Who owes who money optimization

Question

Say you have n people, each who owe each other money. In general it should be possible to reduce the amount of transactions that need to take place. i.e. if X owes Y £4 and

Answer 1

for each debt in debts
  debt.creditor.owed -= debt.amount
  debt.deptor.owed += debt.amount
end

for each person in persons
  if person.owed > 0 then
    deptors.add person
  else if person.owed < 0 then
    creditors.add person
  end
end

deptors.sort_by_owed_desc
creditor.sort_by_owed_asc

for each debtor in deptors
  while debtor.owed > 0
    creditor = creditors.top
    amount = min( debtor.owed, -creditor.owed)
    creditor.owed += amount
    debtor.owed -= amount
    if creditor.owed == 0 then
      creditors.remove_top
    end
    write debtor.name " owes " creditor.name " " amount "€"
  end
end