Maximize revenue from inventory sales
Company: Squarepoint
Role: Data Scientist
Category: Coding & Algorithms
Difficulty: medium
Interview Round: Online Assessment
### Problem
A store has `n` different products. For each product `i` (0-indexed), you are given an integer `quantity[i]` representing how many units of that product are currently in stock.
The store will serve `m` customers. Each customer buys exactly one unit of some product, subject to availability (you cannot sell a product whose stock is 0).
**Pricing rule:**
- When a customer buys one unit of product `i`, the price they pay is equal to the **current** remaining stock of product `i` *before* the purchase.
- After the purchase, the stock of product `i` decreases by 1 (i.e., `quantity[i]--`).
- Thus, if product `i` has stock 5 when a customer arrives and they buy it, that customer pays 5, and the stock becomes 4 for future customers.
The store can choose, for each customer, which product to sell (among those with positive stock) in order to maximize total revenue.
If `m` is larger than the total number of units in stock, then at most the total stock many customers can be served; the remaining customers simply cannot buy anything.
### Input
- An integer `n` – the number of different products.
- An array `quantity` of length `n`, where `quantity[i]` is a non-negative integer representing the initial stock of product `i`.
- An integer `m` – the number of customers, where each customer buys at most one unit as described.
### Output
Return a single integer: the **maximum total revenue** the store can obtain by appropriately choosing which product to sell to each customer.
You should design an efficient algorithm suitable for large `n`, `m`, and quantities.
### Example
Suppose:
- `n = 2`
- `quantity = [2, 3]`
- `m = 3`
One optimal sequence of sales is:
- Customer 1 buys from product 1 (stock 3) → pays 3, stock becomes `[2, 2]`.
- Customer 2 buys from product 0 (stock 2) → pays 2, stock becomes `[1, 2]`.
- Customer 3 buys from product 1 (stock 2) → pays 2, stock becomes `[1, 1]`.
Total revenue = `3 + 2 + 2 = 7`, which is optimal.
Implement a function that computes this maximum revenue.
Overview: This question evaluates algorithmic problem-solving and optimization competencies focused on dynamic resource allocation, revenue maximization, and designing efficient solutions that scale with large n, m, and quantities.
Read the full Squarepoint Data Scientist interview experience this question came from
Each sale from a product earns its current stock before decrementing. Serve at most m customers and choose products to maximize total revenue. Return the maximum revenue.
Constraints
- quantity values are non-negative
- If m exceeds total stock, sell only available units
Examples
Input: ([2, 3], 3)
Expected Output: 7
Input: ([5], 10)
Expected Output: 15
Hints
- Always sell from a product with the current highest stock.
- Batch equal price levels instead of simulating every customer.