CSC 160 Computer Programming for Non-Majors Lecture #10: Conditionals I

1. CSC 160Computer Programmingfor Non-MajorsLecture #10: Conditionals I Prof. Adam M. Wittenstein Wittenstein@adelphi.edu http://www.adelphi.edu/~wittensa/csc160/

2. CW5: part 1 on Booleans • Complete Exercise 4.1.2 from How to Design Programs without using DrScheme. • Feel free to use a calculator - there is one on each of your computers. To get to it the steps are: Start->Programs->Accessories->Calculator.) • What are the results of (> x 3) (and (> 4 x) (> x 3)) (= (* x x) x) for (a) x = 4, (b) x = 2, and (c) x = 7/2 ?

3. Correction from last class:eq? and equal? • The eq? predefined function always returns false for sentences (a.k.a. strings). • There is another predefined function equal? that works just like eq?, except that it also works on sentences/strings. • For simplicity, we will just also use equal?

4. Conditions Conditions are most useful in the context of a program. • We call the functions that use them conditional functions. • We formulate them using conditional expressions.

5. I. Evaluating Conditional Expressions

6. Question 1: Type into Definitions Window ;Variable Definition: (define AGE 10) ;Function Call: (cond [(< AGE 3) ‘toddler] [(and (>= AGE 3) (< AGE 13)) ‘pre-teen] [(and (>= AGE 13) (< AGE 20)) ‘teen] [(>= AGE 20) ‘adult]) ; returns ‘pre-teen Experiment by changing AGE & re-executing

7. Syntax Rule #4: Conditionals (cond [question … answer] … [question … answer]) Often, the last part is what answer do you want for everything else, in which case, the last question is else. (cond [question … answer] … [else answer])

8. Question 2: Exercise 4.3.1 Decide which of these expressions is legal: (cond (cond [(< n 10) 20] [(< n 10) 20] [(> n 20) 0] [(and (> n 20) (<= n 30))] [else 1]) [else 1])

9. Exercise 4.3.1 solution • The expressions are identical except for the third line so look at those. • The second expression does not have an answer on the third line: [(and (> n 20) (<= n 30))] so it is an illegal expression.

10. Question 3: Why is this illegal? (cond [(< n 10) 20] [ * 10 n] [else 555])

11. Because… There is no question on the third line.

12. CW5: part 2 on Conditionals • Complete this simplified version of Exercise 4.3.3 from How to Design Programs without using DrScheme. • Feel free to use a calculator - there is one on each of your computers. To get to it the steps are: Start->Programs->Accessories->Calculator.) • What is the value of:(cond     [(<= N 1000) (* .040 1000)]     [(<= N 5000) (+ 40 (* (- N 1000) .045))]     [else (+ 220 (* (- N 5000) .055))])when n is (a) 500, (b) 2800, and (c) 15000

13. II. Defining a Conditional Function

14. Question 4: interest-rate A bank pays higher interest rates to depositors with larger balances: • over $10,000, 6% • over $5000 and up to $10,000, 5.5% • over $1000 and up to $5000, 4.5% • up to $1000, 4%

15. How do we write this in Scheme?Use a conditional (cond [… …] [… …] [… …] [… …])

16. How do we write this in Scheme?Filling in the questions (cond [(<= amount 1000) …] [(<= amount 5000) …] [(<= amount 10000) …] [( > amount 10000) …])

17. How do we write this in Scheme?Filling in the answers (cond [(<= amount 1000) .040] [(<= amount 5000) .045] [(<= amount 10000) .055] [( > amount 10000) .060])

18. Write the program (define (interest-rate amount) (cond [(<= amount 1000) .040] [(<= amount 5000) .045] [(<= amount 10000) .055] [( > amount 10000) .060]))

19. Strategy for conditionals • Identify number of cases; write cond with that many clauses • If answers are simple, write all the answers & then go back to fill in questions • If questions are simple, write all the questions & then fill in answers

20. III. Designing Conditional Functions

21. Design Recipe – Version 2 • Figure out precisely what you need to do. 1. Understand the problem 2. Function contract 3. NEW STEP – Data Analysis 4. Write examples (in Scheme notation) • Tell the computer how to do it. 5. Write a skeleton 6. NEW STEP – Choose a template 7. Fill in the function body • Check that the computer does it right. 8. Testing and debugging

22. “interest-rate” again • Purpose ;To determine the interest rate given an ;amount of money in the bank. • Contract ; interest-rate: number -> number

23. “interest-rate” again • NEW STEP: Data Analysis ;We take in a number and determine which ;of four intervals it is in. ;We print out a different number for each of ;the intervals.

24. “interest-rate” again • Examples Borderline Cases ;; (interest-rate 0) -> ?? ;; (interest-rate 1000) -> ?? ;; (interest-rate 5000) -> ?? ;; (interest-rate 10000) -> ?? Interval Cases ;; (interest-rate 500) -> ?? ;; (interest-rate 3000) -> ?? ;; (interest-rate 7000) -> ?? ;; (interest-rate 12000) -> ??

25. “interest-rate” again • Examples Borderline Cases ;; (interest-rate 0) -> .040 ;; (interest-rate 1000) -> .040 ;; (interest-rate 5000) -> .045 ;; (interest-rate 10000) -> .055 Interval Cases ;; (interest-rate 500) -> .040 ;; (interest-rate 3000) -> .045 ;; (interest-rate 7000) -> .055 ;; (interest-rate 12000) -> .060

26. “interest-rate” again • Skeleton (define (interest-rate amount) … amount … )

27. “interest-rate” again • NEW STEP: Template So far we only have one template, for conditionals, so we will use that one. (define (interest-rate amount) (cond [ question answer ] … [ question answer ])

28. “interest-rate” again • NEW STEP: Template Since we have four cases, we will have four lines of questions and answers, so the template is refined as follows: (define (interest-rate amount) (cond [ question answer ] [ question answer ] [ question answer ] [ question answer ]))

29. “interest-rate” again • Fill in the Function Body --First fill in the questions. (define (interest-rate amount) (cond [(<= amount 1000) answer] [(<= amount 5000) answer] [(<= amount 10000) answer] [( > amount 10000) answer]))

30. “interest-rate” again • Fill in the Function Body --Now fill in the answers. (define (interest-rate amount) (cond [(<= amount 1000) .040] [(<= amount 5000) .045] [(<= amount 10000) .055] [( > amount 10000) .060]))

31. “interest-rate” again • Testing and Debugging --As always, type each of your examples into the interactions window. --If you get an error message or unexpected answer, debug the program to find your mistake.

32. Question 5: Testing a Program Suppose one of your classmates wrote these examples for interest-rate. Test the program with each of these examples: • (interest-rate 4000) -> .045 • (interest-rate 20000) -> .060 • (interest-rate 6000) -> .040

33. Question 5: Testing a Program • Which example did not return the expected answer? • Is there a mistake in the program? • What step in the design recipe did he / she make the mistake?

34. Question 5: Testing a Program • Which example did not return the expected answer? the third one • Is there a mistake in the program? • What step in the design recipe did he / she make the mistake?

35. Question 5: Testing a Program • Which example did not return the expected answer? the third one • Is there a mistake in the program? no • What step in the design recipe did he / she make the mistake? writing the example

36. In summary… • Functions like interest-rate need to determine which of several conditions holds for the input. • We call them conditional functions. • A conditional function without numbers. • CW6: Practice with Conditionals. • Using conditional functions to enhance our Animations. Coming up…