Find maximum path in grid
Last updated: September 20, 2025
Quick Overview
Given a 2D grid of integers, where each cell represents a cost to traverse, find the maximum path sum from the top-left corner to the bottom-right corner of the grid. You can only move either down or right at any point in time. Return the maximum path sum as an integer.
Capital One
September 20, 202586
6
469 solved
Given a 2D grid of integers, where each cell represents a cost to traverse, find the maximum path sum from the top-left corner to the bottom-right corner of the grid. You can only move either down or right at any point in time. Return the maximum path sum as an integer.
This coding problem is frequently asked during Phone Screen at Capital One. The interviewer is testing your ability to translate a problem into clean, working code while discussing time and space complexity. Capital One expects candidates to write production-quality code, not just solve the puzzle.
What the Interviewer Expects
- Recognize the underlying problem pattern (sliding window, two pointers, BFS/DFS, etc.)
- Discuss multiple approaches and trade-offs before coding
- Implement an optimal solution with clean, production-quality code
- Handle all edge cases including boundary conditions and invalid input
- Optimize both time and space complexity with clear justification
- Test your solution systematically with well-chosen examples
Key Topics to Cover
How to Approach This
- Clarify input constraints and edge cases before writing code.
- Walk through your approach verbally and confirm with the interviewer before coding.
- Start with a brute force solution, then optimize. Mention time and space complexity.
- Test your solution with examples, including edge cases like empty input or duplicates.
- Consider common patterns: sliding window, two pointers, hash map, BFS/DFS, dynamic programming.
Possible Follow-up Questions
- How would you parallelize this solution?
- How would you test this solution thoroughly?
- Can you solve this in a single pass?
- What happens if the input contains duplicates?
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Problem Analysis
This problem can be effectively solved using dynamic programming, as it involves finding an optimal solution by breaking down the problem into simpler subproblems. The key observation is that from any...
Approach
- Initialize a DP table of the same dimensions as the grid. This table will store the maximum path sum to each cell.
- Set the starting cell (0, 0) in the DP table to be the same as the grid...
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