Pseudorandom sequence length N

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Is there a way of generating a pseudorandom sequence of integers length N, where all integers from 0 to N-1 are included within the sequence. N to be an arbitrary and variable number?

Posted 18-May-11 12:27pm

Member 1415146

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Sergey Alexandrovich Kryukov 18-May-11 19:55pm

Of course there is a way. Isn't a nice simple exercise for you? Try is and ask a question if you face a problem.
--SA

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Peter_in_2780 · Accepted Answer · 2011-05-18T14:16:00

Solution 1

Short answer: yes.

Real dumb way (but can be good if N is small):
Create an array of the integers 0 .. N-1
Shuffle it (swap two random* items some large number of times)
Downside - O(N) space and time requirements.
* using whatever PRNG you already have, truncated or scaled to N

Smarter way:
Construct a full-period pseudorandom generator on the fly
For simplicity, choose a mixed congruential PRNG Xn+1 = (a * Xn + c) mod N
Your task is now to select a, c and X0, all in the range 0..N-1
The requirements for full period are:
c is relatively prime to N - if c is prime, that's easy
(a-1) is divisible by all prime factors of N
(a-1) is a multiple of 4 if N is a multiple of 4 (i.e. consider 4 a prime for the line above!)

It's a bit of number-crunching to work these out, but not too bad.
The statistical quality of the resulting PRNG is not likely to be very good, but that probably won't matter if what you really need is just a shuffle of 0..N-1.

Look up wikipedia on 'linear congruential generator' and other pages linked from there if you want more math background.

Cheers,
Peter
If this answers your question, accept it. Vote anyway.

[edit] Silly me - forgot the ( ) mod N in the formula. [/edit]

Posted 18-May-11 14:16pm

Peter_in_2780

Updated 18-May-11 21:19pm

v3

Comments

Sandeep Mewara 19-May-11 3:09am

OP accepts it or not... here is my 5! :)

Dalek Dave 19-May-11 3:45am

Good Answer.

Peter_in_2780 19-May-11 4:04am

You'd like this Excel variant of the dumb one. Col A: 1, 2, 3 ... N Col B: =rand(), cloned N times.
Sort on col B, then delete col B. I use it to randomise a list of topics that are all to be covered, but not in a predictable order (ie different from last semester).

Member 1415146 20-May-11 18:52pm

Thanks. I figured I needed to make my own PRNG, but wasn't really sure how to do that with varying N. Realistically N will be two numbers multiplied together, each number being either between 1 and 10, a multiple of 2 between 10 and 20, or a multiple of 5 between 10 and 50. Hence it seems a=421, c=11 works for all possible cases. What I'd really like to have though is to repeat this and get a different sequence multiple times...

Peter_in_2780 20-May-11 18:59pm

Different parameters => different sequences. If you want to do it the hard way, calculate a and c each time on the fly. However, your largest possible N appears to be 2500, so I'd recommend the dumb way, remembering to seed your "real" PRNG with, say, time() so you get different sequences.

Member 1415146 20-May-11 20:42pm

Different seed just gives me the same sequence with a different start point - far too trivial to see that a fixed sequence is being used if I repeat that a few times. Unless I'm missing the point you're making? Did think about calculating a and c on the fly, however it seems like quite a bit of trouble having to calculate prime factors. I'm not after cryptographic level stuff here, just some way of making it non-obvious to a casual observer that I'm using a generated sequence (there's some post coding going on which helps hide that, but will still result in repeated patterns if I just use a different seed).

Peter_in_2780 20-May-11 21:00pm

Yet more reasons to use the "shuffle" (aka dumb) method. I did say 'parameters', not 'seed'. For numbers <=2500, I'd go brute force. (Saves on brain overload, too! :) )

Member 1415146 20-May-11 20:50pm

...sorry this looks like I'm asking for help with a homework question, when I'm actually a professional software engineer with a mathematical background and should know this stuff. Though my brain is mush after several weeks of pressure getting a delivery out the door (and this is a home project).

Peter_in_2780 20-May-11 21:02pm

I must admit I initially thought "homework" when I saw the original question, but after a minute or so's contemplation, decided it wasn't. Hence an answer (which led to a discussion...) I notice SAK seems to have taken it as homework.