Three types of complexity could be considered when analyzing
algorithm performance. These are worst-case complexity, best-case
complexity, and
average-case complexity. Only worst-case complexity has found to be
useful. Worst-Case running time for a
function, f(n) such that 
where a,b
and c are
constants can be described as a higher bounding limit for the shortest
possible running time for any given "n" beyond some instance of "N"(big
"n") such that 
. In this case, 
is the higher
bounding limit on f(n). 
. We will soon see how
for this example. More useful than best-case, since worst-case will tell
how long an algorithm will run in the worst possible situation.
Average-Case running time for a function, f(n) such that where a,b and c are constants can be described as an average
between best-case and worst-case.
Average-case isn't useful because in most cases it's hard to define the
average.
Best-Case running time for a function, f(n) such that where a,b and c are constants can be described as a lower bounding
limit for the shortest possible running time for any given "n" beyond some
instance of "N"(big "n") such that . In this case, 
is the lower bounding limit on f(n). 
.
We will soon
see how for this example. Best-case performance isn't really
useful because it
doesn't reflect normal operation of the algorithm.
Figure 1: Relationship of Complexity Types