While we're nitpicking:
O() defines an upper bound (typically, but not exclusively, on worst case behaviour)
Ω() defines a lower bound (again typically, but not exclusively, on best-case behaviour)
An algorithm is said to run in Θ(f(n)) if it runs in O(f(n)) and in Ω(f(n)), i.e. the upper and lower bounds are no more than a constant multiple of each other. It is a tighter definition than average-case execution complexity which depends on first defining the properties of an "average" input. I think what you're trying to define above is average-case execution complexity - by definition of the Θ() notation your statement above cannot be true.
BTW mergesort is O(n lg n).
- Menahem
-
Are you posting in the right place? Check out Where do I post X? to know for sure.
-
Posts may use any of the Perl Monks Approved HTML tags. Currently these include the following:
<code> <a> <b> <big>
<blockquote> <br /> <dd>
<dl> <dt> <em> <font>
<h1> <h2> <h3> <h4>
<h5> <h6> <hr /> <i>
<li> <nbsp> <ol> <p>
<small> <strike> <strong>
<sub> <sup> <table>
<td> <th> <tr> <tt>
<u> <ul>
-
Snippets of code should be wrapped in
<code> tags not
<pre> tags. In fact, <pre>
tags should generally be avoided. If they must
be used, extreme care should be
taken to ensure that their contents do not
have long lines (<70 chars), in order to prevent
horizontal scrolling (and possible janitor
intervention).
-
Want more info? How to link
or How to display code and escape characters
are good places to start.
|