Esteemed listers:

I have a scenario where I would like to test various combinations of numbers
in an array and sum them to find a total amount to solve a reconciliation

So, for example, I have the following array of numbers:


In this example, I am looking for any combination that adds up to 13,134.65.
A good tool would be able to find that the 2nd, 3rd, and 5th amounts add up
to the total amount I'm looking for.  In a real-life application, this
problem would involve an array of hundreds, if not thousands, of amounts,
usually to find a small number of amounts to sum up to the difference needed
to reconcile.

Joe Pluta, in a rpg400-l thread, had suggested a solution that is somewhat
workable, but I haven't figured out how to sum all of the 2-amount
combinations before I start with the 3-amount combinations.  In essence, Joe
suggests creating an array (ARR1) loaded with all of the amounts in the
list, a second array (ARR2) whose elements will contain either 1 or 0, and a
third array (ARR3) that contains the multiplication result of the first two.
So, using the example above:

       ARR1  ARR2       ARR3
     185.69    0        0.00
  11,134.60    1   11,134.60
     500.03    1      500.03
   4,841.65    0        0.00
   1,500.02    1    1,500.02
     419.85    0        0.00

ARR2 would be a parsed out binary value with element 1 having the low-order
digit, i.e. '010110' in this case.  ARR2 seems like it should be some sort
of a binary-calculated counter, but it isn't as easy if I'm incrementing by
one and I want to exhaust all 2-amount combinations before I test any
3-amount combinations.  So, I would like to try utilize something like:

00000011 =   3
00000101 =   5
00000110 =   6
00001001 =   9
00001010 =  10
00001100 =  12
11000000 = 192 <= Highest of the 2-digit binary for 8 bits
00000111 =   7 <= The first 3-digit binary
00001011 =  11
00001101 =  13
00001110 =  14
00010011 =  19
11100000 = 224 <= Highest of the 3-digit binary for 8 bits

(Of course, I'd need as many bits as the number of amounts I'm dealing

Is there an easy way to "imcrement" like this?  I haven't been able to think
my way out of this box, so if there are any "outside" thinkers, please weigh
in.  It seems that this type of problem can't be easily solved in RPG.  I
was hoping that MI has something that facilitate the type of solution I'm
thinking of.


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