I had started to program a somewhat similar approach (starting with singletons, then pairs, triples, then I gave it up because it seemed to me that the number of combinations to check might grow too large -- depending on the data, though). I used the CALL ALLCOMBI routine rather than nested DO loops to create the combinations.
Not sure where the "potential of not getting everything assigned to a group" should come from: Since the original dataset has a total of zero, the leftover after taking away any proper subset with sum zero must have a total of zero as well. So, the worst case I could imagine was that at some point the remaining (not further decomposable) subset would be unnecessarily large.
Everyone -THANK YOU. I'm implementing and trying both the "brute force" and the "greedy" applications. I sincerely cannot thank the community enough for the help on this. I was pulling my hair out trying to figure this out, so from the bottom of my grateful heart thank you.
You can replace the pair search with something simpler.
data work.pairs ( keep=iout jout ival jval)
work.leftover (keep=ba:)
;
set work.trans end=last;
array b ba:;
do i= 1 to (dim(b)-1);
if b[i]=. then continue;
j=whichn(-b[i],of b[*]);
if j=0 then continue;
iout=i;
jout=j;
ival = b[i];
jval = b[j];
output work.pairs2
call missing(b[i],b[j],iout,jout);
end;
if last then output work.leftover;
run;
Not that it makes difference overall....
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