Capital One·Software Engineer·Technical Phone Screen·Senior

Senior

Jun 2026

Summary

Capital One applied researcher interview with a grid path problem that looks straightforward until you actually try to implement it. The alternating operator/digit constraint is what makes it interesting, and I definitely underestimated that part going in.

Questions Asked (1)

You're given an m×n grid where each cell holds either an arithmetic operator (+, -) or a digit (0-9). Moving only right or down from the top-left to the bottom-right, find the path that maximizes the value of the resulting arithmetic expression, where valid paths must strictly alternate between digits and operators (no two consecutive digits, no two consecutive operators).

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

My first instinct was just standard DP for max path sum and I started coding that before fully registering the alternating constraint.

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AI HintsAI Generated

Suggested Approach

Model the problem as a dynamic programming problem where the state includes the current cell, the last character type (digit or operator), and the accumulated value. Since the expression must alternate, transitions are constrained by the type of the current cell and the previous type. Maximize the final value at the bottom-right cell.

Pro tip: Clarify with the interviewer whether the expression is evaluated with standard operator precedence or left-to-right; this affects the DP state. Also, consider if negative intermediate values are allowed and how they impact maximization.

1. Understand the problem and constraints

Restate the problem to ensure clarity: grid of digits and operators, move only right/down, alternate types, maximize expression value. Ask about evaluation order and negative numbers.

2. Define the DP state

Define dp[i][j][type][value] or similar, where type indicates whether the last cell was a digit or operator. Since value can be large, consider using a map or optimizing state representation.

3. Determine transitions

From each state, move right or down only if the next cell's type alternates. Update the accumulated value by applying the operator if the next cell is a digit, or storing the operator if the next cell is an operator.

4. Handle base cases and initialization

Start at (0,0). If it's a digit, initialize value; if it's an operator, it's invalid as a starting point (since expression must start with a digit).

5. Compute and return the maximum value

After filling the DP table, the answer is the maximum value among states at (m-1,n-1) where the last cell is a digit (valid expression). If no valid path, return appropriate error.

Key Points to Mention

Dynamic programming with state including position, last type, and accumulated value.
Alternation constraint: transitions only allowed if types differ.
Evaluation order: left-to-right vs. operator precedence; clarify with interviewer.
Handling negative numbers and maximizing expression value.
Time and space complexity: O(m*n*V) where V is number of possible values; discuss optimizations.
Edge cases: no valid path, starting with operator, grid size 1x1.

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