Consider the following version of Knapsack. Given are two weight limits W 1 and W 2 , where W 1 ≤ W 2 . Given are also n items (w 1 , c 1 ), (w 2 , c 2 ), . . . , (w n , c n ), where w i is the weight and c i the cost of the i-th item. We want to find a subset of these items of the highest cost, where the subset weights at least W 1 and at most W 2 . Give an O(nW 2 ) algorithm for this problem. (Recall that the cost (respectively weight) of a subset is the sum of the costs (respectively weights) of the items in the subset

Q: (a) A student has been asked to put some parcels on a shelf. The parcels all weigh different…

A: Answer: We need to write which algorithms would be acceptable so we will see in the more details…

Q: Given a collection of n shapes on the plane, a valid traversal from shape A to shape B is a sequence…

A: The problem at hand involves finding the minimum cost traversal from shape A to shape B in a…

Q: There are n ≥ 2 married couples who need to cross a river. They have a boat that can hold no more…

A: Your answer is given below.

Q: Use the greedy algorithm below to solve the activity problem. Suppose the S={a,a.....an) is a set of…

A: Greedy seems to be a computational technique that develops a solution layer by layer, always…

Q: Based on the pumping lemma, if L is regular, then 3k > 1 (V strings w E L, where |w| >k (3x, y, z (w…

A: A key idea in formal language theory is the Pumping Lemma, which offers a standard for demonstrating…

Q: Let the universal set be R and let A = {x = R: 5 < x≤ 10}, B = {x = R: -5<x<6} and C= {xe R:…

A: (i) The Union operator joins or concatenates the elements of two different sets into a single set.…

Q: Consider the same house rent prediction problem where you are supposed to predict price of a house…

A: The solution to the above question is:

Q: Consider the following instance of 0-1 Knapsack problem: Item Profit Weight 11 9 5 12 6 13 7 4 14 5…

A:

Q: 8. Find the point on the plane 3x + 4y + z = 1 closest to(-1,1,1)

A: Given equation of plane is : 3x + 4y + z = 1

Q: A bottom up dynamic programming method is to be used to solve the subset sum problem. The problem is…

A: This query relates to dynamic programming. The subset sum problem is to be solved through bottom up…

Q: Let A = {m ∈ Z | m ≡ 9 (mod 12)}. Let B = {n ∈ Z | n ≡ 1 (mod 4)}.

A: We are going to prove that set B is not a subset or equal to set A. First find out what is set A and…