Counting Subsets with Target Sum Using Dynamic Programming

Solving combinatorial problems efficiently is a core skill in computer science and algorithm design. This course provides a clear, step-by-step pathway to understanding how to count subsets that sum to a specific target value using dynamic programming. You will transition from brute-force thinking to elegant, optimized algorithms that solve complex counting problems in polynomial time. By the end of this course, you will be able to confidently formulate, analyze, and implement dynamic programming solutions for subset-sum and knapsack-style problems. What you will learn: Understand the core mathematical concepts of subset selection and target sum constraints; Design recursive backtracking solutions to explore the state space of subset combinations; Apply memoization to eliminate redundant calculations and optimize recursive trees; Construct iterative, bottom-up dynamic programming tables for robust state tracking; Optimize space complexity using modern array-reduction techniques; Analyze the time and space complexity of your algorithms using Big O notation. We begin with the fundamental definitions of subsets and recursion, gradually building up to state-space reduction and memory optimization. This text-based course is designed for beginners in algorithms, requiring only a basic understanding of programming logic and variables. Start writing highly optimized, professional-grade algorithmic solutions today.