ALGORITHM ANALYSIS
------------------
Analyze code to determine how much TIME is required to execute an algorithm.

Comparative measure.

Given multiple algorithms to solve a problem,
  which one is better???


Order Notation
--------------
Algorithm A is O(f(n)) or "order f(n)" if
  constants k and n0 exist such that A requires
  no more than k * f(n) operations to solve a
  problem of size n >= n0


What is the "order" of these algorithm runtimes?

(a) 3n + 2  ==>  3n  ==>  O(n)  LINEAR

(b) 5n - 5  ==>  5n  ==>  O(n)

          17n
(c) 14 + -----  ==>  0.1n  ==>  O(n)
          170

      2
     n                      2          2
(d) ---- + 15n - 6  ==> 0.1n   ==>  O(n )
     10                             QUADRATIC


               2              2
(e) 10000 + 36n  - 4n  ==> O(n )


-----------------------
 O(1)  Constant

 O(log n)  Logarithmic

 O(n)  Linear

 O(n log n)

    2
 O(n ) Quadratic

    3
 O(n )

    n
 O(2 )  Exponential



e.g.

 int count = 0;
 for ( int i = 0 ; i < n ; i++ )
 {
   for ( int j = i ; j < n ; j++ )
   {
     count++;
   }
 }