Exercises: Unit 7 — LISP

There are two kinds of exercises here, just as on an ACSL contest.

Short-answer: work out the value with pencil and paper and write one exact answer.
- Write a number as a whole number when it is whole (-3, not -3.0) and as a decimal otherwise (7.5).
- Write a list with single spaces and round brackets, in the same capital letters as the question: (A (B C) D).
- Write the empty list, and "no", as NIL; write "yes" as true.
- Leave out the quote mark: the value of '(A B) is (A B).
Programming: write a complete program that reads the input with input() and prints exactly the output described. Save it as a .py file and run it from a terminal, typing the sample input or feeding it a file. Build new lists with loops and append, as in the lesson.

LISP is on the Intermediate and Senior papers only, so each exercise is marked Intermediate or Senior: the lowest division it belongs to. Do every exercise at or below your division. Exercises marked Challenge are extra practice for when you want more.

Exercise 1: Arithmetic Warm-Up

Division: Intermediate

Evaluate the following expression.

(ADD (MULT 3 4) (SUB 10 7) (SQUARE 2))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: a number

For parents and teachers: report a problem

Exercise 2: Symbols and Decimals

Division: Intermediate

Evaluate the following expression.

(/ (+ 9 (* 2 6) 6) (- 10 2))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: a number

For parents and teachers: report a problem

Exercise 3: Powers and Negatives

Division: Intermediate

Evaluate the following expression.

(MULT (SUB 3 (EXP 2 3)) (DIV 12 (SUB 1 5)) 2)

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: a number

For parents and teachers: report a problem

Exercise 4: One-Call Calculator

Division: Intermediate

The input is one line holding a single LISP statement whose arguments are all whole numbers, such as (DIV 54 4). The function is one of these:

ADD or +, and MULT or *, with 2 to 10 arguments
SUB or -, and DIV or /, with exactly 2 arguments
SQUARE, with 1 argument
EXP, with 2 arguments a n, giving a to the power n

Print the value of the statement. Print a whole number without a decimal point; print any other value as a decimal.

Constraints

The line starts with (, ends with ), and has exactly one space between items.
Every argument is between -1000 and 1000.
For EXP, n is between 0 and 10, and the value is between -1000000000 and 1000000000.
For DIV and /, the second argument is not 0, and the quotient is either a whole number or a decimal with at most 3 digits after the point.

Sample Input

(DIV 54 4)

Sample Output

13.5

The input (- 6 9) prints -3, and (DIV 12 -4) prints -3 as well.

How this is checked: Checked by running your program on 13 test inputs (1 sample, 12 hidden) and comparing its output line by line.

Your code

For parents and teachers: report a problem

Exercise 5: Equal or Not?

Division: Intermediate

Evaluate the following expression.

(EQ (ADD 4 7) (SUB 9 -2))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: `true` or `NIL`, spelled as this book writes them: `true` in small letters, `NIL` in capitals.

For parents and teachers: report a problem

Exercise 6: Is It Positive?

Division: Intermediate

Evaluate the following expression.

(POS (DIV (SUB 3 8) (MULT -2 5)))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: `true` or `NIL`, spelled as this book writes them: `true` in small letters, `NIL` in capitals.

For parents and teachers: report a problem

Exercise 7: Is It Negative?

Division: Intermediate

Evaluate the following expression.

(NEG (SUB (SQUARE 4) 15))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: `true` or `NIL`, spelled as this book writes them: `true` in small letters, `NIL` in capitals.

For parents and teachers: report a problem

Exercise 8: Moon and Stars

Division: Intermediate

Evaluate the following expression.

(CAR (CDR '(SUN (MOON STAR) SKY)))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: A LISP list: round brackets, single spaces between items, the same capital letters as the question, and no quote mark, as in `(A (B C) D)`.

For parents and teachers: report a problem

Exercise 9: One Left Over

Division: Intermediate

Evaluate the following expression.

(CONS 'X (CDR (CAR '((LEFT) RIGHT))))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: A LISP list: round brackets, single spaces between items, the same capital letters as the question, and no quote mark, as in `(A (B C) D)`.

For parents and teachers: report a problem

Exercise 10: The Third Item

Division: Intermediate

Evaluate the following expression.

(CADDR '(RED (GREEN) (BLUE PINK) GOLD))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: A LISP list: round brackets, single spaces between items, the same capital letters as the question, and no quote mark, as in `(A (B C) D)`.

For parents and teachers: report a problem

Exercise 11: Atom or List?

Division: Intermediate

Evaluate the following expression.

(ATOM (CAR (CDDR '(A (B) (C D)))))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: `true` or `NIL`, spelled as this book writes them: `true` in small letters, `NIL` in capitals.

For parents and teachers: report a problem

Exercise 12: Build, Then Turn Around

Division: Intermediate

Evaluate the following expression.

(REVERSE (CONS '(1 2) (CDR '(3 4 5))))

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: A LISP list: round brackets, single spaces between items, the same capital letters as the question, and no quote mark, as in `(A (B C) D)`.

