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

Nick is standing next to a staircase that leads to his apartment. The staircase has `n` total steps; Nick knows he can climb anywhere between `1` and `m` steps in one jump. He thinks about how many ways there are to climb this staircase. He realizes it is a big number since there are a lot of possible combinations. So, he has asked you to write an algorithm for him that tells him the number of possible ways to climb a staircase given `n` (number of steps) and, `m` (number of steps covered in biggest jump). 

# Input

Your algorithm will take as input `n`, the number of steps in the staircase and, `m`, the number of steps covered in the biggest leap. Nick can jump any number of stairs between `1` and `m`. 

```
n = 4
m = 2
```

# Output

Your algorithm will return the number of possible ways to climb the staircase.

```
staircase(n, m) = 5

```

Look at the following visualization as a hint for the challenge.


In this lesson, you will work on an interesting problem that can be solved using 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

Challenge: The Staircase Problem

Problem statement