Settling up in the fewest payments.
A group's expenses paid by different people, settled in the fewest payments, found exactly for small groups, or by paying back only who paid for you.
By Suraj Kumar3 min read
After a trip, everyone owes everyone a little. The fewest payments that settle it can be found exactly.
Who owes whom.
Each expense adds to the payer's balance and takes each sharer's share from theirs; what is left says who is owed and who owes.
The fewest payments.
A group can always be settled in one payment fewer than the people with a balance, but sometimes in fewer still, when it splits into smaller groups that settle among themselves. Finding that is hard in general (Verhoeff, 2004); for up to 14 people the page tries every way and finds the fewest exactly, and past that it says its answer may not be the fewest.
Paying back directly.
Some groups prefer that nobody pays someone they did not owe. Turn on Only pay back who paid for you; it can take more payments.
Further reading
Topics: expense splitter · settle up · fewest payments · split trip costs · roommate expenses
A little less theory. A little more doing.
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