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CS 61A Spring 1998
Midterm 1
Professors Fateman & Forsyth
Question
What will Scheme print in response to the following expressions? If it produces an error or runs forever without a result, just say "error". If it is a procedure, say "procedure". Assume no global variables have been defined beforehand except where noted.
(word '(+2 3) (+2 3))
((lambda (x y z) (* 5 y)) 3 4 7)
;from ex. 1.32, p. 61 (accumulate se '(hurrah) (lambda(x) (word 'hip x)) 1 (lambda (x) (1+x)) 3)
((if 3 - *) 32 2)
(a b c)
(let ((a 5) (* +) (+ *)) a(+ a a))
((lambda (-) (- 2)) (lambda (*) (+ * 4) ))
Question #2 (True or False?)
_______ A Ø (log(2n)) algorithm is slower than a Ø (2 log(n)) algorithm
_______ For small size inputs knowing the Ø order of an algorithm is more useful than for large inputs
_______ If f(x) is Ø (log x), then lim (x => infinity) f(x)/(log x) is zero
_______ If f is defined as (define (f x) (* x x x)) then and applicative-order evaluation of (f (g y))
evaluates (g y) more often than a normal -order evaluation
_______ Function g below defines a linear recursive process
(define (g a b c) (if (> a b) c (+ c ( g (+ a 1) (- b 1) (+ c 1)))))
Question
Write a linear iterative function li-nth that takes a number n and a sentence and returns the n 'th element
of that sentence and an empty sentence if there is no such element. Count from zero. For example,
(li-nth 0 '(1 2 3 4)) 1 (li-nth 2 '(1 2 3 4)) 3 (li-nth 4 '(1 2 3 4)) '()
CS 61A Spring 1998 Midterm 1 Professors Fateman & Forsyth 1
Question
random takes an argument n , and returns a random number from the set {0, 1, ..., n-1}.
Does the following segment of scheme define a function? In one sentence, explain why or why not.
(define (f x) aaaaaa ((lambda (u) aaaaaa ((let ((a 0) aaaaaaa let ((b 1)) aaaaaaa let (random u))) aaaaaaaa (+ 45 x)))
Question
A polynomial can be repeated as a sentence, where the words are the coefficients of the terms. The first element of the sentence represents the term of degree 0 (the constant term), the second represents the term of degree 1, etc. So, for example, 3x² + 2x+ 1 would be '(1 2 3) and 27x 8 + 1 would be '(1 0 0 0 0 0 0 0 27) The polynomial whose coefficients are all zero is represented by '().
Write a function add-polys that takes two polynomials each of arbitrary degree, each represented
as a sentence and returns their sum, represented as a sentence. For example
(add-polys '(1 2 3) '(1 0 0 0 0 0 0 0 27)) (2 2 3 0 0 0 0 0 27)
In this representation, multiplying polynomials by terms (otherwise known as monomials; 9x² is a monomial or term whereas 9x² + 1 is a polynomial with two terms) involves shifting and multiplying.
Write a function term-multiply-poly that takes a polynomial of arbitrary degree represented as a
sentence, a term coefficient and the degree of a term and returns the product represented by a sentence For example, if I wanted to multiply 9x² + 2x + 1 by 7x 3 , I would do:
(term-multiply-poly '(1 2 9) 7 3) (0 0 0 7 14 63)
Quesiton
Write a procedure interleave-2 that takes two sentences s1 and s2 as its arguments. It returns the
sentence whose elements are alternate elements of s1 and s2 beginning witht he first ( the first of s2 ,
the first of s1 , the second of s2 , the second of s1 , and so on). If one sentence is longer than the other,
it behaves as if the shorter were padded with 0's. For example,
(interleave-2 '(1 2 3 4) '(5 6 7 8)) (5 1 6 2 7 3 8 4) (interleave-2 '(9) '(10)) (10 9) (interleave-2 '(9) '(10 11 12)) (10 9 11 0 12 0) (interleave-2 '(1 2 3 4) '(5)) (5 1 0 2 0 3 0 4)
CS 61A Spring 1998 Midterm 1 Professors Fateman & Forsyth 2
