Splitting the account algorithmically and fairly, then :)

Question

I am trying to solve the following real problem that you might run into:

You had lunch with your friends, and you all agreed to split the bill evenly. Except that when the bill finally arrives, you will find that not everyone has enough money for them (if they are, cheap bastards).

So, some of you pay more than others ... After that, you come home and try to decide, "who should, what amount?".

This, I'm trying to solve algorithmically and fairly :)

It seems so easy at first, but I'm stuck with rounding, and what not, I feel like a complete failure;)

Any ideas on how to handle this?

EDIT: some python code to show my confusion

>>> amounts_paid = [100, 25, 30]
>>> total = sum(amounts_paid)
>>> correct_amount = total / float(len(amounts_paid))
>>> correct_amount
51.666666666666664
>>> diffs = [amnt-correct_amount for amnt in amounts_paid]
>>> diffs
[48.333333333333336, -26.666666666666664, -21.666666666666664]
>>> sum(diffs)
7.1054273576010019e-015

, ?

:)

>>> amounts_paid = [100, 50, 150]
>>> total = sum(amounts_paid)
>>> correct_amount = total / float(len(amounts_paid))
>>> correct_amount
100.0
>>> diffs = [amnt-correct_amount for amnt in amounts_paid]
>>> diffs
[0.0, -50.0, 50.0]
>>> sum(diffs)
0.0

Answer 1

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total_cents = 100 * total;
base_amount = Floor(total_cents / num_people);
cents_short = total_cents - base_amount * num_people;
while (cents_short > 0)
{
    // add one cent to a random person
    cents_short--;
}

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Answer 2

http://www.billmonk.com/

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Answer 3

-, =) . Dev ~ 45 . perl... .

~/sandbox/$ ./bistro_math.pl 
Anna owes Bill 7.57
Anna owes Mike 2.16
John owes Mike 2.62

~/sandbox/$ cat bistro_math.pl 
#!/usr/bin/perl
use strict;
use warnings;

### Dataset.
###    Bill total:  50.00
###    Paid total:  50.00
my @people = (
  { name => 'Bill', bill =>  5.43, paid => 13.00 },
  { name => 'Suzy', bill => 12.00, paid => 12.00 },
  { name => 'John', bill => 10.62, paid =>  8.00 },
  { name => 'Mike', bill =>  9.22, paid => 14.00 },
  { name => 'Anna', bill => 12.73, paid =>  3.00 },
);

### Calculate how much each person owes (or is owed: -/+)
calculate_balances(\@people);

### Tally it all up =)  This algorithm is designed to have bigger lenders
### paid back by the fewest number of people possible (they have the least
### hassle, since they were the most generous!).
sub calculate_balances {
  my $people = shift;

  ### Use two pools    
  my @debtors;
  my @lenders;

  foreach my $person (@$people) {
    ### Ignore people who paid exactly what they owed.
    $person->{owes} = $person->{bill} - $person->{paid};

    push @debtors, $person if ($person->{owes} > 0);
    push @lenders, $person if ($person->{owes} < 0);
  }

  LENDERS: foreach my $lender (@lenders) {
    next if ($lender->{owes} >= 0);

    DEBTORS: foreach my $debtor (@debtors) {
      next if ($debtor->{owes} <= 0);

      my $payment = ($lender->{owes} + $debtor->{owes} < 0) 
        ? abs $debtor->{owes} 
        : abs $lender->{owes};

      $lender->{owes} += $payment;
      $debtor->{owes} -= $payment;

      $debtor->{pays} = [] if (not exists $debtor->{pays});
      print "$debtor->{name} owes $lender->{name} $payment\n";

      next LENDERS if ($lender->{owes} >= 0);
    }
  }
}

exit;
~/sandbox/$ 

Answer 4

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Answer 5

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