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I got the basic structure pretty fast: compute each person's net balance by adding what they paid and subtracting their share of each transaction.
Start by clarifying the problem: compute each person's net balance by summing what they paid minus their share of each transaction. Then, to minimize transfers, use a greedy two-pointer approach on sorted balances (creditors and debtors) to settle debts, or if any valid set is acceptable, simply match each debtor with a creditor. Discuss trade-offs between minimal transfers (NP-hard in general) and practical greedy solutions.
Pro tip: Mention that minimizing the number of transactions is equivalent to the NP-hard partition problem, so in practice a greedy approach that settles largest debts first is optimal enough and runs in O(n log n). This shows you understand both theory and real-world engineering constraints.
Ask whether the goal is minimal transfers or any valid set, and confirm that all amounts are in the same currency and divisible to the smallest unit. Also clarify if a person can both owe and be owed (net balance).
For each transaction, add the total amount to the payer's balance and subtract each participant's equal share. After processing all transactions, each person has a net balance (positive = should receive, negative = should pay).
If minimal transfers are required, note that it's NP-hard and propose a greedy heuristic: sort balances, then repeatedly match the largest creditor with the largest debtor. If any valid set is fine, simply pair each debtor with a creditor until all balances are zero.
Write code to compute balances and generate transfers. Handle floating-point precision by using integers (e.g., cents) and ensure the sum of balances is zero. Consider empty transactions or single-person groups.
Discuss time complexity: O(T + P log P) for sorting balances, where T is transactions and P is people. Mention that the greedy approach may not yield the absolute minimum transfers but is efficient and practical.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.