Who owes whom (design Splitwise)

Paise not decimals, three splits behind one call, five balances that add to zero, and 9 payments cut to 4.

Before you start. Five short recaps.

• An invariant (The object that keeps its own rules (encapsulation and invariants)) is a sentence that must stay true, here “all balances add up to zero”.
• A strategy (Swap the rule, keep the class (Strategy and Factory)) is several interchangeable rules for one job, here the ways to split a bill, each its own class answering the same call.
• A ledger (The Two Ledgers Must Agree (Distributed Transactions)) is a list of entries you only add to and never erase.
• A class is a blueprint for objects.
• A low-level design round is one interview hour spent writing the classes inside one program.