The activity selection problem is a classic optimization problem that seeks to select the maximum number of non-overlapping activities from a given set, each with a start and end time. It is commonly solved using a greedy algorithm that prioritizes activities with the earliest finish time to ensure the optimal solution.
When solving a big problem, it's often easier to break it into smaller parts, called sub-problems, that are easier to solve. Once you solve all the little parts, you can put them together to solve the big problem, like building a puzzle by connecting small pieces.
Dynamic algorithms are a class of algorithms that solve problems by breaking them down into simpler subproblems, solving each subproblem just once, and storing their solutions – typically using a table – to avoid redundant work. This approach is particularly effective for optimization problems and those that exhibit overlapping subproblems and optimal substructure, leading to significant efficiency improvements over naive methods.