For parents and teachers: report a problem

Exercise 13: REVERSE in Python

Division: Intermediate

The input is one line holding a LISP list of atoms, such as (A B C D). Store its atoms in a Python list. Print two lines:

the value of (REVERSE L), where L is the list
the value of (REVERSE (CDR L))

Print each list the LISP way, with round brackets and single spaces, and print an empty list as NIL.

Constraints

The list has between 1 and 20 atoms.
Each atom is a word of capital letters or a whole number, with no brackets inside it.
The line starts with (, ends with ), and has exactly one space between atoms.

Sample Input

(A B C D)

Sample Output

(D C B A)
(D C B)

For the input (SOLO), the output is (SOLO) and then NIL.

How this is checked: Checked by running your program on 4 test inputs (1 sample, 3 hidden) and comparing its output line by line.

Your code

Also check yourself

The automatic check cannot see these, so tick each one when your work does it.

Store its atoms in a Python list

For parents and teachers: report a problem

Exercise 14: CONS in Python

Division: Intermediate

The first line of input holds one atom X. The second line holds a LISP list of atoms, L, such as (B C). Store the atoms of L in a Python list. Print two lines:

the value of (CONS X L)
the value of (CONS (CAR L) (CONS X (CDR L)))

Print each list the LISP way, with round brackets and single spaces.

Constraints

X is a word of capital letters or a whole number, with no brackets inside it.
L has between 1 and 20 atoms, each of the same form as X.
The second line starts with (, ends with ), and has exactly one space between atoms.

Sample Input

Z
(B C)

Sample Output

(Z B C)
(B Z C)

How this is checked: Checked by running your program on 3 test inputs (1 sample, 2 hidden) and comparing its output line by line.

Your code

Also check yourself

The automatic check cannot see these, so tick each one when your work does it.

Store the atoms of L in a Python list

For parents and teachers: report a problem

Exercise 15: Stored, Then Worked Out

Division: Intermediate

Consider the following program.

(SETQ A '(SUB 20 (MULT 3 4)))
(SETQ B (EVAL A))
(ADD B (EVAL A) (SQUARE B))

What is the value of the final statement?

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: a number

For parents and teachers: report a problem

Exercise 16: A Function Calls a Function

Division: Intermediate

Consider the following program.

(DEF TWICE (N) (MULT 2 N))
(DEF F (A B) (SUB (TWICE A) B))
(F (F 5 3) 4)

What is the value of the final statement?

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: a number

For parents and teachers: report a problem

Exercise 17: Resolved Twice

Division: Senior

Consider the following program.

(SET 'X 5)
(SETQ Y '(X 7))
(SET 'Z (CAR Y))
(MULT (EVAL Z) (CADR Y) 2)

What is the value of the final statement?

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: a number

For parents and teachers: report a problem

Exercise 18: Rotate Twice

Division: Senior

Consider the following program.

(DEFUN ROT (L) (CONS (CAR (REVERSE L)) (REVERSE (CDR (REVERSE L)))))
(ROT (ROT '(1 2 3 4)))

What is the value of the final statement?

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: A LISP list: round brackets, single spaces between items, the same capital letters as the question, and no quote mark, as in `(A (B C) D)`.

For parents and teachers: report a problem

Exercise 19: Four Shortcuts

Division: Senior

Consider the following program.

(SETQ M '((1 2 3) (4 5) 6))
(ADD (CAAR M) (CADR (CADR M)) (CAR (CDDAR M)) (CAR (CDAR M)))

What is the value of the final statement?

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: a number

For parents and teachers: report a problem

Exercise 20: Shortcuts in Python

Challenge
Division: Senior

The first line of input holds the name of one of these functions: CAR, CDR, CADR, CDDR or CADDR. The second line holds a LISP list of atoms, L, such as (P Q R S). Print the value of the function applied to L.

The value is either an atom, which you print as it is, or a list, which you print the LISP way, with round brackets and single spaces. Print an empty list as NIL.

Work through the letters between the C and the R from right to left, as LISP does, rather than writing a separate case for each name.

Constraints

L has between 1 and 20 atoms.
Each atom is a word of capital letters or a whole number, with no brackets inside it.
The second line starts with (, ends with ), and has exactly one space between atoms.
The list is always long enough: every A step is taken on a list with at least one atom.

Sample Input

CDDR
(P Q R S)

Sample Output

(R S)

For the same list, CADDR prints R, and for the list (P Q), CDDR prints NIL.

How this is checked: Checked by running your program on 7 test inputs (1 sample, 6 hidden) and comparing its output line by line.

Your code

Also check yourself

The automatic check cannot see these, so tick each one when your work does it.

Work through the letters between the C and the R from right to left, as LISP does, rather than writing a separate case for each name

For parents and teachers: report a problem

Exercise 21: Sum of Squares, Halved

Challenge
Division: Senior

Consider the following program.

(DEFUN SUMSQ (A B) (+ (SQUARE A) (SQUARE B)))
(SETQ P (REVERSE '(2 (1 3) 4)))
(DIV (SUMSQ (CAR P) (CADR (CADR P))) (CADDR P))

What is the value of the final statement?

How this is checked: Checked by comparing your answer with the expected answer.

Answer format: a number

For parents and teachers: report a problem

Back to Unit 7 — LISP