Math | 代写Ai | Lab代写 – 这是一个涉及数学偏理论的AI代写任务

University of Delaware CISC 108: Introduction to Computer Science I Fall 2016

### lab 1

- Goals

Relevant sections of text:HtDP/2e Prologue and Chapters 1

This weeks lab will help you to practice:

- usingDrRacket: interactions vs. definitions; stepper; error messages; indentation
- simple image functions; using the Help Desk
- function composition: write more complex functions by combining simpler functions.

Note: Exchange email addresses and phone numbers with your partner. Decide on your next meeting time this week in case you dont finish. Make surebothnames are at the top of your lab submission!

- Using DrRacket

Problem 1.

You may remember from mathclass that the distance from the origin point (0,0) to any point (x, y) in the cartesian plane is

```
distance(x, y) =
```

```
x^2 +y^2 ,
```

which is a function composed from other, more basic math functions (addition, squaring, and square root).

This function can be written in BSL as follows:

;; distance: Number Number -> Number[This is the SIGNATURE] ;; Consumes:[PURPOSE STATEMENT incl. parameter descriptions] ;; Number x : x-coordinate of a point in 2d-plane ;; Number y : y-coordinate of the point ;; Produces: the distance from origin to point (x,y).

(define (distance x y) (sqrt (+ (* x x) (* y y))))

Follow the step-by-step instructions below.

- Copy this definition to theDrRacketdefinitionswindow (the top window).
- PressRun. Notice which parts of the code are still in black/orangethose have not yet beentested.
- Callthe function (i.e., run the program) by typing(distance 3 4)at the prompt in theinteractionswindow (lower window). Notice that the entire function definition is now tested. (Whether the answer is correct is a different issue 🙂
- Now call the function to find the distance from the origin to the point (5,5). (Note: you can hitescapefollowed bypto haveDrRacketscroll backwards through the previous expressions that you typed at the interactions prompt.) Do you recall that#iindicates that the result is aninexactnumber? 1

- Testing: to properly test a function, there should be at least one test per function. (Well be even more specific about this next week.) The black/orange coloring when you press Runindicates that that part of your code has not been tested. Tests on individual functions like this are calledunit tests. We will typically write the tests (as examples)BEFORE writing the function. (After all, if you dont know what the function is supposed to do, how can you possibly write the body?! Review Section 3.5On Testing.) The most common unit testing function ischeck-expect. For example, in the definitions pane add: (check-expect (distance 0 0) 0) ; the distance from (0,0) to (0,0) ; should be 0 However,check-expectcan only be used for checking exact equality of things. It will not work for inexact numbers. Try it: to the definitions pane add the following and pressRun: (check-expect (distance 5 5) 7.071) Note the error, note what is highlighted. The Unit Test Results window may be closed, or docked to the definitions and interactions panes. (When docked there will be three panes, not two). To test functions that return inexact numbers, use check-within. This unit testing function lets you say how close the answer must be to pass the test. Is within 0.1 close enough? 0.000001? For example, (check-within (distance 5 5) 7.071 0.0001) ; result must be between [7.0709 and 7.0711], inclusive Write two unit tests for the distance function, one withcheck-expectand one with check-within.
- Call the function in the interactions window on incorrect arguments:(distance 4 "red"). Read and understand the error message!! What is highlighted in the definitions window? What if you type(distance true 10)in the interactions pane?
- Using the Stepper: Put(distance 3 4)in thedefinitionswindow at the bottom. Press theStep button. This will bring up a separate window which lets you see how DrRacketis evaluating your program. Step through the program, making sure that you can correctly predict what the next step will be each time. Note that this is just simple algebraic substitution that you have used since middle school. Use the stepper anytime you are confused about what your function is doing.
- Save your program and tests aslab1.rktusing theSave Definitionsoption in the file menu. There is nothing else to turn in for problem 1.

Problem 2.

