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

We saw in the last chapter what we mean by the [top-down approach](https://www.educative.io/courses/dynamic-programming-in-python/approaches-of-dynamic-programming#top-down-approach). It essentially means that we start looking at the problem as a whole, then break it down into smaller and smaller units, and then evaluate those units that produce the answer to our original problem. Recursion acts as a natural way to write a top-down dynamic algorithm. The process of storing evaluated results in the top-down approach is called **memoization**. 


# Memoization
No, we did not make a typo, its memoization, without an r. Memoization is defined as:

> *The act of storing results of costly function call, and retrieving them from the store when needed again to avoid re-evaluation.*

## The way to memoize

The most typical way to memoize results is by using **hashtables**. Hashtables are arrays that can be indexed using variable types other than integers. As we have already seen, we may need to store results against strings, floats, and even objects. Hashtables allow us to do all of this quite easily. The only condition for using hashtables is that keys should be unique. In Python, we can use the dictionary data structure as a hash table. The dictionary allows us to store data in the form of key-value pairs in an unordered collection of data values. The code snippet below shows the usage of a dictionary in Python.


In this lesson, we will learn about a result storing technique used in top-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

What is Memoization?