LinkedIn·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

LinkedIn SWE interview with a 2D matrix problem requiring both point updates and range sum queries. Pretty classic data structures territory but the efficiency requirement is what makes it interesting.

Questions Asked (1)

Given a 2D integer matrix and a series of queries, implement a system that handles two operations efficiently: updating a single cell's value, and returning the sum of all elements within a rectangular submatrix defined by half-open row and column ranges.

Algorithms & Data StructuresSystem Design

Author's notes

The naive approach works fine for small inputs but you know they're looking for something smarter.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and requirements, then propose a solution using a 2D Binary Indexed Tree (Fenwick Tree) to support point updates and rectangle sum queries in O(log n * log m) time. Discuss the trade-offs between this approach and a naive method, and explain how to handle half-open ranges by converting them to inclusive indices.

Pro tip: Mention that you would first consider the constraints: if updates are infrequent, a 2D prefix sum array with O(1) queries and O(n*m) updates might be acceptable, but for balanced performance, a 2D BIT is optimal. Also, note that half-open ranges [r1, r2) and [c1, c2) can be handled by subtracting sums at r2-1 and c2-1.

1. Clarify requirements and constraints

Ask about the matrix size, number of queries, frequency of updates vs. queries, and whether the matrix is static or dynamic. Confirm the half-open range semantics.

2. Discuss naive approaches and their trade-offs

Explain that a brute-force update is O(1) but query is O(n*m), while a prefix sum array gives O(1) query but O(n*m) update. Highlight the need for a balanced data structure.

3. Propose an efficient data structure

Introduce a 2D Binary Indexed Tree (Fenwick Tree) that supports point updates and prefix sum queries in O(log n * log m). Explain how to compute rectangle sums using inclusion-exclusion.

4. Detail the implementation

Describe how to initialize the 2D BIT from the matrix, update a cell by adding the delta, and query the sum over a rectangle using four prefix sum queries. Handle half-open ranges by adjusting indices.

5. Analyze complexity and edge cases

State time complexity: O(log n * log m) per update and query, space O(n*m). Discuss edge cases like empty ranges, out-of-bounds indices, and large values requiring 64-bit integers.

Key Points to Mention

2D Binary Indexed Tree (Fenwick Tree) for point updates and range sum queries
Inclusion-exclusion principle for rectangle sum: sum(r2, c2) - sum(r1, c2) - sum(r2, c1) + sum(r1, c1)
Half-open ranges [r1, r2) and [c1, c2) mean rows r1 to r2-1 and columns c1 to c2-1
Time complexity: O(log n * log m) per operation, space O(n*m)
Alternative: 2D Segment Tree, but BIT is simpler and more memory-efficient
Handling large sums with 64-bit integers to avoid overflow

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.