Homework 6: Scheme, Scheme Lists

hw06.zip

Due by 11:59pm on Wednesday, July 31

Instructions

Download hw06.zip. Inside the archive, you will find a file called hw06.scm, along with a copy of the ok autograder.

Submission: When you are done, submit the assignment by uploading all code files you've edited to Gradescope. You may submit more than once before the deadline; only the final submission will be scored. Check that you have successfully submitted your code on Gradescope. See Lab 0 for more instructions on submitting assignments.

Using Ok: If you have any questions about using Ok, please refer to this guide.

Readings: You might find the following references useful:

Grading: Homework is graded based on correctness. Each incorrect problem will decrease the total score by one point. This homework is out of 2 points.

The 61A Scheme interpreter is included in each Scheme assignment. To start it, type python3 scheme in a terminal. To load a Scheme file called f.scm, type python3 scheme -i f.scm. To exit the Scheme interpreter, type (exit).

Scheme Editor

All Scheme assignments include a web-based editor that makes it easy to run ok tests and visualize environments. Type python3 editor in a terminal, and the editor will open in a browser window (at http://127.0.0.1:31415/). Whatever changes you make here will also save to the original file on your computer! To stop running the editor and return to the command line, type Ctrl-C in the terminal where you started the editor.

The Run button loads the current assignment's .scm file and opens a Scheme interpreter, allowing you to try evaluating different Scheme expressions.

The Test button runs all ok tests for the assignment. Click View Case for a failed test, then click Debug to step through its evaluation.

Recommended VS Code Extensions

If you choose to use VS Code as your text editor (instead of the web-based editor), install the vscode-scheme extension so that parentheses are highlighted.

Before:

After:

In addition, the 61a-bot (installation instructions) VS Code extension is available for Scheme homeworks. The bot is also integrated into ok.

Required Questions

Getting Started Videos

These videos may provide some helpful direction for tackling the coding problems on this assignment.

To see these videos, you should be logged into your berkeley.edu email.

YouTube link

Scheme

Q1: Pow

Implement a procedure pow that raises a base to the power of a nonnegative integer exp. The number of recursive pow calls should grow logarithmically with respect to exp, rather than linearly. For example, (pow 2 32) should result in 5 recursive pow calls rather than 32 recursive pow calls.

Hint:

x^2y = (x^y)²

x^2y+1 = x(x^y)²

For example, 2¹⁶ = (2⁸)² and 2¹⁷ = 2 * (2⁸)².

You may use the built-in predicates even? and odd?. Also, the square procedure is defined for you.

Scheme doesn't have while or for statements, so use recursion to solve this problem.

(define (square n) (* n n))

(define (pow base exp)
  'YOUR-CODE-HERE
)

Use Ok to test your code:

python3 ok -q pow

Q2: Repeatedly Cube

Implement repeatedly-cube, which receives a number x and cubes it n times.

Here are some examples of how repeatedly-cube should behave:

scm> (repeatedly-cube 100 1) ; 1 cubed 100 times is still 1
1
scm> (repeatedly-cube 2 2) ; (2^3)^3
512
scm> (repeatedly-cube 3 2) ; ((2^3)^3)^3
134217728

For information on let, see the Scheme spec.

(define (repeatedly-cube n x)
    (if (zero? n)
        x
        (let
            (_________________)
            (* y y y))))

Use Ok to test your code:

python3 ok -q repeatedly-cube

Q3: Cadr

Define the procedure cadr, which returns the second element of a list. Also define caddr, which returns the third element of a list.

(define (cddr s)
  (cdr (cdr s)))

(define (cadr s)
  'YOUR-CODE-HERE
)

(define (caddr s)
  'YOUR-CODE-HERE
)

Use Ok to test your code:

python3 ok -q cadr-caddr

Scheme Lists

Q4: Ascending

Implement a procedure called ascending?, which takes a list of numbers s and returns True if the numbers are in non-descending order, and False otherwise.

A list of numbers is non-descending if each element after the first is greater than or equal to the previous element. For example...

(1 2 3 3 4) is non-descending.
(1 2 3 3 2) is not.

Hint: The built-in null? procedure returns whether its argument is nil.

Note: The question mark in ascending? is just part of the procedure name and has no special meaning in terms of Scheme syntax. It is a common practice in Scheme to name procedures with a question mark at the end if it returns a boolean value.

(define (ascending? s)
  'YOUR-CODE-HERE
)

Use Ok to unlock and test your code:

python3 ok -q ascending -u
python3 ok -q ascending

Q5: My Filter

Write a procedure my-filter, which takes a predicate pred and a list s, and returns a new list containing only elements of the list that satisfy the predicate. The output should contain the elements in the same order that they appeared in the original list.

Note: Make sure that you are not just calling the built-in filter function in Scheme - we are asking you to re-implement this!

(define (my-filter pred s)
  'YOUR-CODE-HERE
)

Use Ok to unlock and test your code:

python3 ok -q filter -u
python3 ok -q filter

Q6: No Repeats

Implement no-repeats, which takes a list of numbers s. It returns a list that has all of the unique elements of s in the order that they first appear, but no repeats.

For example, (no-repeats (list 5 4 5 4 2 2)) evaluates to (5 4 2).

Hint: You may find it helpful to use filter with a lambda procedure to filter out repeats. To test if two numbers a and b are not equal, use (not (= a b)).

(define (no-repeats s)
  'YOUR-CODE-HERE
)

Use Ok to test your code:

python3 ok -q no_repeats

Check Your Score Locally

You can locally check your score on each question of this assignment by running

python3 ok --score

This does NOT submit the assignment! When you are satisfied with your score, submit the assignment to Gradescope to receive credit for it.

Submit Assignment

Submit this assignment by uploading any files you've edited to the appropriate Gradescope assignment. Lab 00 has detailed instructions.

Extra Credit (1 pt)

During Office Hours and Project Parties, the staff will prioritize helping students with required questions. We will not be offering help with this question unless the queue is empty.

Q7: Longest Increasing Subsequence

Write the procedure longest-increasing-subsequence, which takes in a list lst and returns the longest subsequence in which all the terms are increasing.

Note: the elements do not have to appear consecutively in the original list. For example, the longest increasing subsequence of (1 2 3 4 9 3 4 1 10 5) is (1 2 3 4 9 10). Assume that the longest increasing subsequence is unique.

Hint: The built-in procedures length (documentation) and filter (documentation) might be helpful to solving this problem.

; helper function
; returns the values of lst that are bigger than x
; e.g., (larger-values 3 '(1 2 3 4 5 1 2 3 4 5)) --> (4 5 4 5)
(define (larger-values x lst)
    'YOUR-CODE-HERE)

(define (longest-increasing-subsequence lst)
    ; the following skeleton is optional, remove if you like
    (if (null? lst)
        nil
        (begin
            (define first (car lst))
            (define rest (cdr lst))
            (define large-values-rest
                'YOUR-CODE-HERE)
            (define with-first
                'YOUR-CODE-HERE)
            (define without-first
                'YOUR-CODE-HERE)
            (if 'YOUR-CONDITION-HERE
                with-first
                without-first))))

Use Ok to test your code:

python3 ok -q longest-increasing-subsequence

Exam Practice

The following are some Scheme List exam problems from previous semesters that you may find useful as additional exam practice. These questions have no submission component; feel free to attempt them if you'd like some practice!