RE: Combinations & Permutations..... sort of

After some more thinking, I believe I've figured out the total.

For 10 items, there are 4,037,913 possible combinations.

Calculated as:
for x01 = 1 to 1
Total += 1
for x02 = 1 to 2
Total += 1
<and so on>
for x10 = 1 to 10
Total += 1
endfor
endfor
endfor

Smaller sample size is definitely in order.

From: roger.harman@xxxxxxxxxxx
To: rpg400-l@xxxxxxxxxxxx
Subject: Combinations & Permutations..... sort of
Date: Mon, 29 Sep 2014 17:17:55 -0700

Put your math hats on......

I'm looking at a means to *attempt* to auto-match payments to invoices. We do not want to apply payments to oldest first and end up with a partial payment or credit leftover.

Pick an arbitrary number of invoices for the attempt - say 10.

Any combination of 1 or more of these 10 invoices that total the payment amount would be considered a match.
Could be invoice 1, or 2, or.... Could be invoices 2 and 5 and 8..... etc.

I assume it's going to have to be a brute force approach but I'm stumped on the total # of possible matches. Combinations & permutations I understand (3 out of 10, etc) but this "1 or 2 or (1 and 2) or (2 and 5 and 8)" is giving me a mind block. I do know it's a big number and I'll likely cut back the sampling size.

Any suggestions or clarifications would be very welcome.

Thanks.



Roger Harman


COMMON Certified Application
Developer – ILE RPG on IBM i on Power





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