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

Let's bring into practice our recursion skills and solve the first coding challenge of this course. 

# Problem statement

Given a string, `str`, you are required to output an array containing all the possible permutations of that string. By permutation, we simply mean all the different arrangements of the characters of that string.

## Input

Your input will be a single string `str`.

```
str = "abc"
```

## Output

Your function should return a list of all possible permutations of the string `str`.

```
permutations(str) = ["abc", "acb", "bac", "bca", "cab", "cba"]
```

You should not change the prototype of function `permutations`, as this will affect testing. You can make another function of the desired prototype and call it from `permutations`.

# Coding challenge

Carefully think about what the base case will be and how you will make recursive calls. You may look at hints if you feel stuck. Best of luck!


Let’s practice our recursion skills and solve the first coding challenge of this course.


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: Find All Permutations of a String