Dynamic Programming: Fibonacci Numbers

This lecture introduces dynamic programming as an algorithmic paradigm, focusing on the main idea of saving computation by remembering previous calculations. The instructor explains the concept using Fibonacci numbers as an example, demonstrating the inefficiency of the naive approach and presenting solutions like top-down with memoization and bottom-up methods. The lecture also covers key elements in designing a dynamic programming algorithm, such as optimal substructure. Additionally, the instructor discusses the rod cutting problem, where the goal is to maximize revenue by deciding how to cut a metal rod into pieces based on given prices. Various algorithms for solving the rod cutting problem are presented, emphasizing recursive formulations and optimal revenue calculations.