CPSC 212-1			Name: _____________________________
Quiz #1				January 17, 2001

Closed books. Closed notes. Calculators OK. 20 points. 10 minutes. 
Weight of each question in parentheses. Please use a pencil. For 
more space, use the back of the sheet.

1. (8) Evaluate each of the following sums:

(a)	1 + 2 + 3 + ...  + n      = n(n+1)/2

(b)	1 + 2 + 3 + ...  + (n+1)  = (n+1)(n+2)/2

(c)	27 + 30 + 33 + ... + 3n   = 3(9 + 10 + ... + n) = 3(n(n+1)/2  -  8*9/2)
                                  = 3(n(n+1)/2  - 36)

(d)	1 + 4 + 9 + ... + n2      = n(n+1)(2n+1)/6


2. (8)  Evaluate each of the following.  Use the letters "A", "Q", "P", 
   "K", "W", "L", "R", "M", "G", "T", "V" and "E" where appropriate.

   4K = 2^12   64T = 2^46   8P = 3^53   512E = 2^69

3. (4) What is the order of complexity of each of the following:

Quicksort on an array of N elements    
   O(n^2) worst case, O(n log n) average case

Finding the median value (50th percentile) of a sorted set of N values
   O(1)

Finding the 10th  largest value in an unsorted set of N values (assume N>10)
   O(n)

Assume that an int NxN array is checkerboard-colored (some elements are 
considered "red", the other are "black").  What is the complexity of taking the 
sum of all of the "red" elements. 
   O(n^2)