Maximize Items

Maximize Items

What is this problem about?

The Maximize Items problem is a Database/SQL challenge. You are managing a warehouse with a specific total square footage. You have a table containing item categories (e.g., 'prime_eligible' and 'not_prime'), the square footage each item requires, and the total number of items available. You are mandated to fill the warehouse by strictly prioritizing 'prime_eligible' items first. Once you have stocked as many prime items as possible, you must use the remaining square footage to stock 'not_prime' items. Your query must return the item category and the total number of items stocked.

Why is this asked in interviews?

This question is widely used by companies like Amazon to test a candidate's ability to perform sequential allocation using SQL. It evaluates your skills with Common Table Expressions (CTEs), aggregate SUM() functions, and most importantly, using the remainder (modulo) or division arithmetic to carry over available resources from one aggregate calculation to the next.

Algorithmic pattern used

This problem relies on Chained CTEs and Math Operations.

1. CTE 1 (Prime Allocation): Calculate the total square footage required for exactly one full batch (one of every item) of 'prime_eligible' goods. Divide the total warehouse size by this batch size to see how many full batches fit. Multiply this by the total prime items to get the total prime items stocked.
2. CTE 2 (Non-Prime Allocation): Calculate the remainder square footage using the modulo operator against the total warehouse size. Use this remaining space to calculate how many 'not_prime' items can be stocked using the same division logic.
3. Final Query: UNION ALL the results of the two CTEs into the final output format.

Example explanation

Warehouse size: 500,000 sq ft. Prime items: 10 items. Total size for 1 of each = 1,000 sq ft. Total size for all 10 = 10,000 sq ft. Not Prime items: 5 items. Total size for 1 of each = 500 sq ft.

Let's assume the warehouse holds "batches". If the total prime volume is 10,000, we can fit 50 batches of ALL prime items into the 500,000 sq ft warehouse ($50 \times 10,000 = 500,000$). Remaining space = $500,000 \pmod{10,000} = 0$. Since remainder is 0, we can fit exactly 0 non-prime items. Result: 500 prime items (50 batches * 10 items), 0 non-prime items.

Common mistakes candidates make

A very common mistake is trying to allocate items individually rather than by "batches". SQL is not a procedural language; you cannot write a WHILE loop to place items one by one. You must use division (FLOOR(TotalSpace / PrimeBatchSize)) to mathematically calculate how many fit instantly. Another mistake is joining the prime and non-prime tables incorrectly, resulting in Cartesian products that inflate the square footage sums.

Interview preparation tip

When tackling sequential allocation SQL problems like Maximize Items, always utilize CTEs (WITH clauses) to store intermediate mathematical results. Calculate the Prime space used, then pass (Total_Space - Prime_Space_Used) into the next CTE for Non-Prime calculations. Keep the logic modular and sequential.