CS 307: Study Guide for Exam 2
Date: Friday, November 2, 2001, in class.
All Material on Exam 1 Study Guide is Included for This Exam.
Hailperin, Chapter 8.
Run at least two of the exam2 lessons on the Scheme Tutor; print
out your results and hand them in on the day of the exam.
The Tutor contains previous exam questions to help you to prepare for the exam.
- Recursion over binary trees.
- Destructive operations on lists.
You should know the following Lisp functions. Be able to give the result
for a simple call to each function.
dotimes dolist while every some map for-each
eval apply lambda
- List Structure: Combinations of car and cdr.
assoc assq assv list-tail list-ref
copy-tree subst sublis set-car! set-cdr!
subset? intersection union set-difference subset
- Predicates and Logical:
string? list? vector? char?
char-alphabetic? char-numeric? char=? char<=?
char-lower-case? char-whitespace? char char>?
char-upper-case? char>=? char-ci=? char-ci
char-ci>? char-ci<=? char-ci>=? string=?
string string>? string<=? string>=?
string-ci=? string-ci string-ci>? string-ci<=?
- Vectors, Characters, Strings:
make-vector vector vector-ref vector-set!
vector-length vector->list list->vector vector-fill
char-upcase char-downcase char->integer integer->char
make-string string-length string string-ref
string-set! string->list list->string string-fill!
Write Scheme programs for each of these:
- Given as input a list structure (tree) containing some numbers
(and possibly other things), write a function to add up
the cubes of all the numbers.
- Write a function (count lst tree) that will count the
number of occurrences of items in the list lst in the list
structure tree. The items in list lst will be simple
items such as symbols, numbers, or boolean values. Example:
(count '(a 3) '((b 3 a) (c 3 (7 a)))) = 4
- Write a function that will return the sum of the even numbers
in a list structure (tree) that may contain things that are not numbers.
- Write a function (total items prices) that will compute
the total cost of a list of items. prices is a list
((item price) ...). Example:
(total '(bread milk) '((eggs .69) (milk 1.89) (bread 1.39)))
- Write a recursive function that translates a prefix expression (as
in Lisp) to an infix expression (as in Pascal). Assume operators
+ - * / , where - can be either unary or binary.
(infix '(+ a (* b c))) = (a + (b * c))
- Write a function (average lst wts) to compute a weighted
average of grades. lst is a list of sublists (item grade).
wts is a list of sublists (item weight) in arbitrary order.
For each element of lst, look up the corresponding weight for
that item, multiply the grade by it, and add to the total.
(average '((midterm 80) (homework 75) (final 90))
'((homework .2) (final .5) (midterm .3)))
= .3 * 80 + .2 * 75 + .5 * 90 = 84
- Write a function (weight tree lst) to compute the "weight" of
a tree structure. Each pair has a weight of 2. Symbols that are in
lst have a weight of 3. All other items have a weight of 0.
(weight '((a 3) (b c d)) '(a b)) = 20
- Write a function (path goal tree) that will return the list of
successive car's and cdr's necessary to reach the first occurrence of the
simple item goal in the structure tree. If goal
does not occur in tree, return #f.
(path 'c '((a b) (c d))) = (cdr car car)
- Write a function (opposite lst opp) that returns a list of
the opposite of each item in lst. opp is a list of
sublists, ((item opposite) ...). If an item in lst
does not have an opposite, nothing is included in the output for it.
(opposite '(up cat ernie) '((ernie bert) (up down)))
= (down bert)
- A student likes Scheme so much that he writes his grocery
list as an expression using the operators + and *. Write a
function (cost groceries prices) to calculate the cost of the
groceries given a list of dotted pairs ((item . price) ...).
(cost '(+ bread (* 2 milk) (+ nuts (* 2 (* 6 beer))))
'((beer . 0.8) (milk . 1.2)(nuts . 2)(bread . 1.5)))
- Write a function (largest tree) that finds the largest
number in a tree. The tree contains at least one number.
You may assume that all the numbers are positive.
(largest '((+ a 7) b (11 c))) = 11
- A mobile is a symbol, a number, or a list of two mobiles.
A mobile is balanced if it is a symbol or a number, or if it
is a list, its sub-mobiles are balanced, and its sub-mobiles
weigh the same. Symbols have a weight of 1; numbers weigh
the amount of the number, and other things weigh nothing.
Write a function (balanced m) to determine whether a
mobile m is balanced; write other functions if needed.
(balanced '((1 A) 2) ) = #t
- Write a function (total items bargains prices) as
follows. items is a list ((quantity item) ...) giving items
purchased. bargains is a list (item ...) of items that are
on sale for 1.00 . prices is a list ((item price) ...) of
item prices. Any item that is not in bargains or prices is
free. Compute the total cost of all items purchased.
(total '((6 beer) (1 milk) (1 bag)) '(beer nuts bread)
'((oats 2.00) (milk 1.69) (apple .50)))
- Write a function (weight tree) to compute the weight
of a tree structure. Each pair has a weight of 2. symbols
have a weight of 1. numbers have a weight equal to the
number value. Anything else weighs 0.
(weight '((a 3) 7)) => 19 ; 4 pairs, 1 sym, 3, 7
- A family tree is a list (mother name father) where
mother and father are family trees (or #f if unknown) and
name is a symbol. Write a function (relative tree name)
that returns a list giving the relation of name to the person
whose family tree is given by the argument tree.
(relative '(#f john #f) 'john) => () ; john himself
(relative '((#f mary (#f bill #f)) john (#f fred #f))
=> (mother father) ; bill is john's mother's father
- A car approaching an intersection can go one of three
ways: left, straight, or right. An intersection is
represented as a list (left straight right) of possibilities.
Each possibility is an intersection or a destination (non-
pair). Write a function (follow int directions), where int
is an intersection, that will follow the list of directions
(each of which is L, S, or R) and return the
subtree or destination denoted by the directions. If the directions
continue past the intersection lists, return #f.
(follow '(a b c) '(r)) => c ; right turn goes to c
(follow '(a (b c (d e f)) g) '(s r l)) => d
; straight to (b c (d e f)), right to (d e f), left to d
Convert between list structure and box diagrams (both ways).
You will be asked to write definitions for terms selected from the list
below. Definitions are given at the back of the lecture notes.
access time alist array
ASCII association list atom
binary search binary tree byte
Caesar cipher case insensitive case sensitive
CD-ROM character character code
code concatenation cons cell
data abstraction decryption destructive operation
disk driver dynamic
element encapsulation encryption
enumerate file functional programming
garbage hiding I/O
index initialize input/output
interface intersection isomorphism
key mapping nesting
polynomial port private
proper subset public public key
public-key cryptosystem read-only memory ROM
runtime scalar set
set difference string structure sharing
subset substitution substring
union vector whitespace