Find maximum path in matrix
Last updated: December 26, 2025
Quick Overview
Given a matrix of integers, find the maximum path sum from the top-left corner to the bottom-right corner, where you can only move down or right at any point in time. Implement an efficient solution using Dynamic Programming to compute the maximum path sum, and return the resulting value. The input will be a 2D array of integers, and the output will be a single integer representing the maximum path sum.
Databricks
December 26, 202538
12
2,967 solved
Given a matrix of integers, find the maximum path sum from the top-left corner to the bottom-right corner, where you can only move down or right at any point in time. Implement an efficient solution using Dynamic Programming to compute the maximum path sum, and return the resulting value. The input will be a 2D array of integers, and the output will be a single integer representing the maximum path sum.
Coding interviews at Databricks 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
- Quickly identify the optimal approach and its theoretical basis
- Handle complex algorithm design with multiple interacting components
- Write concise, elegant code under time pressure
- Prove correctness of your approach and discuss alternative solutions
- Optimize beyond the obvious: discuss constant factor improvements
- Address follow-up variations and explain how the solution generalizes
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 test this solution thoroughly?
- How would you parallelize this solution?
- What happens if the input contains duplicates?
- Can you solve this in a single pass?
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Problem Analysis
To find the maximum path sum in a matrix from the top-left corner to the bottom-right corner, we can leverage the dynamic programming (DP) approach. The reason the DP method is applicable here is that...
Approach
- Initialize a DP Table: Create a 2D list
dpof the same dimensions as the matrix, wheredp[i][j]will store the maximum path sum to the cell(i, j). - Base Case: Set the starting po...
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