🎉 init

shared/utils/balances.ts

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+import type { Expense, Participant, ParticipantId, Settlement } from '../types'
+import { computeSplit } from './split'
+
+export function calculateBalances(
+  participants: Participant[],
+  expenses: Expense[],
+): { netBalances: Record<ParticipantId, number>, settlements: Settlement[] } {
+  const netBalances: Record<ParticipantId, number> = {}
+  for (const participant of participants) {
+    netBalances[participant.id] = 0
+  }
+
+  // A settlement payment (fromId pays toId) is folded in as a regular
+  // expense: payerId = fromId, participantIds = [toId]. The math is
+  // identical to a one-person split, so no separate handling is needed here.
+  for (const expense of expenses) {
+    netBalances[expense.payerId] = (netBalances[expense.payerId] ?? 0) + expense.amountCents
+    const shares = computeSplit(expense.amountCents, expense.participantIds)
+    for (const [participantId, share] of Object.entries(shares)) {
+      const id = Number(participantId)
+      netBalances[id] = (netBalances[id] ?? 0) - share
+    }
+  }
+
+  const settlements = simplifyDebts(netBalances)
+
+  return { netBalances, settlements }
+}
+
+function simplifyDebts(netBalances: Record<ParticipantId, number>): Settlement[] {
+  const creditors: { id: ParticipantId, amount: number }[] = []
+  const debtors: { id: ParticipantId, amount: number }[] = []
+
+  for (const [id, amount] of Object.entries(netBalances)) {
+    if (amount > 0) creditors.push({ id: Number(id), amount })
+    else if (amount < 0) debtors.push({ id: Number(id), amount: -amount })
+  }
+
+  creditors.sort((a, b) => b.amount - a.amount)
+  debtors.sort((a, b) => b.amount - a.amount)
+
+  const settlements: Settlement[] = []
+  let ci = 0
+  let di = 0
+
+  while (ci < creditors.length && di < debtors.length) {
+    const creditor = creditors[ci]
+    const debtor = debtors[di]
+    const amount = Math.min(creditor.amount, debtor.amount)
+
+    if (amount > 0) {
+      settlements.push({ fromId: debtor.id, toId: creditor.id, amountCents: amount })
+    }
+
+    creditor.amount -= amount
+    debtor.amount -= amount
+
+    if (creditor.amount === 0) ci++
+    if (debtor.amount === 0) di++
+  }
+
+  return settlements
+}