Actually, selecting with an exact probability of 1/3 (or any other rational fraction less than one) is feasible with even a source of single random bits. I saw the technique described once in "Mathematical Games" in Scientific American once.
Represent 1/3 as a binary fraction: .01010101...
and generate random numbers bit by bit, starting from the decimal point, calling this a new binary fraction. If the next bit we generate is 1 where there is a 0 in the target, then quit -- we are over 1/3. If the next bit is 0 where there is a 1 in the target, then quit -- we are under 1/3 and we can accept the case. If it's equal, keep generating bits. The probability we will have to continue adding bits halves with each bit.
This approach can make the Fisher-Yates shuffle arbitrarily accurate. It would be possible, but messy, to apply it to sort values that compared equal, too. With this enhancement both shuffles should be fair, but Fisher-Yates wins by being O(N) instead of O(NlogN).
-
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.
|