0/1 Knapsack Problem Using Dynamic Programming - Tutorial & Source Code

Описание: 01 Knapsack Problem defined and explained. In this tutorial we explain why a greedy rule does not work and present a dynamic programming algorithm that fills out a table. The running time complexity of the dynamic programming algorithm is pseudo-polynomial, not quadratic, even though the table is two dimensional. Understanding the running time complexity gives a sense of why this problem is hard and why it's called "weakly NP-complete".

Source code of minimal implementation in JavaScript:
https://bitbucket.org/StableSort/play...

Source code implementation in Java:
https://bitbucket.org/StableSort/play...

Wikipedia: https://en.wikipedia.org/wiki/Knapsac...

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. 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.

Weak NP-completeness: https://en.wikipedia.org/wiki/Weak_NP...

This is a common problem that is given during coding interviews in engineering firms such as Google and Microsoft.

Written and narrated by Andre Violentyev