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
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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.
Chapter 16 Solutions
Introduction to Algorithms
Ch. 16.1 - Prob. 1ECh. 16.1 - Prob. 2ECh. 16.1 - Prob. 3ECh. 16.1 - Prob. 4ECh. 16.1 - Prob. 5ECh. 16.2 - Prob. 1ECh. 16.2 - Prob. 2ECh. 16.2 - Prob. 3ECh. 16.2 - Prob. 4ECh. 16.2 - Prob. 5E
Ch. 16.2 - Prob. 6ECh. 16.2 - Prob. 7ECh. 16.3 - Prob. 1ECh. 16.3 - Prob. 2ECh. 16.3 - Prob. 3ECh. 16.3 - Prob. 4ECh. 16.3 - Prob. 5ECh. 16.3 - Prob. 6ECh. 16.3 - Prob. 7ECh. 16.3 - Prob. 8ECh. 16.3 - Prob. 9ECh. 16.4 - Prob. 1ECh. 16.4 - Prob. 2ECh. 16.4 - Prob. 3ECh. 16.4 - Prob. 4ECh. 16.4 - Prob. 5ECh. 16.5 - Prob. 1ECh. 16.5 - Prob. 2ECh. 16 - Prob. 1PCh. 16 - Prob. 2PCh. 16 - Prob. 3PCh. 16 - Prob. 4PCh. 16 - Prob. 5P
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- Given a knapsack of capacity W = 1.5Kg, solve the following 0/1 knapsack problem using DP. Illustrate the procedure and determine the subset of items. With Pythonarrow_forwardThe heuristic path algorithm is a best-first search in which the objective function is f(n)= 3w*g(n) + (2w+1) * h(n), 0≤w<3. For what values of w is this algorithm guaranteed to be optimal?arrow_forwardWhat is the time complexity of the best-known algorithm for solving the Traveling Salesman Problem (TSP)? Can this problem be solved in polynomial time, or is it an example of an NP-hard problem?arrow_forward
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