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

## Fibonacci numbers algorithm with tabulation

In the [last lesson](https://www.educative.io/courses/dynamic-programming-in-python/the-fibonacci-numbers-algorithm-with-tabulation), we saw a bottom-up implementation of the Fibonacci numbers algorithm. We discussed how the time complexity of that algorithm was *O(n)*, thanks to tabulation. However, due to tabulation, our space complexity also rose to **O(n)**. 


# Fibonacci numbers algorithm with tabulation

In the [last lesson](https://www.educative.io/courses/dynamic-programming-in-python/the-fibonacci-numbers-algorithm-with-tabulation), we saw a bottom-up implementation of the Fibonacci numbers algorithm. We discussed how the time complexity of that algorithm was *O(n)*, thanks to tabulation. However, due to tabulation, our space complexity also rose to **O(n)**. 


In this lesson, we will learn a better way to tabulate the Fibonacci numbers algorithm for better space complexity.


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

Optimizing the Fibonacci Numbers Algorithm

Fibonacci numbers algorithm with tabulation