The "value per pound" greedy strategy didn't work to solve the 0-1 knapsack problem. Would the "price per inch" greedy strategy work for the rod-cutting problem? Price-per-Inch Strategy: Given a rod of length n, first cut off a piece of length i, where 1

The "value per pound" greedy strategy didn't work to solve the 0-1 knapsack problem. Would the "price per inch" greedy strategy work for the rod-cutting problem? Price-per-Inch Strategy: Given a rod of length n, first cut off a piece of length i, where 1

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Introduction to Greedy Algorithm

A greedy algorithm is a problem-solving method that makes the locally optimal selection at every stage to reach a globally optimal solution. It solves a problem in two stages: Scanning the list of items and Optimization. However, in most problems, the greedy algorithm fails to provide a globally optimal solution.

Question

The "value per pound" greedy strategy didn't work to solve the 0-1 knapsack problem. Would the "price
per inch" greedy strategy work for the rod-cutting problem?
Price-per-Inch Strategy: Given a rod of length n, first cut off a piece of length i, where 1 <i<n,
having maximum price per inch, and then continue by applying the same strategy to the remaining piece
of length n- i.
If the above strategy always yields an optimal solution, then provide a pseudo code describing the
greedy algorithm for the rod-cutting problem. Otherwise, provide a counter example.

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