Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 16.2, Problem 3E
Program Plan Intro

To give the algorithm for the knapsack problem where the items when sorted by increasing weight is same as the items when sorted by the decreasing value.

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For a double knapsack problem, assume follwoing 2 algorithms used. (1) Use the regular subset sum knapsack algorithm  to pick a maximum-value solution S1​ that fits in the first knapsack, and then use it again on the remaining items to pick a maximum-value solution S2​ that fits in the second knapsack. (2) Use the Knapsack algorithm to pick a maximum-value solution S that would fit in a knapsack with capacity C1​+C2​, then partition S arbitrarily into two sets S1​ and S2​ with total sizes at most C1​ and C2​, respectively.   Which of the following statements are true? (Choose all that apply.) a) Algorithm (1) is guaranteed to produce an optimal solution to the double-knapsack problem but algorithm (2) is not. b) Algorithm (2) is guaranteed to produce an optimal solution to the double-knapsack problem but algorithm (1) is not. c) Algorithm (1) is guaranteed to produce an optimal solution to the double-knapsack problem when C1​=C2​. d) Neither algorithm is guaranteed to produce an…
If a Genetic Algorithm only finds local optimal solutions, what should be done to find a better one globally?
Apply the bottom-up dynamic programming algorithm to the followinginstance of the knapsack problem: Item Weight Value 1 3 $25 2 2 $30 3 1 $15 4 4 $40 5 5 $50 Capacity W = 8.
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