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    <p>Sounds like you want an algorithm which is guaranteed to produce a cycle from 0 to n-1 without any repeats. There are almost certainly a whole bunch of these depending on your requirements; <a href="http://en.wikipedia.org/wiki/Group_theory" rel="nofollow noreferrer">group theory</a> would be the most helpful branch of mathematics if you want to delve into the theory behind it.</p> <p>If you want fast and don't care about predictability/security/statistical patterns, an LCG is probably the simplest approach. The wikipedia page you linked to contains this (fairly simple) set of requirements:</p> <blockquote> <p>The period of a general LCG is at most m, and for some choices of a much less than that. The LCG will have a full period if and only if:</p> <ol> <li>c and m are relatively prime,</li> <li>a - 1 is divisible by all prime factors of m</li> <li>a - 1 is a multiple of 4 if m is a multiple of 4</li> </ol> </blockquote> <p>Alternatively, you could choose a period N >= n, where N is the smallest value that has convenient numerical properties, and just discard any values produced between n and N-1. For example, the lowest N = 2<sup>k</sup> - 1 >= n would let you use <a href="http://en.wikipedia.org/wiki/LFSR" rel="nofollow noreferrer">linear feedback shift registers</a> (LFSR). Or find your favorite cryptographic algorithm (RSA, AES, DES, whatever) and given a particular key, figure out the space N of numbers it permutes, and for each step apply encryption once.</p> <p>If n is small but you want the security to be high, that's probably the trickiest case, as any sequence S is likely to have a period N much higher than n, but is also nontrivial to derive a nonrepeating sequence of numbers with a shorter period than N. (e.g. if you could take the output of S mod n and guarantee nonrepeating sequence of numbers, that would give information about S that an attacker might use)</p>
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    1. POGenerating shuffled range using a PRNG rather than shuffling
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