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

This post got me thinking and searching...Apparently, this sort of algorithm is not simple and is the subject of a number of patent applications.
It has the tinge of a fun puzzle. But it is evidently not trivial.

https://www.legionpatent.com/patents/8103561/
http://www.google.com.ar/patents/US8103561


Paul Therrien
Andeco Software, LLC
225-229-2491
paultherrien@xxxxxxxxxxxxxxxxxx
www.andecosoftware.com

-----Original Message-----
From: RPG400-L [mailto:rpg400-l-bounces@xxxxxxxxxxxx] On Behalf Of John McKee
Sent: Monday, September 29, 2014 9:50 PM
To: RPG programming on the IBM i (AS/400 and iSeries)
Subject: Re: Combinations & Permutations..... sort of

I believe you are potentially counting combinations twice. Check this page:

http://www.mathwords.com/c/combination_formula.htm

Picking invoices 1 and 4 is the same as picking invoices 4 and 1.

Maybe I am misunderstanding. Wouldn't be the first time.

John McKee

On Mon, Sep 29, 2014 at 8:02 PM, Roger Harman <roger.harman@xxxxxxxxxxx>
wrote:

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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