Suppose we have a rod of length n inches and we also have an array of positive integer prices P$,$ where

P$[$i$]$ denotes the selling price $($$$)$ of a piece that is i inches long. Suppose now we have to pay a cost of

$$1$ per cut. You are only allowed to cut the rod into $($positive$)$ integer sized pieces. Define the profit we

make as the revenue $($sum of prices of the pieces$)$ minus the total cost of cutting. We want an algorithm

that finds a way to cut the rod maximizing our profit. For your DP algorithm, use the for the array which stores values of the subproblems