It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.The problem often arises in resource allocation where there are financial constraints and is studied in fields such as combinatorics, computer science, complexity theory, cryptography, applied mathematics, and daily fantasy sports.
I call this the "Grocery Store" variant because I like to think of it as being like Supermarket Sweep where participants race to fill a shopping cart with the highest valued items possible.
Since the grocery store has lots of stock available, it's fine to pick the same item multiple times. Let function to ensure we select the subproblem parameters that yield the highest value.
A multiple constrained problem could consider both the weight and volume of the boxes.
(Solution: if any number of each box is available, then three yellow boxes and three grey boxes; if only the shown boxes are available, then all but the green box.) The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
On the other hand, if an algorithm finds the optimal value of the optimization problem in polynomial time, then the decision problem can be solved in polynomial time by comparing the value of the solution output by this algorithm with the value of k .
Thus, both versions of the problem are of similar difficulty.
In this post, we'll explain two variations of the knapsack problem: Before we dive in, though, let's first talk briefly about what Dynamic Programming entails.
You may have heard the term "dynamic programming" come up during interview prep or be familiar with it from an algorithms class you took in the past.
The bounded knapsack problem (BKP) removes the restriction that there is only one of each item, but restricts the number One example of the unbounded knapsack problem is given using the figure shown at the beginning of this article and the text "if any number of each box is available" in the caption of that figure.
The knapsack problem is interesting from the perspective of computer science for many reasons: There is a link between the "decision" and "optimization" problems in that if there exists a polynomial algorithm that solves the "decision" problem, then one can find the maximum value for the optimization problem in polynomial time by applying this algorithm iteratively while increasing the value of k .