Subj : efficient way of processing m combinations of n numbers in p sets
To   : comp.programming
From : Mike
Date : Tue Aug 16 2005 04:29 am

Hi,


I am trying to process all combinations of 6 sets of numbers (using
VB).  The
minimum number in each set will be 2 and the maximum number is
definable but will be the same for all 6 sets.  The increment in each
set is also definable and is also the same for each set.


As an example, if I set the Maxnumber as 4 and the increment as 1, I
would end up with the following possibilities:


2,2,2,2,2,2
3,2,2,2,2,2
2,3,2,2,2,2
3,3,2,2,2,2
2,2,3,2,2,2
3,2,3,2,2,2
2,3,3,2,2,2
3,3,3,2,2,2
....
....
4,4,4,4,4,4 etc
After each of the combinations is found I wish to perform a
calculation.


The way I am running it at the moment is 6 nested for loops as in the
following:


Stp = 1  'increment between numbers in each set
Maxnumber = 4   'largest number in each set.


For i = 2 To Maxnumber Step Stp
For j = 2 To Maxnumber Step Stp
For k = 2 To Maxnumber Step Stp
For l = 2 To Maxnumber Step Stp
For m = 2 To Maxnumber Step Stp
For n = 2 To Maxnumber Step Stp


    '     perform calc on i,j,k,l,m and n


next n
next m
next l
next k
next j
next i


The problem I have is that as soon the maximum number is set too high
or the increment is too low, the number of calculations increases
exponentially and the pc freezes.  Ideally I am looking to perform
these types of calculations in under 2 seconds.  The ideal ranges would

be from 2 to 50 in each set with an increment of 0.1, so 2, 2.1,
2.2....up to 50.


I would be really grateful if someone could offer some advice on how to

perform these calculations in a more efficient manner.  For example,
would placing all possibilities into an array first and then performing

calculations at the end offer any improvements?


My final question is would it be possible to vary the number of for
loops involved e.g. in the above example, if I only had 3 sets of
numbers I would only need 3 for loops to work through all of the
possibilities. 


Many thanks in advance, 


Mike

.