Capital One·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

May 2026Remote

Summary

Capital One technical screen, one algorithmic problem the whole time. The problem was dressed up as a grid traversal thing but it's basically just DP with some expression parsing layered on top. Felt manageable once I stopped overthinking the operator handling.

Questions Asked (1)

Given an n x m grid where cells contain digits or +/- operators, find the maximum value of any path from the top-left to the bottom-right cell, moving only right or down. The value of a path is the arithmetic result of reading the digits and operators along it in order.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

I went straight to DFS and it took me an embarrassingly long time to realize memoization on just (row, col) might not be enough depending on how you handle operator state mid-path.

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AI HintsAI Generated

Suggested Approach

Clarify the problem constraints and edge cases, then propose a dynamic programming solution that tracks the maximum value for each cell, considering operator precedence and associativity. Discuss potential pitfalls like negative numbers and division by zero, and compare with alternative approaches like brute-force or Dijkstra-like search.

Pro tip: Mention that you would first confirm whether standard arithmetic precedence applies or if the expression is evaluated strictly left-to-right, as this drastically changes the DP state and solution.

1. Clarify the problem

Ask about operator precedence, associativity, handling of negative numbers, division by zero, and whether the grid can contain multi-digit numbers. Confirm the exact evaluation rules.

2. Define the DP state

Decide what each DP cell represents. If evaluation is left-to-right, dp[i][j] can store the maximum value achievable at cell (i,j). If precedence matters, you may need to track both max and min values or use expression trees.

3. Derive the recurrence

For each cell, consider the two possible predecessors (from top and left). Combine their values with the current cell's operator or digit, and take the maximum. Handle edge cases like starting cell and cells with operators.

4. Analyze complexity and trade-offs

The DP solution runs in O(n*m) time and space. Discuss if space can be optimized to O(m). Compare with brute-force (exponential) and note that DP is optimal for this problem.

5. Test with examples

Walk through a small example to verify the recurrence and edge cases. Mention potential issues like integer overflow and how to handle them.

Key Points to Mention

Dynamic programming approach with state definition and recurrence relation
Handling of operator precedence and associativity (left-to-right vs standard)
Edge cases: negative numbers, division by zero, single row/column grids
Time and space complexity analysis (O(n*m) time, O(n*m) or O(m) space)
Comparison with alternative approaches (brute-force, BFS/Dijkstra) and why DP is better
Potential need to track both maximum and minimum values if negative numbers are present

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