Exercise 4 20= 10+4+6 The rod-cutting problem consists of a rod of n units long that can be cut into integer-length pieces. The sale price of a piece i units long is Pi for i = 1,...,n. We want to apply dynamic programming to find the maximum total sale price of the rod. Let F(k) be the maximum price for a given rod of length k. 1. Give the recurrence on F(k) and its initial condition(s). 2. What are the time and space efficiencies of your algorithm? Now, consider the following instance of the rod-cutting problem: a rod of length n=5, and the following sale prices P1=2, P2=3, P3=7, P4=2 and P5=5.

Exercise 4 20= 10+4+6 The rod-cutting problem consists of a rod of n units long that can be cut into integer-length pieces. The sale price of a piece i units long is Pi for i = 1,...,n. We want to apply dynamic programming to find the maximum total sale price of the rod. Let F(k) be the maximum price for a given rod of length k. 1. Give the recurrence on F(k) and its initial condition(s). 2. What are the time and space efficiencies of your algorithm? Now, consider the following instance of the rod-cutting problem: a rod of length n=5, and the following sale prices P1=2, P2=3, P3=7, P4=2 and P5=5.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter12: Review Of Calculus And Probability

Section12.5: Random Variables, Mean, Variance, And Covariance

Problem 5P

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