Solving Dynamic Programming Problems

There are two popular ways to solve DP problems: the tabular method and memoization. In the tabular method, we build a matrix that stores the intermediate values one by one in the lookup table. On the other hand, in the memoization method, we store the same values in an unstructured way. Here, unstructured way refers to the fact that the lookup table may be filled all at once.

Imagine you're a baker and are selling cakes to shops. Your job is to sell cakes and make the maximum profit out of it. For simplicity, we will assume that all other costs are fixed, and the highest price offered for your product is the only indicator of profits earned, which is a fair assumption for most business cases. So, naturally, you'd wish to sell all your cakes to the shop offering the highest price, but there's a decision to make as there are multiple shops that offer different prices on different sizes of cakes. So, you have two choices: how much...