MathWorks·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

MathWorks software engineer interview with a meaty constraint-satisfaction problem that required both a clean implementation and a real discussion of the underlying theory. Not your typical coding round.

Questions Asked (1)

You have a rectangular grid of R rows and C columns. A set of named entities must each occupy exactly one distinct cell. Relational clues constrain their placement (e.g. 'Alice is directly above Bob', 'Carol is in row 3'). Given the grid, entities, clues, and a target entity P, determine whether P's position is uniquely determined. If yes, return the (row, column). If not, report that no unique solution exists. Also discuss your modeling approach, constraint propagation, search strategy, and how complexity scales.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

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Suggested Approach

Model the problem as a Constraint Satisfaction Problem (CSP) with variables for each entity's row and column, and constraints from the clues. Use constraint propagation (e.g., arc consistency) to prune domains, then perform backtracking search to find all solutions. If all solutions agree on P's position, it's unique; otherwise, report no unique solution.

Pro tip: Emphasize the importance of early detection of inconsistency and the use of heuristics like MRV (Minimum Remaining Values) to make search efficient. Also, mention that for uniqueness, you need to find all solutions or prove that only one exists, which can be done by searching for a second solution after finding the first.

1. Model as CSP

Define variables for each entity's row and column, with domains 1..R and 1..C. Translate each clue into constraints (e.g., 'Alice directly above Bob' means row_Alice = row_Bob - 1 and col_Alice = col_Bob).

2. Constraint Propagation

Apply arc consistency (AC-3) to prune domains by removing values that cannot satisfy constraints. For example, if Carol is in row 3, remove row 3 from all other entities' domains.

3. Search Strategy

Use backtracking search with MRV and degree heuristics to assign values. After finding a solution, continue search to find a second solution; if found, P's position is not unique.

4. Uniqueness Check

If the search completes with exactly one solution, return P's position. If multiple solutions exist, report no unique solution. If no solution, report inconsistency.

5. Complexity Analysis

Discuss worst-case exponential time due to NP-hardness, but note that constraint propagation and heuristics often make it efficient for typical puzzle sizes. Space complexity is linear in the number of variables.

Key Points to Mention

CSP formulation with variables, domains, and constraints
Constraint propagation techniques like AC-3 and forward checking
Backtracking search with MRV and degree heuristics
Uniqueness requires finding all solutions or proving only one exists
Complexity: NP-hard in general, but practical for small grids
Handling of relational clues (e.g., directly above, same row, etc.)

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