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I jumped straight to simulating the original edges and got tangled up.
First, compute each person's net balance by summing credits and debits. Then, use a greedy or backtracking approach to settle the balances with the minimum number of transactions, leveraging the fact that the total sum of balances is zero. Focus on explaining the algorithm and its complexity, and discuss potential optimizations.
Pro tip: Mention that the problem is NP-hard in general (minimum transactions is equivalent to partitioning into zero-sum subsets), so for large inputs a greedy approach is often used, but for small n, backtracking with pruning can find the optimal. This shows awareness of practical constraints.
Iterate through the list of debts and calculate the net balance for each person (credits minus debits). Only people with non-zero balances need to be considered.
Decide between a greedy approach (settle largest creditor with largest debtor) and an optimal backtracking approach. Explain the trade-offs: greedy is O(n log n) but may not be optimal; backtracking is exponential but finds the minimum.
For greedy: repeatedly match the largest positive balance with the largest negative balance, transferring the minimum of the two amounts. For optimal: use DFS/backtracking to try all possible settlements, pruning when the current transaction count exceeds the best found.
Discuss time and space complexity. Handle edge cases: no debts, already settled, large amounts, and floating-point precision if amounts are not integers.
Walk through a small example to verify correctness. Compare greedy vs optimal on a case where greedy fails to show understanding.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.