Deck 11: Analyzing Algorithm Efficiency

Question 1

Express the following statement using Θ-notation:

Answer 1

Question 2

Use O-notation to express the following statement:

Answer 2

Question 3

Let h be the function whose graph is shown below. Carefully sketch the graph of 2h.

Answer 3

Question 4

Express the following statement using O-notation:

Question 5

Draw a careful graph of the function f defined by the formula
for all integers n.

Question 6

Question 7

Consider the statement:
Express this statement using O-notation.

Question 8

Describe the operation of the sequential search algorithm.

Question 9

Consider the statement:
Express this statement using

Question 10

Explain why the following statement is true. (You may use the theorem on polynomial orders.)

Question 11

Question 12

Sketch the graph of

Question 13

(a) Find the total number of additions and multiplications that must be performed when the
following algorithm is executed. Show your work carefully.
(b)

Question 14

Describe the operation of the insertion sort algorithm.

Question 15

Question 16

Express the following statement using Ω-notation.:

Question 17

Consider the statement:
Express this statement using

Question 18

Question 19

If x is a real number and
Why?

Question 20

Question 21

Describe the operation of the binary search algorithm.

Question 22

Describe the operation of the merge sort algorithm.