Introduction to Unbounded Knapsack
Explore the unbounded knapsack problem, a dynamic programming pattern where you maximize item value in a knapsack with no limit on item quantity but constrained capacity. Understand when to apply this pattern through practical examples and learn to differentiate it from other knapsack variants like 0/1 Knapsack. This lesson prepares you to identify and solve problems involving repetition and capacity constraints efficiently.
We'll cover the following...
Overview
A knapsack is defined as a bag carried by hikers or soldiers for carrying food, clothes, and other belongings. The Knapsack problem, as the name suggests, is the problem faced by a person who has a knapsack with a limited capacity and wants to carry the valuable important items. In other words, we are given
In this pattern, we will be discussing 5 problems related to this pattern. The following diagram shows an overview of this pattern.
The Unbounded Knapsack is a special case of the Knapsack problem where there's no limit on the number of instances of each kind of item in the knapsack. The unbounded knapsack is different from 0/1 Knapsack in a way that we are allowed to use multiple samples of an item. However, in the Unbounded Knapsack too, we can't take fractions of an item. We either have to take the complete item or leave it.
Mathematically, we can understand it as: Given