CISC 280 review sheet for first midterm exam

sample question types

• A problem similar to exercise 1.1, i.e. "Evaluate this, this, and this expression."
  
  
• Evaluate calls to functions which are defined in the question. For example, there are four definitions of a function named f on page 64. Be sure you can evaluate

  (f 0 0), (f 0 1), (f 1 0), and (f 1 1) 

  for each of the 4 forms of definition.
  
  
• Problems meant to show you know the special forms. For example, you find that a certain implementation of Scheme is lacking "cond". Redefine the following procedure using "if".

  (define (foobar x y)
     (cond ((= x y) 12)
  	 ((< x y) (- y x))
  	 (else (square x)) ))
  

  
  
  
• short answer or true/false questions about programming concepts we've covered such as
  the distinction between an iteration (or tail recursion) and a linear recursion that is not an iteration.
  
  
  the order of growth of the two ways of doing exponentiation, of gcd, of fast or slow prime?
  
  
  Numeric issues such as absolute versus relative accuracy, horizontal vs. vertical comparison. For example in sqrt let us say r is the (unknown) true square root of x and g is a guess of r. It matters whether we stop because g^2 is near x or because g is near x/g, hence near r (horizontal vs vertical accuracy). Also it matters what we mean by "near". If we stop because g-x/g is near zero (absolute accuracy), we get different results than if we stop because ((g-x/g)/x is small (relative accuracy).
  
  
  Astronomical vs super-astronomical numbers. The approximation 2^10 ~ 10^3.
  
  
  procedures as parameters and as general methods,
  
  
• Problems about writing procedures in scheme:
  (a) writing procedures which are possible directly from memory (i.e. have been defined in the book or in class, or have been homework. For example, define sqrt, factorial, fib, expt, slow-expt-mod, fast-expt-mod, gcd, sum, length, fixed-point, the functions about the digits of a number. Note it is not expected that you will rote memorize these, rather that you will remember the specifications and the methods enough to be able to recreate procedures to compute them.
  
  
  (b) writing specified procedures which are only similar to ones we've done. For example, define a procedure to compute the odd part of a positive integer. Every integer can be written as a power of 2 times an odd number. This procedure returns the odd number. For example,

  (odd-part 5) --> 5, because 5 = (2^0)*5,
  (odd-part 20) --> 5, because 20 = (2^2)*5,
  (odd-part 48) --> 3, because 48 = (2^4)*3,
  (odd-part 32) --> 1, because 32 = (2^5)*1,
  

saunders@cis.udel.edu