Dynamic Programming: Fibonacci Numbers

This lecture introduces dynamic programming as an algorithmic paradigm, focusing on the concept of memoization. Starting with the Fibonacci numbers, the instructor explains the top-down and bottom-up approaches, illustrating how to save computation time by remembering previous calculations. The lecture covers the implementation of memoization for Fibonacci numbers, showcasing the efficiency of the bottom-up method. Key elements in designing a dynamic programming algorithm, such as optimal substructure, are discussed. The lecture concludes with a detailed explanation of rod cutting as an application of dynamic programming, emphasizing the structural theorem and its proof.