Case Study 3 Part 1 - Euclidean Algorithm 1. Use the Euclidean Algorithm to find the greatest common divisor of ( integers 396 and 480. (Show all workings) Part 2 Problem: Measuring Efficiency One challenge we will face is how to compare the efficiencies of two or more algorithms, to determine which is more efficient. We will have to use a common measure for example time or space First, we must determine what is most important to us (time or space or some other measure). Then compare the efficiencies (e.g., how much time each algorithm takes to execute, or how much space each algorithm uses). The challenge of timing an algorithm may introduce unwanted bias or overheads, therefore, we need a method that makes comparison fair. We are usually interested in the order of growth of the running time of an algorithm, not in the exact running time. Asymptotic notation gives us a method for classifying functions according to their rate of growth. Scenario: Bigi-Xam 9.0 is a mobile app development workshop and competition hosted by the government and an international partner. The final entry date is March 01, 2023 and the winner will be announced on June 1, 2023. You have been invited to the panel of judges for the most efficient business app category. Show how you would rank each of the following four (4) business apps, from 1 (most efficient) to 4 (least efficient) using Big O. Note that c in each of the algorithms below represents the number of customers that the business app will have to process. Show all your workings and ranking scale. f(c) = 84 +59c(log)) + 150c +590c(log)) + 203c +5900c(log)) f(c) = 412c + (111* 10c) + 2048 f(c) = 9 (c*c*c*c*c)+7(cc) + 351c +c+ ½ c² + ½ c² f(c) = 1/2 c² + 1/4 c² + 1/8 c² + 1/16 c² + 1/32 c² + 7(c* c) App a) App b) App c) App d)

Case Study 3 Part 1 - Euclidean Algorithm 1. Use the Euclidean Algorithm to find the greatest common divisor of ( integers 396 and 480. (Show all workings) Part 2 Problem: Measuring Efficiency One challenge we will face is how to compare the efficiencies of two or more algorithms, to determine which is more efficient. We will have to use a common measure for example time or space First, we must determine what is most important to us (time or space or some other measure). Then compare the efficiencies (e.g., how much time each algorithm takes to execute, or how much space each algorithm uses). The challenge of timing an algorithm may introduce unwanted bias or overheads, therefore, we need a method that makes comparison fair. We are usually interested in the order of growth of the running time of an algorithm, not in the exact running time. Asymptotic notation gives us a method for classifying functions according to their rate of growth. Scenario: Bigi-Xam 9.0 is a mobile app development workshop and competition hosted by the government and an international partner. The final entry date is March 01, 2023 and the winner will be announced on June 1, 2023. You have been invited to the panel of judges for the most efficient business app category. Show how you would rank each of the following four (4) business apps, from 1 (most efficient) to 4 (least efficient) using Big O. Note that c in each of the algorithms below represents the number of customers that the business app will have to process. Show all your workings and ranking scale. f(c) = 84 +59c(log)) + 150c +590c(log)) + 203c +5900c(log)) f(c) = 412c + (111* 10c) + 2048 f(c) = 9 (ccc*cc)+7(cc) + 351c +c+ ½ c² + ½ c² f(c) = 1/2 c² + 1/4 c² + 1/8 c² + 1/16 c² + 1/32 c² + 7(c c) App a) App b) App c) App d)