Solving the Stable Matching Problem with the Gale-Shapley Algorithm

Matching two groups based on preferences is a classic problem in computer science and economics, from pairing students with colleges to allocating medical residents. This text-based course guides you through the foundational concepts of matching theory and the mechanics of the Gale-Shapley algorithm. By working through clear, step-by-step written explanations and practical exercises, you will gain a solid grasp of how stable matchings are formed and verified. What you'll learn: - Understand the core concepts of matching theory, preference lists, and stability definitions - Trace the step-by-step execution of the Gale-Shapley algorithm using written walkthroughs - Analyze the mathematical properties of the algorithm, including termination and optimality - Implement the algorithm conceptually and in clean, modern Python code with type hints - Apply stable matching principles to modern real-world scenarios like resource allocation - Practice solving matching problems manually with structured written exercises The course starts with basic definitions and key terminology before moving on to execution mechanics and code implementation. It is designed for beginners in algorithms, mathematics, or computer science, requiring no advanced prerequisites. Start reading to master algorithmic resource allocation.