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

## What are the Fibonacci numbers?

Fibonacci numbers are a series of numbers given by the following set of formulas:

$Fib(0) = 0$

$Fib(1) = 1$

$Fib(n) = Fib(n-1) + Fib(n-2)$

This is a classic example of recursion. The first two equations give us the **base cases**, while the third equation is the **recursive step**. Verbally, we can define *n$^{th}$ Fibonacci number as sum of (n-1)$^{th}$ and (n-2)$^{th}$ Fibonacci numbers*.

## Are Fibonacci numbers more than just a formula?

Well, yes! Look at the visualization in Figure 1.






# What are the Fibonacci numbers?

Fibonacci numbers are a series of numbers given by the following set of formulas:

$Fib(0) = 0$

$Fib(1) = 1$

$Fib(n) = Fib(n-1) + Fib(n-2)$

This is a classic example of recursion. The first two equations give us the **base cases**, while the third equation is the **recursive step**. Verbally, we can define *n$^{th}$ Fibonacci number as sum of (n-1)$^{th}$ and (n-2)$^{th}$ Fibonacci numbers*.

# Are Fibonacci numbers more than just a formula?

Well, yes! Look at the visualization in Figure 1.






In this lesson, we will learn about a flagship application of recursion, the Fibonacci numbers.

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

The Fibonacci Numbers

What are the Fibonacci numbers?

Are Fibonacci numbers more than just a formula?