Knapsack Problem
The Knapsack Problem is a classic combinatorial optimization problem in computer science and operations research, where the goal is to select a subset of items with given weights and values to maximize total value without exceeding a weight capacity. It serves as a fundamental example for studying algorithmic techniques like dynamic programming, greedy algorithms, and branch-and-bound. Variations include the 0/1 knapsack (each item can be taken at most once), unbounded knapsack (items can be taken multiple times), and fractional knapsack (items can be divided).
Developers should learn the Knapsack Problem to master dynamic programming and optimization concepts, which are essential for solving real-world problems such as resource allocation, budget planning, and inventory management. It is commonly used in algorithm interviews and courses to teach efficient problem-solving strategies, and understanding it helps in tackling similar NP-hard problems in fields like logistics, finance, and machine learning.