Calculate Inventory Purchases with Buy-X-Get-Y-Free Coupons

Compute the total price of a requested quantity of one inventory item, then support an optional buy-X-get-Y-free coupon for that item. Implement `purchase_total(inventory: string[][], item: string, quantity: int, buy: int, free: int) -> string`. ### Constraints & Assumptions These coupon and error semantics are explicit practice choices where the report is incomplete. Quantity is the total number of units the customer receives, including any free units. For each complete group of `buy + free` units, charge for `buy`; any remaining units are charged up to `buy`. Thus with buy 5/get 2, quantities 3, 6, and 7 pay for 3, 5, and 5 units respectively. No free units are added beyond the requested quantity. - Each inventory row is `[name,stock,unitPrice]`; names are unique nonempty ASCII identifiers. Stock is a nonnegative integer string. Unit price is a nonnegative decimal string with exactly two digits after the point. - At most 1000 inventory rows, stock and quantity at most 1000000, and unit price at most `1000000.00`. Quantity is nonnegative. - `buy == 0` and `free == 0` means no coupon. Otherwise `1 <= buy <= 1000000` and `0 <= free <= 1000000`. - Return `UNKNOWN_ITEM` if the item does not exist. Otherwise return `OUT_OF_STOCK` if quantity exceeds stock. No inventory mutation occurs. - On success return the total with exactly two fractional digits and no currency symbol. Parse and calculate using integer cents, not binary floating point. ### Examples ```text inventory = [["A","50","0.25"],["B","10","1.50"]] item = "A", quantity = 7, buy = 5, free = 2 result = "1.25" ``` For the same item, quantity 3 costs `0.75`; quantity 0 costs `0.00`; quantity 51 returns `OUT_OF_STOCK`. Without a coupon, seven units cost `1.75`. Explain how the function avoids decimal rounding errors and why an incomplete qualifying purchase cannot receive the full advertised free quantity. In an interview, clarify whether quantity denotes paid units or received units before selecting the coupon formula. ```hint Separate units from money First determine how many of the received units are chargeable. Then multiply by an exact integer price and format the final cents. ```