Quiz bigO #2

9 points total, 3 points per problem
Grading -
* 1) -.5 for each f that is out of position
* 2) -.5 or -1 per line
* 3) 

Note: ^ is exponentiation, so n^2 is n squared.

1) Put the following in bigO order from smallest to largest
 f1(n) = 2n^2 - nlog(n) + n + 1000    (basically n^2)
 f2(n) = n (log(n))^2 + n^(3/2) + 100 (basically n^(3/2))
 f3(n) = 2^(sqrt(n))
 f4(n) = 2^(2^(n^(1/4)))
 f5(n) = 5n + 10000000000000000000000
 
Answer: f5, f2, f1, f3, f4

2) Say what's true
  f1(n) = 10 n^2 + n(log(n)), f2(n) = 16 n^2 - 10n, f3(n) =  n log(n)
             n^2                         n^2                 n log(n)
	     
               <=  <   >=     >       =
  (choices are: O, o, Omega, omega, Theta)
  f1 is __ of f2: O, Omega, Theta
  f2 is __ of f3: Omega, omega
  f3 is __ of f1: O, o

3) Recursion tree
   - per level (level #, # nodes, input size, running time/node, total running time / level)
   - # levels total
   - total running time
   T(n) = 1 * T(n/10) + n
Answers: 

   Half credit to do    T(n) = 2 * T(n/4) + n