I started by grouping invoices by customer and amount, which felt right, but then I fumbled the FIFO part for a few minutes.
Clarify the problem constraints and edge cases, then propose an efficient algorithm using hash maps to group invoices by customer and amount, and a priority queue or sorted list to select the earliest due date. Walk through the algorithm step-by-step, analyze time and space complexity, and discuss potential optimizations or trade-offs.
Pro tip: Demonstrate awareness of real-world payment matching complexities like partial payments, multiple invoices per payment, and currency differences, and mention how your algorithm could be extended to handle them.
Ask about input sizes, data types, whether amounts are in the same currency, and if there are any constraints on matching (e.g., partial payments, multiple invoices per payment). Confirm that each invoice can be matched at most once and that we need to return unmatched items.
Use a hash map to group invoices by customer ID and amount, storing them in a min-heap keyed by due date for efficient retrieval of the earliest due invoice. Track matched invoices and payments to compute unmatched lists.
Iterate through payments, for each payment look up the customer-amount key in the hash map, pop the earliest due invoice from the heap if available, record the match, and mark both as matched. After processing, collect unmatched payments and invoices.
State time complexity: O(P log I) where P is number of payments and I is max invoices per customer-amount group, due to heap operations. Space complexity: O(I + P). Mention potential optimizations like sorting invoices by due date per group or using a balanced BST.
Walk through a small example, including cases with no matches, multiple matches, and ties in due dates. Discuss how to handle ties (e.g., any deterministic rule) and ensure the algorithm returns correct unmatched lists.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.