Find maximum path in grid
Last updated: March 21, 2026
Quick Overview
Given a 2D grid of integers, find the maximum sum of values along any path from the top-left corner to the bottom-right corner, where you can only move either down or right at any point in time. The input is a grid represented as a list of lists, and the output should be a single integer representing the maximum path sum.
NVIDIA
March 21, 202610
7
4,354 solved
Given a 2D grid of integers, find the maximum sum of values along any path from the top-left corner to the bottom-right corner, where you can only move either down or right at any point in time. The input is a grid represented as a list of lists, and the output should be a single integer representing the maximum path sum.
Coding interviews at NVIDIA focus on problem-solving approach as much as the final solution. The interviewer wants to see you break down the problem, consider edge cases, and optimize iteratively. Communication throughout the process is key.
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 modify your solution to handle streaming input?
- How would you test this solution thoroughly?
- How would you parallelize this solution?
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Problem Analysis
This problem is a classic example of dynamic programming. The reason dynamic programming applies here is that we can break down the problem into smaller subproblems: specifically, the maximum path sum...
Approach
- Initialize a 2D array
dpof the same dimensions as the grid, wheredp[i][j]will hold the maximum sum to reach the cell(i, j). - Set
dp[0][0] = grid[0][0], since the maximum sum to reac...
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