Average Case

Question 1

What is the intuition behind average case algorithms?

Answer 1

Question 2

What is the definition of Expectation of variable T?

Answer 2

Question 3

Find the expectation of T for the following:

Answer 3

Question 4

Find the expactation of the following:

Answer 4

Question 5

What is a Randomized Algorithm?

Answer 5

Question 6

What is the randomized algorithm type: Las Vegas?

What is an example of this algorithm?

Answer 6

Question 7

What is the randomised algorithm type; Monte Carlo?

Answer 7

Question 8

What are the advantages/disadvantages of randomized algorithms in general?

Answer 8

Question 9

What are the advantages/disadvantages of Las Vegas algorithms?

Answer 9

Question 10

What are the advantages/disadvantages of Monte Carlo algorithms?

Answer 10

Question 11

Why does it make more sense to think about expected time instead of worst-case time for Las Vegas algorithms?

Answer 11

Question 12

How would you use a Monte Carlo algo to approximate the value of Pi using only addition, multiplation, and division?

Answer 12

Question 13

What would the code look like for the following Algo?

What would the run time be?

Answer 13