Transform your slow recursive solutions into lightning-fast dynamic programming algorithms! This video shows you exactly how to identify overlapping subproblems and apply memoization to dramatically improve time complexity. We will dive deep into two fundamental subset sum problems using memoization: 1. Count all possible ways to form a sum 2. Find minimum elements needed for a sum Both problems look different but share the same optimization technique that transforms O(2^N) solutions into efficient O(N×M) algorithms. ⸻ Chapters: 00:00 Introduction - When to Optimize Recursion 00:47 Problem 1: Subset Sum Count 01:16 Identifying Subproblems 03:50 Defining Function State (N, M) 04:15 Recursive Solution Implementation 04:38 Inductive Step 04:56 Base Cases Explained 05:51 Tracing the Recursion Tree 06:23 Complexity Analysis 07:34 Spotting Overlapping Subproblems 08:35 Adding Memoization Magic 09:17 Time Complexity: O(2^N) → O(N×M) 10:15 Problem 2: Minimum Elements for Sum 11:11 Investing the Include/Exclude Approach 11:49 Adapting the Recursive Approach 13:12 Base Case Variations 14:28 Tracing the Updated Recursion Tree 15:30 Overlapping Subproblems 16:15 Adding the Cache 16:28 Final Complexity Analysis 16:44 Summary & Practice Resources ⸻ What you'll master: - How to identify when memoization will help - The complete 5-step process (recursion + optimization) - Converting O(2^N) solutions to O(N×M) - Two classic DP problems solved step-by-step - Understanding overlapping subproblems - When and how to cache recursive results Key Insights: - Not all recursive problems benefit from memoization - State representation is crucial (N, M in these examples) - The difference between counting ways vs. finding minimum - How changing return values changes the entire solution Practice These Patterns: Visit to: - Access complete code in C++, Java, and Python - Practice more subset sum variations - See memoization applied to other problems - Get curated FAANG interview problems Perfect for: - LeetCode medium/hard problem solvers - Engineers preparing for coding interviews - Students learning dynamic programming Prerequisites: - Understanding of basic recursion (watch my Recursion series!) - Familiarity with time complexity - Basic array manipulation Coming next: More dynamic programming patterns and LeetCode hard problems explained! Connect with me: LinkedIn: Practice: #DynamicProgramming #Memoization #Recursion #CodingInterview #DSA #Algorithms #SubsetSum #FAANG