1. Let A = {a1, ..., an} and B = {b1, ..., bm} be two sets...

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Question

1. Let A = {a1, ..., an} and B = {b1, ..., bm} be two sets...

1. Let A = {a₁, ..., a_n} and B = {b₁, ..., b_m} be two sets of numbers. Consider the problem of finding their intersection, i.e., the set C of all the numbers that are in both A and B.

a. Design a presorting based algorithm for solving this problem and determine its efficiency class.

2. Estimate how many searches will be needed to justify time spent on presorting an array of 10³ elements if sorting is done by mergesort and searching is done by binary search.

3. Solve the following system by Gaussian elimination:

x₁ + x₂ + x₃ = 2

2x₁ + x₂ + x₃ = 3

x₁ - x₂ + 3x₃ = 8

4. Solve the system of problem #3 by computing the inverse of its coefficient matrix and then multiplying it by the vector on the right-hand side.

5. For each of the following lists, construct an AVL tree by inserting their elements successively, starting with the empty tree.

a. 1, 2, 3, 4, 5, 6

b. 6, 5, 4, 3, 2, 1

c. 3, 6, 5, 1, 2, 4

6. Construct a heap for the list 1, 8, 6, 5, 3, 7, 4 by the bottom-up algorithm.

7. Construct a heap for the list 1, 8, 6, 5, 3, 7, 4 by successive key insertions (top-down algorithm).

8. Apply Horner's rule to evaluate the polynomial

p(x) = 3x⁴ - x³ + 2x + 5 at x = -2.

engineering Computer-Science

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Answer 1

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