Solution Files

Topics

Consult this section if you need a refresher on the material for this lab. It's okay to skip directly to the questions and refer back here should you get stuck.

Data Abstractions

Example Data Abstractions

Rational

Recall that a rational number is any number that can be expressed as p / q, where p and q are integers.

; Creates the rational number n/d (Assume n, d are integers and d != 0)
; Note that the constructor simplifies the numerator and denominator.
(rational n d)

; Gets the numerator of rational number r
(numer r) 

; Gets the denominator of rational number r
(denom r)

; Adds two rational numbers x and y
(add-rational x y)

; Multiplies two rational numbers x and y
(mul-rational x y)

Trees

Below is a Scheme-ified data abstraction of the Tree class we've been working with this semester.

; Constructs tree given label and list of branches
(tree label branches)

; Returns the label of the tree
(label t)

; Returns the list of branches of the given tree
(branches t)

; Returns #t if t is a leaf, #f otherwise
(is-leaf t)

Questions

What Would Scheme Do?

Q1: WWSD: Data Abstractions

Let's familiarize ourselves with some Scheme data abstractions!

If you need a refresher on the tree and rational abstractions, refer to this lab's introduction or Monday 04/11's lecture.

Use Ok to test your knowledge with the following "What Would Python Display?" questions:

python3 ok -q abstractions -u
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scm> (load rational.scm)
scm> (define x (rational 2 5))

scm> (numer x)

scm> (denom x)

scm> (define y (rational 1 4))

scm> (define z1 (add-rational x y))

scm> (numer z1)

scm> (denom z1)

scm> (define z2 (mul-rational x y)) ; don't forget to reduce the rational!

scm> (numer z2)

scm> (denom z2)

scm> (load tree.scm)
scm> (define t (tree 1 (list (tree 2 nil)) ))

scm> (label t)

scm> (length (branches t))

scm> (define child (car (branches t)))

scm> (label child)

scm> (is-leaf child)

scm> (branches child)

scm> (load tree.scm)
scm> (define b1 (tree 5 (list (tree 6 nil) (tree 7 nil)) )) 

scm> (map is-leaf (branches b1))    ; draw the tree if you get stuck!

scm> (define b2 (tree 8 (list (tree 9 (list (tree 10 nil)) )) )) 

scm> (map is-leaf (branches b2))    ; draw the tree if you get stuck!

scm> (define t (tree 11 (list b1 b2)))

scm> (label t)

scm> (map (lambda (b) (label b)) (branches t)) ; draw the tree if you get stuck!

Code Writing Questions

Remember that when working with data abstractions, you should not break the abstraction barrier if possible! Later questions will have abstraction checks, where the underlying representation of the abstraction will be changed; thus, attempting to refer to specifics of the implementation will break. Attempt to use the functions you are creating to interface with the classes whenever possible.

Cities

Say we have an abstract data type for cities. A city has a name, a latitude coordinate, and a longitude coordinate.

Our data abstraction has one constructor:

• (make-city name lat lon): Creates a city object with the given name, latitude, and longitude.

We also have the following selectors in order to get the information for each city:

• (get-name city): Returns the city's name
• (get-lat city): Returns the city's latitude
• (get-lon city): Returns the city's longitude

Here is how we would use the constructor and selectors to create cities and extract their information:

scm> (define berkeley (make-city 'Berkeley 122 37))
berkeley
scm> (get-name berkeley)
Berkeley
scm> (get-lat berkeley)
122
scm> (define new-york (make-city 'NYC 74 40))
new-york
scm> (get-lon new-york)
40

All of the selector and constructor functions can be found in the lab file, if you are curious to see how they are implemented. However, the point of data abstraction is that we do not need to know how an abstract data type is implemented, but rather just how we can interact with and use the data type.

