Gain insights into dynamic programming, explore recursion basics, and delve into advanced techniques like Bottom-Up optimization. Discover ways to solve complex problems more efficiently with hands-on coding challenges.

Dynamic programming is something every developer should have in their toolkit. It allows you to optimize your algorithm with respect to time and space — a very important concept in real-world applications.

In this course, you’ll start by learning the basics of recursion and work your way to more advanced DP concepts like Bottom-Up optimization. Throughout this course, you will learn various types of DP techniques for solving even the most complex problems. Each section is complete with coding challenges of varying difficulty so you can practice a wide range of problems.

By the time you’ve completed this course, you will be able to utilize dynamic programming in your own projects.

Dynamic Programming in Python: Optimizing Programs for Efficiency

# Problem statement

You are given a rod of length `n` meters. You want to sell the rod and earn revenue. You can cut the rod into multiple smaller pieces of sizes $1$ through $n$ and sell them too. You are given the price of each size of the rod. Since you want to earn more, you will have to look for the optimal cuts on the rod that would earn the most revenue.

# Input

Your function would get as input `n`, the original length of the rod. You can cut the rod into different pieces of sizes $1,2,$ up to $n$. The price for each of these pieces is given in a list of size $n$ called `prices`.

```
n = 4
prices = [2,3,7,8]
```

# Output

Your function should return the optimal amount of revenue you can get out of the rod provided `n` and `prices`.

```
n = 4
prices = [2,3,7,8]
rodCutting(n, prices) = 9
```

# Coding challenge

You may write either a bottom-up or a top-down dynamic programming algorithm. If you plan to write a recursive algorithm first, you may check its correctness by setting the `stressTesting` variable to `False`. 

Think carefully about the problem. Think about strategies to memoize or tabularize the problem, and then write the code. Best of luck!


In this lesson, you will solve another famous dynamic programming challenge, the rod cutting problem.

Chapter 1: From Recursion to Dynamic Programming

Chapter 2: Top-Down Dynamic Programming with Memoization

Chapter 3: Bottom-Up Dynamic Programming with Tabulation

Chapter 4: Practice Problems

Challenge: The Rod Cutting Problem

Problem statement