1. CPSC 171 Introduction to Computer Science 3 Levels of Understanding Algorithms More Algorithm Discovery and Design

2. Announcements Last day to Add/Drop Sept 11 Wipe Down Computer Keyboards and Mice Read Chapter 2 Homework 2 due this Friday (Hand in electronically or paper copy) Lab 1 due this Thursday (Hand in electronically)

3. Recall That… An Algorithm is … Three types of pseudocode instructions Sequential (computation, input, output) Conditional (if then else) Iterative (while and do/while)

4. Creating Algorithms Given a description of what an algorithm is supposed to do “Design an algorithm to beat me in the game of 21” Create an Algorithm to do it How?

5. Game Time Who can beat me in the game 21? Objective: Get your opponent to say the number 21. Rules: One player goes first starting counting from 1. On each turn a player may say one or two consecutive numbers. You must begin where your opponent left off. The first person to say the number 21 loses. There is a way to always beat me!

6. 3 Levels of Tasks Level 1 Given: An algorithm and the input to the algorithm Do: State the output Level 2 Given: A description and an algorithm Do: Decide if the algorithm is correct Level 3: Given: A description Do: Design an algorithm

7. Level 1 Description: Given a bank account starting balance and the interest rate print out the interest earned and the final balance. Code: get balance, rate assign earned to be balance*rate assign total to be balance+earned print “amount earned is “ print earned print “ending balance is “ print total Input: balance is 100, rate is 0.05 Output: ??

8. Level 1 Code: Get num1, num2 Set average to be (num1+num2)/2 If num1 > average then print “You did better than average” Else print “you did worse than average” Input: num1 is 10 and num2 is 8 Output: ??

9. Level 1 Code: Get num1, num2 Set total to be num1 While num1 < num2 Update total to be total + num2 Update num1 to be num1 + num1 If total > (num1 + num2) then Print “total is big” Else Print “total is small” Print total Input: num1 is 10 and num2 is 8 Output: ?? Input: num1 is 5 and num2 is 11 Output: ??

10. Level 2 Given: A description and an algorithm Do: Decide if the algorithm is correct Here is what to do: Make up your own input Make sure to test boundary conditions

11. Level 2 Description:Given two numbers, calculate their average and print “You did better than average” if the first number is larger than the average or print “You did worse than average” if the first number is smaller than the average Code: Get num1, num2 Set average to be (num1+num2)/2 If num1 > average then print “You did better than average” Else print “you did worse than average” Input: ?? Output: ?? Is the Algorithm correct?

12. Level 2 Description: Calculate the average of a set of numbers provided by the user. Print out the average. Code: Print “how many numbers?” Get counter Set total to be 0 While counter > 0 print “enter the next number” Get number Set total to be total + number Set counter to be counter – 1 Set average to be total / counter Print “The average of the numbers is” Print average Input: ?? Output: ?? Is the Algorithm correct?

13. Level 2 Description: Calculate the average of a set of numbers provided by the user. Print out the average. Code: Print “how many numbers?” Get number_of_numbers Set counter to be 1 Set total to be 0 While counter < number_of_numbers print “enter the next number” Get number Set total to be total + number Set counter to be counter + 1 Set average to be total / number_of_numbers Print “The average of the numbers is” Print average Input: ?? Output: ?? Is the Algorithm correct?

14. Level 3 Level 3: Given: A description Do: Design an algorithm Start with sequential algorithms Add in conditionals Add in loops

15. Level 3 – Sequential Operations Design an algorithm to: 1. Given the base and height of a triangle and output the triangle’s area. 2. Output the flying time between two cities given the mileage M between them and the average speed of the airplane. 3. Given an accounts starting balance, interest rate, and yearly service charge, output the end of year balance.

16. Level 3 – Conditional Operations Design an algorithm to: 1. Compute and display the value x/y if the value of y is not 0. If y is 0 then display “unable to perform the division.” 2. Compute the area and circumference of a circle given the radius r if the radius is greater than or equal to 1.0; otherwise you should compute only the circumference.

17. Level 3 – Conditional Operations Design an algorithm to: Given an accounts starting balance, interest rate, and yearly service charge, output the end of year balance. Subtract the service charge only if the starting balance is below $1,000.

18. Designing Algorithms When designing algorithms you first have to understand the description so well that you can clearly explain each step Go Forth and Multiply: Multiply two numbers using repeated addition Sequential search: Find a particular value in an unordered collection Find maximum: Find the largest value in a collection of data

19. Example 1: Go Forth and Multiply Task Implement an algorithm to multiply two numbers, a and b, using repeated addition Algorithm outline Create a loop that executes exactly b times, with each execution of the loop adding the value of a to a running total

20. Figure 2.10 Algorithm for Multiplication via Repeated Addition Algorithm: Go Forth and Multiply

21. Example 2: Looking, Looking, Looking Task Find a particular person’s name from an unordered list of telephone subscribers Algorithm outline Start with the first entry and check its name, then repeat the process for all entries

22. Example 2: Looking, Looking, Looking (continued) Algorithm discovery Finding a solution to a given problem Naïve sequential search algorithm For each entry, write a separate section of the algorithm that checks for a match Problems  Only works for collections of exactly one size  Duplicates the same operations over and over

23. Example 2: Looking, Looking, Looking (continued) Correct sequential search algorithm Uses iteration to simplify the task Refers to a value in the list using an index (or pointer) Handles special cases (such as a name not found in the collection) Uses the variable Found to exit the iteration as soon as a match is found

24. Figure 2.13 The Sequential Search Algorithm

25. Example 3: Big, Bigger, Biggest Task Find the largest value from a list of values Algorithm outline Keep track of the largest value seen so far (initialized to be the first in the list) Compare each value to the largest seen so far, and keep the larger as the new largest

26. Example 3: Big, Bigger, Biggest (continued) Once an algorithm has been developed, it may itself be used in the construction of other, more complex algorithms Library A collection of useful algorithms An important tool in algorithm design and development

27. Example 3: Big, Bigger, Biggest (continued) Find Largest algorithm Uses iteration and indices as in previous example Updates location and largest so far when needed in the loop

28. Figure 2.14 Algorithm to Find the Largest Value in a List