Reread HtDP/2e Section 2.3,Composing Functions. Included are two solutions to the following sample problem:

```
Sample ProblemThe owner of a monopolistic movie theater in a small town has
complete freedom in setting ticket prices. The more he charges, the fewer people
can afford tickets. The less he charges, the more it costs to run a show because
attendance goes up. In a recent experiment the owner determined a relationship
between the price of a ticket and average attendance.
At a price of $5.00 per ticket, 120 people attend a performance. For each 10-cent
change in the ticket price, the average attendance changes by 15 people. That is, if
the owner charges $5.10, some 105 people attend on the average; if the price goes
down to $4.90, average attendance increases to 135. Let us translate this idea into
```

```
a mathematical formula:
```

```
avg. attendance= 120people
```

```
$(change in price)
$0. 10
```

```
15 people
```

```
Stop! Explain the minus sign before you proceed.
Unfortunately, the increased attendance also comes at an increased cost. Every
performance comes at a fixed costs of $180 to the owner plus a variable cost of $0.
per attendee.
The owner would like to know the exact relationship between profit and ticket
price so that he can maximize his profit.
```

The first solution follows the correct design philosophy of defining one function per task:

;; attendees: Number -> Number ;; Consumes: ;; Number ticket-price : the price of one ticket in dollars ;; Produces: the number of people who will attend at that price (define (attendees ticket-price) (+ 120 (* (/ 15 0.1) (- 5.0 ticket-price))))

;; revenue: Number -> Number ;; Consumes: ;; Number ticket-price : the price of one ticket in dollars ;; Produces: the revenue generated, i.e. ticket price times ;; the number of attendees. (define (revenue ticket-price) (* (attendees ticket-price) ticket-price))

;; cost: Number -> Number ;; Consumes: ;; Number ticket-price : the price of one ticket in dollars ;; Produces: the costs incurred; costs have both a fixed [$180] and ;; variable [$.04 per attendee] part. (define (cost ticket-price) (+ 180 (* 0.04 (attendees ticket-price))))

;; profit: Number -> Number ;; Consumes: ;; Number ticket-price : the price of one ticket in dollars ;; Produces: the profit: revenues minus costs. (define (profit ticket-price) (- (revenue ticket-price) (cost ticket-price)))

Problem 2.1: Determine the potential profit for the following ticket prices: $1, $2, $3, $4, and $5. Which price should the owner of the movie theater choose to maximize his profits? Determine the best ticket price down to a dime. Place the answers as a comment in yourlab1.rktfile.

The alternative, poorly-thought-out definition is as follows:

;; No signature and purpose statement? ;; Lose most points for this function! (define (profit.bad price)

#### (- (* (+ 120

#### (* (/ 15 0.1)

```
(- 5.0 price)))
price)
(+ 180
(* 0.
(+ 120
(* (/ 15 0.1)
(- 5.0 price)))))))
```

Problem 2.2: After studying the cost structure of a show, the owner discovered several ways of lowering the cost. As a result of his improvements, he no longer has a fixed cost. He now simply pays $1.50 per attendee. Modify both programs to reflect this change. (You do not have to keep the originals). When the programs are modified, test them again with ticket prices of $3, $4, and $5 and compare the results. Add at least one unit test example for each function. Notice that DrRacketdoes not register your definition window edits in the interactions window until you pressRun. (You may wish to try running the program before and after you pressRunto see what happens.)

- String Arithmetic and the Help Desk

You may want to re-read HtDP/2e sections 1.2 and 1.3. Just as we can compose+, -,sqrt, sin, etc. for numbers, computation as the algebra of things allows us to compose functions on strings, images, boolean truth values, and any combination. Although you (I hope) have spent 12 years learning the common arithmetic number operations, computer languages tend to define their own operations on strings and images. (Even if your high school didnt teach them to you, mathematicians also named all the boolean operations, e.g.,and,or, andnot; these will come into play more next week). The book describes several string operations:

- string-appendconcatenates two given strings into one. Think ofstring-appendas an operation that is just like+. While+consumes two (or more) numbers and produces a new number,string-appendconsumes two (or more) strings and produces a new string;
- string-lengthconsumes a string and produces a (natural) number;
- string-ithconsumes a stringsand extracts the one-character substring located at theith position (counting from 0);
- number->stringconsumes a number and produces a string;
- substring.. .hmmm, I wonder what this does? Look this up in theHelp Deskand find out what it does. If the documentation appears confusing, experiment with the function in the interaction area.

