CSC 160 Computer Programming for Non-Majors Lecture #10: Conditionals I Prof. Adam M. Wittenstein

CW5: part 1 on Booleans Complete Exercise from How to Design Programs without using DrScheme. Complete Exercise 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: 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 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 ?

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?

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.

I. Evaluating Conditional Expressions

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

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])

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

Exercise 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.

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

Because… There is no question on the third line.

CW5: part 2 on Conditionals Complete this simplified version of Exercise from How to Design Programs without using DrScheme. Complete this simplified version of Exercise 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: 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) (* )] [(<= N 5000) (+ 40 (* (- N 1000).045))] [else (+ 220 (* (- N 5000).055))]) when n is (a) 500, (b) 2800, and (c) What is the value of: (cond [(<= N 1000) (* )] [(<= N 5000) (+ 40 (* (- N 1000).045))] [else (+ 220 (* (- N 5000).055))]) when n is (a) 500, (b) 2800, and (c) 15000

II. Defining a Conditional Function

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%

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

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

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

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

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

III. Designing Conditional Functions

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

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

“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.

“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) -> ??

“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

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

“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 ])

“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 ]))

“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]))

“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]))

“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.

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

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?

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?

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

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…