Q2: Distance

We will now implement the function distance, which computes the Euclidean distance between two city objects; the Euclidean distance between two coordinate pairs (x1, y1) and (x2, y2) can be found by calculating the sqrt((x1 - x2) ** 2 + (y1 - y2) ** 2). Use the latitude and longitude of a city as its coordinates; you'll need to use the selectors to access this info!

You may find the following methods useful:

• (expt base exp): calculate base ** exp
• (sqrt x) calculate sqrt(x)

(define (distance city-a city-b)
    (define lat-1 (get-lat city-a))
    (define lon-1 (get-lon city-a))
    (define lat-2 (get-lat city-b))
    (define lon-2 (get-lon city-b))
    (sqrt (+ (expt (- lat-1 lat-2) 2) (expt (- lon-1 lon-2) 2)))
)

Use Ok to test your code:

python3 ok -q city_distance
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Q3: Closer city

Next, implement closer-city, a function that takes a latitude, longitude, and two cities, and returns the name of the city that is relatively closer to the provided latitude and longitude.

You may only use the selectors and constructors introduced above and the distance function you just defined for this question.

Hint: How can you use your distance function to find the distance between the given location and each of the given cities?

(define (closer-city lat lon city-a city-b)
    (define new-city (make-city 'arb lat lon))
    (define dist1 (distance city-a new-city))
    (define dist2 (distance city-b new-city))
    (if (< dist1 dist2) (get-name city-a) (get-name city-b))
)

Use Ok to test your code:

python3 ok -q city_closer
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Teachers and Students

In the following questions, you'll be implementing data abstractions for students and teachers:

1. The teacher abstraction keeps track of the teacher's name, the class they teach, and the students enrolled in their class. Specifically, a teacher's name and class are atomic symbols, and their students is a list of student objects.
2. The student abstraction keeps track of a student's name and number of classes attended. Specifically, a student's name is an atomic symbol, and their classes is a list of atomic symbols representing all classes attended. For example, if a student had attended cs61a and astronomy, their classes list would be (cs61a astronomy).

You can find the constructors for these classes below:

(define (student-create name classes) (cons name classes))
(define (teacher-create name class students) (cons name (cons class students)))

Q4: Teachers and Students: Selectors

Implement student-get-name, student-get-classes, teacher-get-name, teacher-get-class, and teacher-get-students. These functions take in a student or teacher abstraction, and return the relevant attribute; for example, student-get-name takes a student as input, and returns the name.

(define (student-get-name student)
    (car student)
)

(define (student-get-classes student)
    (cdr student)
)

(define (teacher-get-name teacher)
    (car teacher)
)

(define (teacher-get-class teacher)
    (car (cdr teacher))
)

(define (teacher-get-students teacher)
    (cdr (cdr teacher))
)

Use Ok to test your code:

python3 ok -q teacher_student_selectors
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Q5: Students: Attend Class

Implement student-attend-class. This method takes in a student and a class as input, and returns a new student abstraction with the class list updated to reflect the class attended.

Be sure to keep the abstraction barrier in mind!

(define (student-attend-class student class)
    (student-create (student-get-name student) (cons class (student-get-classes student)))
)

Use Ok to test your code:

python3 ok -q student_attend_class
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Q6: Teachers: Hold Discussion

Implement teacher-hold-class. This method takes in a teacher as input, and emulates holding a class. Specifically, the function should return a new updated teacher, where all student objects in the teacher's students list have updated class lists to reflect their attendance.

Be sure to keep the abstraction barrier in mind! Feel free to use any of the functions implemented in previous parts of this lab. You may also find the map function useful.

(define (teacher-hold-class teacher)
    (define class (teacher-get-class teacher))
    (define new-students
        (map (lambda (x) (student-attend-class x class)) (teacher-get-students teacher))
    )
    (teacher-create (teacher-get-name teacher) (teacher-get-class teacher) new-students)
)

Use Ok to test your code:

python3 ok -q teacher_hold_class
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Submit

Make sure to submit this assignment by running:

python3 ok --submit