11. Dynamic Programming

This chapter delves into the world of dynamic programming, a method for solving complex problems by breaking them down into simpler subproblems. The narrative begins with a knapsack problem, where hikers must pack a knapsack with limited capacity to maximize benefits. The chapter explains how dynamic programming can be used to solve this problem efficiently. It introduces Bellman's equation and the principle of optimality, which are central to understanding dynamic programming. The text also explores the concept of backward recursion, demonstrating how it can be used to solve problems systematically. Additionally, the chapter discusses optimal stopping problems, using the secretary problem as an example. The conclusion highlights the versatility of dynamic programming in solving a wide range of resource allocation problems, making it a valuable tool for professionals in various fields.