In the rod cutting problem, we are given a rod of length n, along with pi, which indicates the price of a rod/piece of length pi, for i = 0,1, 2, ....,n. Consider the following instance: Po = 0, pi = 2, p2 = 7,p3 = 15, p4 = 16 and n = 4. Let r; denote the maximum profit you can obtain by cutting a rod of length i into smaller pieces (or by making no cuts). What is the respective value of rɔ, rı, ...,rq? You must show how you obtained the values by applying the recurrence.

In the rod cutting problem, we are given a rod of length n, along with pi, which indicates the price of a rod/piece of length pi, for i = 0,1, 2, ....,n. Consider the following instance: Po = 0, pi = 2, p2 = 7,p3 = 15, p4 = 16 and n = 4. Let r; denote the maximum profit you can obtain by cutting a rod of length i into smaller pieces (or by making no cuts). What is the respective value of rɔ, rı, ...,rq? You must show how you obtained the values by applying the recurrence.

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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Given a rod of length n inches and an array of prices that contains prices of all pieces of size smaller than n. Determine the maximum value obtainable by cutting up the rod and selling the pieces. For example, if length of the rod is 8 and the values of different pieces are given as following, then the maximum obtainable value is 22 (by cutting in two pieces of lengths 2 and 6) length 1 2 3 4 5 6 7 8 price | 1 5 8 9 10 17 17 20 And if the prices are as following, then the maximum obtainable value is 24 (by cutting in eight pieces of length 1 Please provide the solution in the assembly programming language and please use both recursion and dynamic programing method to solve the problem.
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