Search icon CANCEL
Subscription
0
Cart icon
Your Cart (0 item)
Close icon
You have no products in your basket yet
Arrow left icon
Explore Products
Best Sellers
New Releases
Books
Videos
Audiobooks
Learning Hub
Free Learning
Arrow right icon
Arrow up icon
GO TO TOP
C++ Data Structures and Algorithm Design Principles

You're reading from   C++ Data Structures and Algorithm Design Principles Leverage the power of modern C++ to build robust and scalable applications

Arrow left icon
Product type Paperback
Published in Oct 2019
Publisher
ISBN-13 9781838828844
Length 626 pages
Edition 1st Edition
Languages
Arrow right icon
Authors (4):
Arrow left icon
Anil Achary Anil Achary
Author Profile Icon Anil Achary
Anil Achary
John Carey John Carey
Author Profile Icon John Carey
John Carey
Payas Rajan Payas Rajan
Author Profile Icon Payas Rajan
Payas Rajan
Shreyans Doshi Shreyans Doshi
Author Profile Icon Shreyans Doshi
Shreyans Doshi
Arrow right icon
View More author details
Toc

Table of Contents (11) Chapters Close

About the Book 1. Lists, Stacks, and Queues FREE CHAPTER 2. Trees, Heaps, and Graphs 3. Hash Tables and Bloom Filters 4. Divide and Conquer 5. Greedy Algorithms 6. Graph Algorithms I 7. Graph Algorithms II 8. Dynamic Programming I 9. Dynamic Programming II 1. Appendix

The Knapsack Problem(s)

In this section, we will discuss the standard knapsack problem, also known as the 0-1 knapsack problem, which is known to be NP-complete, and thereby does not allow us to have any polynomial-time solution. Then, we will turn our discussion toward a version of the knapsack problem called the fractional knapsack problem, which can be solved using a greedy approach. Our focus in this section is to demonstrate how even subtle differences between how a problem is defined can lead to large changes in the solution strategies.

The Knapsack Problem

Suppose you are given a set of objects, O = {O1, O2, …, On}, with each having a certain weight, Wi, and a value of Vi. You are also given a bag (or a knapsack) that can carry only a total weight of T units. Now, say you are tasked with finding out about a set of objects to keep in your bag so that the total weight is less than or equal to T, and the total value of the objects is the maximum it can possibly be.

A real-world example...

lock icon The rest of the chapter is locked
Register for a free Packt account to unlock a world of extra content!
A free Packt account unlocks extra newsletters, articles, discounted offers, and much more. Start advancing your knowledge today.
Unlock this book and the full library FREE for 7 days
Get unlimited access to 7000+ expert-authored eBooks and videos courses covering every tech area you can think of
Renews at $19.99/month. Cancel anytime
Banner background image