Started by computing net balances per person which felt right, then tried to explain the backtracking approach.
First, compute each person's net balance by summing all amounts they lent and borrowed. Then, use a greedy or backtracking approach to match the largest creditor with the largest debtor, settling as much as possible in each transaction, to minimize the total number of transactions. This reduces the problem to finding the minimum number of transfers to zero out all balances.
Pro tip: Mention that while the greedy approach is intuitive and often optimal, the problem is NP-hard in general, so for large inputs you might need heuristics or acknowledge the complexity. Also, clarify that the minimum number of transactions is at most n-1 where n is the number of people with non-zero net balance.
Iterate through all loan records and calculate the net amount each person is owed or owes. This simplifies the problem to a list of positive and negative balances that sum to zero.
Separate people into debtors (negative net balance) and creditors (positive net balance). Ignore anyone with zero balance as they are already settled.
Repeatedly match the largest debtor with the largest creditor, transferring the minimum of their absolute amounts. This reduces at least one balance to zero per transaction, minimizing the number of transactions in many cases.
For an exact minimum, use backtracking or dynamic programming to explore all possible matchings, but note that this is exponential. In practice, greedy is often sufficient and efficient.
Discuss time complexity: O(n log n) for sorting balances plus O(n) for matching, where n is the number of people. Mention edge cases like all balances zero, or a single person owing multiple others.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the graph's structure and the specific efficiency bottleneck (e.g., cycle detection, shortest path, or debt settlement). Then propose a combination of algorithmic optimizations (e.g., union-find, topological sort) and domain-specific pruning (e.g., ignoring small debts, netting balances) to reduce the problem size. Finally, discuss trade-offs between exactness and performance, and suggest heuristics like greedy matching or threshold-based pruning.
Pro tip: Emphasize that in real-world systems like Stripe, perfect optimality is often sacrificed for scalability and simplicity—show you understand the business context by proposing heuristics that maintain correctness within acceptable bounds.
Ask about the graph's properties (directed/undirected, weighted, dynamic) and the specific operation that needs to scale (e.g., cycle detection, debt settlement). Identify the current algorithm and its complexity.
Analyze where the current algorithm fails at scale (e.g., O(n^2) or O(n^3) operations). Suggest efficient data structures (e.g., adjacency lists, union-find) and algorithms (e.g., topological sort, strongly connected components) to reduce complexity.
Propose domain-specific pruning: ignore debts below a threshold, net balances to reduce edges, or use greedy matching to settle debts approximately. Discuss how these affect accuracy and performance.
Explain the trade-offs between exactness and scalability, and how you would validate the heuristic's impact (e.g., via simulation or A/B testing). Mention monitoring and fallback strategies.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.