meanings. Memoization comes from the Latin word “memo,” which means “to be remembered.” It refers to a technique in computer science where the results of expensive function calls are stored and reused to avoid redundant calculations. In contrast, memorization refers to the process of learning and committing information to memory...