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1. Give a variation of generic merge algorithm for computing A⊖B, which is set of elements that are in A or B, but not in both.

2. Suppose that we implement the set ADT by representing each set using a balanced search tree. Describe and analyze algorithms for each of the methods in

the set ADT.

3. Provide a pseudo code description for performing methods insert and remove on a set implemented with sorted sequence.

4. Let S = {a,b,c,d,e, f,g} be a collection of objects with benefit-weight values as follows: a:(12,4), b:(10,6), c:(8,5), d:(11,7), e:(14,3), f :(7,1), g:(9,6). What is an optimal solution to the fractional knapsack problem for S assuming we have a sack that can hold objects with total weight 18? Show your work.

5. Suppose we are given a set of tasks specified by pairs of the start times and finish times as T = {(1,2),(1,3),(1,4),(2,5),(3,7),(4,9),(5,6),(6,8),(7,9)}. Solve the task scheduling problem for this set of tasks.

[url removed, login to view] is the best way to multiply a chain of matrices with dimensions that are

1 0 x 5, 5 x 2, 2 x 20, 20 x 1 2, 1 2 x 4, and 4 x 60? Show your work.

[url removed, login to view] that ( X - A ) U (X - B) = X - (A n B) , for any three sets X, A, and B .

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