Payback

Settles debts within a group with the fewest number of transactions.

Background

For a group of $n$ debtors and creditors the worst case for the minimum number of transactions to balance the debts is $n-1$ where each person pays the next person the amount they owe and the last person pays nobody.

The number of transactions can be reduced if the group can be partitioned into multiple groups such that each group's total debt is zero. Then the number of transactions required is $n-m$ where $m$ is the number of groups.

Payback finds the group partitionings with the most partitions to minimise the number of transactions required to settle all debts.