Dynamic Programming

[!NOTE] This module explores the core principles of Dynamic Programming, deriving solutions from first principles and hardware constraints to build world-class, production-ready expertise.

Dynamic Programming (DP) is a method for solving complex problems by breaking them down into simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems and optimal substructure. This module takes you from the basic concepts of recursion and memoization to advanced state optimization techniques.

Module Contents

  1. Introduction to Dynamic Programming

Master the fundamentals of Dynamic Programming. Learn about overlapping subproblems, optimal substructure, and the trade-off between Memoization and Tabulation.

  1. Bottom Up vs TopDown

Detailed comparison of Top-Down (Memoization) and Bottom-Up (Tabulation) Dynamic Programming approaches with interactive visualizations.

  1. Classic Problems

Master the 0/1 Knapsack Problem and Longest Common Subsequence (LCS) with interactive visualizations and step-by-step explanations.

  1. Matrix DP

Learn how to solve grid-based Dynamic Programming problems like Unique Paths and Minimum Path Sum with interactive obstacle visualizers.

  1. Subset Partition

Solve Subset Sum and Partition Equal Subset Sum problems using Dynamic Programming. Interactive visualizations included.

  1. Space Optimization

Learn how to optimize Dynamic Programming solutions from O(N) space to O(1) and O(N2) to O(N) using rolling arrays.

  1. State Design

Master advanced DP state design using State Machines. Learn to solve the ‘Best Time to Buy and Sell Stock with Cooldown’ problem.

  1. Module Review: Dynamic Programming

Review key Dynamic Programming concepts with flashcards and a comprehensive cheat sheet.

Practice

[!NOTE] Looking for hands-on algorithmic exercises? We have migrated all coding challenges for this module into the Problem Vault to give you a centralized, focused practice environment.

Module Chapters