A permutations producing algorithm request.

[Stanislaw L. Olejniczak]

A question about a (?) simple algorithm and the "best" implementation:

In last few years I have repeatedly encountered a need to have an
algorithm to produce all permutations of a given ordered set.  To make
sure I am making sense; I follow with, I hope, a clear example at the end.
I have never felt I have found a "best" solution.  If you know of a
generally accepted, or at least one you would recommend, algortihm, I
would appreciate either its definition or appropriate references.

>From past experience I will not promise a summary, but I will send raw
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As to an example:
Lets say that I have three variables, A, B, C, that can take mA to nA, mB
to nB, and mC to nC values, respectively, where it is not given that any
of those values equals any other, though ranges can overlap:  ex>;
A: 1,2,3
B: 2,3,4,5
C: 7,8
I need to produce ordered sets:
1,2,7
1,2,8
1,3,7
1,3,8
1,4,7
1,4,8
1,5,7
1,5,8
2,2,7
2,2,8
etc.
3,5,7
3,5,8
2,7,1
2,8,1
3,7,1
3,8,1
etc.
for all possible permutations of A, B and C values.  Duplicates are O.K.,
but if the algorithm would (optionaly) elimate them, that WOULD be nice.
Any suggestions would be most welcomed.

-- 
Stan Olejniczak               Internet:         slores at umiami.miami.edu
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