Tute 2, CSE2304, CSSE, Monash, Semester 1, 2002

Group A: week 4, 25-28 March (Fri 29th -> 12 April),
Group B: week 5,   8-11 April (Fri 12th -> 19 April)

Class: Prepare your answers before the tute!

Tutors: (i) The purpose of the tutorials is not to solve the prac's! (ii) The purpose of the tutorials is to check answers, and to discuss particular sticking points, not to simply make answers available. It will only be possible to cover all questions if the class has prepared them all in advance.

1. x, y and z are integer variables. Give code to determine if exactly two of x, y and z are even. Use as few tests (==, !=, <, <=, > >=, odd(), even()) as possible. (For this question it is "unethical" to treat an int as a boolean or v.v..)
   
   
2. A[0..N-1] is an array of N integers.
   Give efficient code to find the position of the second largest element in A. Resolve ties arbitrarily.
   Give assertions, pre- & post-conditions, loop-invariants and arguments why your code terminates and is correct.
   
   
3. A[0..N-1] is an array of N integers.
   Give efficient code to find the second largest value in A.
   You cannot assume that the elements of A are all different, but you can assume that they do not all hold the same value.
   Give assertions, pre- & post-conditions, loop-invariants and arguments why your code terminates and is correct.
   
   

4. for i from Lo1 to Hi1 do

   for j from Lo2 to Hi2 do

   body

   end_for

   end_for

   How many times is `body' executed if
   1. Lo1 = 0, Hi1 = n, Lo2 = 0, Hi2 = i
   2. Lo1 = -n, Hi1 = n, Lo2 = i-2, Hi2 = i+2
   3. Lo1 = 0, Hi1 = n-1, Lo2 = -i, Hi2 = i
   
   
   
5. "Words" made of matched parentheses can be ordered lexicographically if we consider  "(" < ")".
   e.g. ((())) < (()()) < (())() < ()(()) < ()()()
   If the string S contains a word of `n' pairs of matched parantheses, give an algorithm to change S so that it contains the next word in lexicographical order.