Squarepoint·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Squarepoint Data Scientist interview with a greedy/algorithmic problem that looks deceptively simple but has some real edge cases to think through. One question, coding focused, no behavioral stuff from what I can tell.

Questions Asked (1)

A store has n products each with some stock quantity. Customers buy one unit at a time, and the price paid equals the current stock level before the sale (so stock of 5 means the customer pays 5, then stock drops to 4). Given m customers, figure out how to assign sales to maximize total revenue. What's an efficient algorithm for large inputs?

Algorithms & Data Structures

Author's notes

The greedy insight is pretty clean once you see it: always sell from the product with the highest current stock, because that gives you the biggest price right now.

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AI HintsAI Generated

Suggested Approach

Model the problem as selecting the top m marginal revenues from all possible sales across products, where each product's marginal revenues form a decreasing sequence (stock, stock-1, ..., 1). Use a max-heap to efficiently extract the m largest values, updating each product's next marginal revenue after each sale. This greedy approach is optimal because marginal revenues are non-increasing.

Pro tip: Emphasize that the greedy choice is optimal due to the non-increasing marginal revenues, and mention that for very large m, a binary search on the price threshold can achieve O(n log max_stock) time, which is more efficient than heap-based O(m log n) when m is huge.

1. Understand the problem and marginal revenue

Recognize that each sale from a product yields revenue equal to its current stock, and after the sale, the next sale from that product yields one less. Thus, each product generates a sequence of marginal revenues: stock, stock-1, ..., 1.

2. Formulate as top-m selection

The total revenue from m sales is the sum of the m largest marginal revenues across all products. Since each product's sequence is sorted in descending order, we need to merge these sequences and pick the top m.

3. Choose an efficient algorithm

Use a max-heap to store the next available marginal revenue for each product. Repeatedly extract the maximum, add it to revenue, and push the next marginal revenue from that product (if any). This runs in O((n + m) log n) time.

4. Optimize for large inputs

If m is very large (e.g., up to 10^9), use binary search to find a threshold price p such that the number of marginal revenues >= p is at least m. Then compute the sum of all revenues > p and add the remaining needed revenues at price p. This achieves O(n log max_stock) time.

5. Analyze complexity and edge cases

Discuss time and space complexity, and handle edge cases such as m exceeding total stock (then sell all units) or n=0. Also mention that the greedy approach is optimal because marginal revenues are non-increasing.

Key Points to Mention

Marginal revenue per product forms a decreasing sequence: stock, stock-1, ..., 1.
The problem reduces to selecting the top m values from these sequences.
Greedy algorithm using a max-heap is optimal due to non-increasing marginal revenues.
Time complexity: O((n + m) log n) with heap; can be improved to O(n log max_stock) using binary search on price threshold.
For large m, binary search on the price threshold avoids iterating m times.
Edge cases: m >= total stock (sell all), n=0, or stock=0.

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