The Help Desk: Access the help desk from the menuHelpHelp Desk. This will bring up your webbrowser. Look underTeachingHow to Design Programs Languages. This will bring up all the teaching languages, and we are currently using BSL (Beginning Student Language). Click on the appropriate topic, e.g., Strings, and scroll down until you find an entry for the function you are interested in (substring). Alternatively, you can typesubstringinto the search box[.. .search manuals.. .]; make sure to only click on the result that is provided fromlang/htdp-beginnerfor now!

Problem 3. Define the functionstring-first, which extracts the first character from a non- empty string. Dont worry about empty strings. The signature for this function is

;; string-first: String -> String

From now on we assume that without being reminded, you will have a contract, purpose statement, and at least one example/unit test for each function that you write.We will discuss testing in more detail next week.

Problem 4. Define the function string-last, which extracts the last character (as a string) from a non-empty string. Dont worry about empty strings.

Problem 5. Define the functionstring-join, which consumes two strings and appends them with _ in the middle.

Problem 6. Define the functionstring-insert, which consumes a string and a numberiand which inserts * at theithposition of the string (counting from the left, starting at 0). Assume iis a number between 0 and the length of the given string (inclusive). Also ponder the question whetherstring-insertshould deal with empty strings. If we insert * at position 5 in the string helloworld, we expect the resulthello_world. We can write this example explicitly as a unit test:

(check-expect (string-insert "helloworld" 5) "hello_world")

Make sure that all of these functions and unit tests are included in your filelab1.rkt.

- Images and More Function Composition

See HtDP/2e section 1.4,.. ..

In class we will play with some built-in image-processing functions. To use them, you will load a library of previously defined functions by starting your definitions file with the line

```
(require 2htdp/image)
```

From the Help menu, choose Help Desk. UnderTeachingyou will seeHow to Design Programs Teachpacksclick on it. Then click onHTDP/2e Teachpacksin the upper left menu. In Sections 2.2 (Image Guide) and 2.3 (Images: image.rkt) you will find a complete description of all the functions in theimagelibrary. Yes, some of the concepts there have not been covered yet in class, but at this point the examples should be mostly clear and you should feel free to experiment in the DrRacketInteractions pane. Make it a habit to try to answer your own questions using the Help Desk before asking the TA or LA.

Here is an expression that will display a solid red circle of radius 10:

(circle 10 "solid" "red")

Notice that this conforms to the definition of a compound expression. (The operator/function name iscircle. The three arguments supplied to thecircleoperator are a number, 10, and two strings, solidandred.)

Problem 7. Use multiple image primitives, composed together, to create an image of a simple boat of your own design (have fun). Since the boat is always the same, define it as a constant:

;; a very unimaginative boat image using only one primitive (define MY-BOAT (ellipse 60 20 "solid" "Chartreuse"))

Problem 8. Define the functionimage-area, which computes the area of a given image.Note: The area is also the number of pixels in the picture.

DrRacketcan import images (e.g., from the web), either by cut-and-paste or theInsertImage… menu item. Consider an image like this:

This can be inserted inDrRacketby copying and pasting into a definition:

(define PALM )

Problem 9. Define the functionpinwheelthat consumes an image and produces a new image con- sisting of four copies of the image, each rotated around the center. For example,(pinwheel PALM) should produce something like:

Your function should work onPALM,MY-BOAT, or any image you pass in as an argument. For your unit tests, use any images you think appropriate.

Problem 10. Define an imageBACKGROUND, starting with a 500200 empty-scene, and adding some water (e.g., aLightSeaGreenrectangle) and an island with a palm tree.

Problem 11. Define a functiondraw-boatthat consumes a natural number (interpreted as the number of clock ticks that have gone by) and produces an image ofMY-BOATon top of the BACKGROUND, where the boat moves 3 pixels every clock tick, and when the boat leaves the right side it simply reappears on the left and continues. (Hint:look up the definition of the arithmetic operationmoduloin the Help Desk; consider(modulo 501 500),(modulo 502 500), etc.)

Make sure the line(require 2htdp/universe) occurs in your definitions area. Then add this as the final line in your definitions: (animate draw-boat). When you clickRun, an animation window should pop up with your background and boat, and the boat should begin moving across the background, wrapping around forever. Close the animation window and your unit tests will complete as usual.

Turn in your single filelab1.rktfile with all of your definitions, documentation, and tests from this lab using Sakai.MAKE SURE THAT SAKAIPROVIDES YOU WITH A RECIEPT!!! No receipt, no grade!