Dynamic Programming: Solving the Company Party Problem

Many real-world optimization problems involve making decisions across hierarchical structures where choices at one level directly constrain options at the next. Understanding how to model and solve these scenarios is a key milestone in mastering algorithmic design. This text-based course guides you through the classic Company Party problem—maximizing total satisfaction while ensuring no direct supervisor and employee are invited together. You will learn how to break down complex hierarchical constraints, apply mathematical formulation, and implement an elegant dynamic programming solution using clean, modern Python code. What you'll learn: * Understand the core principles of dynamic programming, recursion, and memoization. * Map hierarchical organizational structures to tree data structures. * Formulate recurrence relations for maximum independent sets on trees. * Implement the optimization algorithm using modern Python type hints and clean structures. * Trace execution step-by-step to see how local decisions yield global maximums. * Practice with written exercises that reinforce algorithmic complexity analysis. The course begins with foundational concepts of recursion and memoization before moving step-by-step into tree structures, mathematical formulation, and the final optimized implementation. Designed for beginning developers and computer science students, this course requires only basic programming familiarity. Start reading today to master dynamic programming patterns for hierarchical data.