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Knew this one from grinding leetcode but still fumbled the opening explanation.
Model the problem as a graph where each person is a node and debts are edges, then compute each person's net balance. The goal is to minimize transactions by greedily matching the largest creditor with the largest debtor, which is a common heuristic for the debt settlement problem.
Pro tip: Acknowledge that the greedy approach is not always optimal (the problem is NP-hard), but it works well in practice and is what most interviewers expect. Mention that for small groups, you could use backtracking or dynamic programming to find the exact minimum.
Ask if the goal is to minimize the number of transactions or the total amount transferred, and confirm that all debts are to be settled exactly.
For each person, calculate the net amount they owe or are owed by summing all their transactions. This reduces the problem to settling these net balances.
Create two lists: one for people with positive net balance (creditors) and one for negative net balance (debtors).
Repeatedly match the largest creditor with the largest debtor, settling the smaller of the two amounts, and update their balances. Count each match as one transaction.
Discuss the time complexity (O(n log n) with sorting) and note that while greedy is not always optimal, it often yields the minimum or near-minimum number of transactions.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.