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

# Comparison

Both top-down dynamic programming and bottom-up dynamic programming have their own pros and cons. Knowing these pros and cons can help you choose the algorithm's design approach based on your problem's requirements.

| Operation | Top-Down | Bottom-Up |
| --- | --- | --- |
| Ease of problem formulation | ✅ It is easier to formulate a problem in top-down dynamic programming because of its recursive nature | Thinking about a problem in a bottom-up manner can be slightly less intuitive|
| Stack management | Stack memory can quickly explode in top-down algorithms, thus making them less practical for larger inputs | ✅ In bottom-up algorithms, stack memory is never an issue because there are no recursive calls |
| Cost of recursion | Recursive calls can entail a lot of computation cost | ✅ There is no excessive computation cost due to recursive calls |
| Code readability | ✅ Top-down algorithms are typically much easier to read and comprehend | Bottom-up algorithms can sometimes be difficult to grasp |
| Subproblems solved | ✅ In top-down algorithms, we only evaluate a result on ad-hoc basis, i.e., when it is needed, meaning results that are not needed are never evaluated | Since we evaluate results in order starting from smallest to the largest, we may end up evaluating results that are not needed |

In this lesson, we will look at the pros and cons of top-down dynamic programming and bottom-down dynamic programming.

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

Top-Down vs Bottom-Up

Comparison