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

Remember how matrix multiplication works. Given two matrices $A$ and $B$  of dimensions $(n \times m)$ and $(m \times l)$, the resulting matrix we get is $AB$ whose dimensions are $(n \times l)$. We’ve shown how matrix multiplication occurs in the example below.

# Problem statement

Remember how matrix multiplication works. Given two matrices $A$ and $B$  of dimensions $(n \times m)$ and $(m \times l)$, the resulting matrix we get is $AB$ whose dimensions are $(n \times l)$. We’ve shown how matrix multiplication occurs in the example below.

In this lesson, you will solve a problem to find the minimum number of primitive multiplications required for a matrix chain multiplication.

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 Matrix Chain Multiplication

Problem statement