Meta·Software Engineer·Technical Phone Screen·Senior

Senior

Apr 2026

Summary

Meta coding round, one problem the whole session. It looked like a grid traversal thing at first but the arithmetic expression constraint made it way more involved than I expected.

Questions Asked (1)

You're given a 2D character grid containing single-digit numbers, '+', and '-'. Find a path through the grid that forms a valid arithmetic expression and returns the maximum possible value. You can start at any digit cell, and must move either entirely right or entirely down (no direction changes). Digits and operators must strictly alternate in the expression.

Algorithms & Data Structures

Author's notes

My first instinct was pure DFS and I started coding before fully thinking through the alternating constraint.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and edge cases first, then propose a dynamic programming solution that processes each row and column independently, tracking the best expression value ending at each cell. Explain how to handle alternating digits and operators, and analyze time and space complexity.

Pro tip: Mention that you would validate the input grid for invalid characters or impossible expressions, and discuss how to extend the solution if diagonal moves were allowed. This shows attention to detail and scalability.

1. Clarify the problem

Ask about grid size, character set, whether expressions can start with an operator, and if negative intermediate values are allowed. Confirm that paths are straight lines (right or down) and that digits and operators must alternate.

2. Define state and recurrence

Define DP state as the maximum value of a valid expression ending at cell (i, j) with a specific parity (last character being digit or operator). Derive transitions from left and top neighbors, ensuring alternation.

3. Handle initialization and base cases

Initialize DP for cells that can start an expression (digit cells) and for cells that are operators (invalid as start). Set unreachable states to negative infinity.

4. Compute and track maximum

Iterate through the grid in row-major order, filling the DP table. Keep track of the global maximum value among all valid expressions ending at any cell.

5. Analyze complexity and edge cases

State time complexity O(R*C) and space O(R*C) or O(C) with optimization. Discuss edge cases like single-cell grids, no valid expressions, and overflow handling.

Key Points to Mention

Dynamic programming with state representing the maximum value ending at each cell and the type of last character (digit or operator).
Alternation constraint: transitions only allowed if the previous character type is opposite to the current cell's type.
Direction constraint: only moves from left or top are considered, ensuring straight paths.
Initialization: only digit cells can start an expression; operator cells cannot be starting points.
Time and space complexity: O(R*C) time, O(R*C) space (can be optimized to O(C) space).
Edge cases: empty grid, no valid expression, negative numbers, and integer overflow.

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