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    <p>I just remembered a similar problem from a class I took years ago; that is, iterating (relatively) randomly through a set (completely exhausting it) given extremely tight memory constraints. If I'm remembering this correctly, our solution algorithm was something like this:</p> <ol> <li>Define the range to be from 0 to some number <em><code>N</code></em></li> <li>Generate a random starting point <em><code>x[0]</code></em> inside <em><code>N</code></em></li> <li>Generate an iterator <em><code>Q</code></em> less than <code>N</code></li> <li>Generate successive points <em><code>x[n]</code></em> by adding <code>Q</code> to the previous point and wrapping around if needed. That is, <code>x[n+1] = (x[n] + Q) % N</code></li> <li>Repeat until you generate a new point equal to the starting point.</li> </ol> <p>The trick is to find an iterator that will let you traverse the entire range without generating the same value twice. If I'm remembering correctly, any relatively prime <code>N</code> and <code>Q</code> will work (the closer the number to the bounds of the range the less 'random' the input). In that case, a prime number that is not a factor of <code>N</code> should work. You can also swap bytes/nibbles in the resulting number to change the pattern with which the generated points "jump around" in <code>N</code>.</p> <p>This algorithm only requires the starting point (<code>x[0]</code>), the current point (<code>x[n]</code>), the iterator value (<code>Q</code>), and the range limit (<code>N</code>) to be stored.</p> <p>Perhaps someone else remembers this algorithm and can verify if I'm remembering it correctly?</p>
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    1. POHow can I randomly iterate through a large Range?
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    1. POHow can I randomly iterate through a large Range?
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    1. COI think this is as good as you can get if you won't store the tried inputs and can't have duplicates. There is really no need for a truly random shuffle if you are going to test all inputs and they don't interfere. To spread the choices out as much as possible, use a Q close to the golden section (2N/(1+sqrt(5))).
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    2. COThis sounds almost exactly like what I want to do. I am not overly concerned about randomness, but it is very important. If anyone knows the name of this algorithm, that would be great.
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    3. COI'm not sure if there's a name for the algorithm. The specific principle it's based off of (a mathematical property of prime numbers with respect to modular arithmetic) might have a name though.
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