#Dynamic Programming

Given a grid representing a unique paths problem, provide a brute force solution as well as an optimal one. You need to explain the time complexity of both solutions.

You are given an array where each element represents the price of a stock on a given day. Write an algorithm to determine the maximum profit you can achieve by buying on one day and selling on another. Discuss the constraints and provide examples.

In the Mice and Cheese problem, you need to calculate the maximum amount of cheese that can be eaten by two mice given their starting points and the positions of the cheese. Formulate a plan and provide a solution algorithm to address this problem.

Discuss a variation of the 'Coco eating banana' problem from LeetCode. Explain the approach you would take to solve this problem, including any assumptions and edge cases.

Discuss a simple dynamic programming and recursion problem similar to the rod cutting problem. Provide the algorithm and time complexity analysis.