My own accounting python euler problem

[John Machin]

On Nov 8, 8:39 am, vsoler <vicente.so... at gmail.com> wrote:
> In the accounting department I am working for we are from time to time
> confronted to the following problem:
>
> A customer sends us a check for a given amount, but without specifying
> what invoices it cancels. It is up to us to find out which ones the
> payment corresponds to.
>
> For example, say that the customer has the following outstanding
> invoices:  $300, $200, $50; and say that the check is for $250. This
> time it is clear, the customer is paying bills $200 and $50.
>
> However, let's now say that the outstanding invoices are $300, $200,
> $100 and that the check is for $300. In this case there are already
> two possibilities. The customer is paying the $300 invoice or the $200
> and $100. In other words, there is more than one solution to the
> problem.

The problems that you mention are only a SUBSET of the total problem.
Example: oustanding invoices are for 300, 200, and 100 and the cheque
is for 450 -- in general the total of the cheque amounts does not
equal the total of any possible selection of outstanding invoice
amounts.

I would be very surprised if a real accounting department did not
already have a set of business rules for dealing with a problem that
has existed since invoices and cheques were invented.

I would be extremely surprised if a real accounting department could
be persuaded to imagine a subset of their unpaid/underpaid/overpaid
invoice problem as being an instance of the (extended) knapsack
problem :-)