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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

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Product type Paperback
Published in Oct 2019
Publisher
ISBN-13 9781838828844
Length 626 pages
Edition 1st Edition
Languages
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Authors (4):
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Anil Achary Anil Achary
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Anil Achary
John Carey John Carey
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John Carey
Payas Rajan Payas Rajan
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Payas Rajan
Shreyans Doshi Shreyans Doshi
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Shreyans Doshi
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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...

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