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Dynamic Programming in Python: Optimizing Programs for Efficiency

Learn about dynamic programming in Python, delve into recursion basics, explore advanced DP techniques, and discover practical coding challenges to optimize algorithms for real-world applications.

4.7

47 Lessons

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LEARNING OBJECTIVES

Identify recursion types and write correct recursive functions with clear base cases in Python
Analyze time complexity of naive recursion on problems like Fibonacci, permutations, and N-Queens
Determine when dynamic programming applies using optimal substructure and overlapping subproblems
Implement top-down DP with memoization using Python dictionaries to avoid repeated subproblems
Implement bottom-up DP with tabulation arrays and build solutions in the correct subproblem order
Optimize DP space usage (e.g., Fibonacci O(1) space) by managing minimal state
Solve classic DP challenges (knapsack, LCS, edit distance, TSP, matrix chain) and compare approaches

Learning Roadmap

47 Lessons3 Quizzes16 Challenges

Chapter 1: From Recursion to Dynamic Programming

Get familiar with transitioning from recursion to dynamic programming and optimizing algorithms efficiently.

Introduction

What is Recursion?

Thinking Recursively

The Fibonacci Numbers

Challenge: Find All Permutations of a String

Solution Review: Find All Permutations of a String

Challenge: Place N Queens on an NxN Chessboard

Solution Review: Place N Queens on an NxN Chessboard

Is Plain Recursion Good Enough?

What is Dynamic Programming?

Approaches of Dynamic Programming

Where to Use Dynamic Programming

Quiz

Chapter 2: Top-Down Dynamic Programming with Memoization

Get started with efficient top-down dynamic programming using memoization techniques for optimization.

What is Memoization?

The Fibonacci Numbers Algorithm with Memoization

Challenge: The Staircase Problem

Solution Review: The Staircase Problem

Challenge 2: The Knapsack Problem

Solution Review: The Knapsack Problem

Quiz

Chapter 3: Bottom-Up Dynamic Programming with Tabulation

10 Lessons

Work your way through bottom-up dynamic programming, tabulation, optimization, and practical problem-solving.

Chapter 4: Practice Problems

17 Lessons

Apply your skills to solve diverse dynamic programming challenges efficiently and enhance problem-solving techniques.

Solving Sudoku and the 8-Queens Puzzle as Constraint Satisfaction

Project

Certificate of Completion

Showcase your accomplishment by sharing your certificate of completion.

Developed by MAANG Engineers

Every Educative lesson is designed by a team of ex-MAANG software engineers and PhD computer science educators, and developed in consultation with developers and data scientists working at Meta, Google, and more. Our mission is to get you hands-on with the necessary skills to stay ahead in a constantly changing industry. No video, no fluff. Just interactive, project-based learning with personalized feedback that adapts to your goals and experience.

ABOUT THIS COURSE

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.

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