Find minimum cost in grid
Last updated: October 17, 2025
Quick Overview
Given a 2D grid where each cell contains a cost value, write a function to find the minimum cost to travel from the top-left corner to the bottom-right corner, moving only down or right. The function should return the minimum total cost as an integer. The grid will be represented as a list of lists of integers.
Morgan Stanley
October 17, 20255
14
4,148 solved
Given a 2D grid where each cell contains a cost value, write a function to find the minimum cost to travel from the top-left corner to the bottom-right corner, moving only down or right. The function should return the minimum total cost as an integer. The grid will be represented as a list of lists of integers.
Morgan Stanley uses this problem in the Phone Screen to evaluate your algorithmic thinking. They expect you to discuss multiple approaches, analyze trade-offs between them, and implement the optimal solution with clean, readable code.
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 test this solution thoroughly?
- Can you solve this iteratively instead of recursively (or vice versa)?
- How would you modify your solution to handle streaming input?
- What is the worst-case input for your solution?
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Practice DSA ProblemsSample Answer
Problem Analysis
The problem requires finding the minimum cost path in a 2D grid from the top-left corner to the bottom-right corner, moving only down or right. This scenario is best approached using Dynamic Programmi...
Approach
We will create a DP table where each cell (i, j) represents the minimum cost to reach that cell. The steps are as follows:
- Initialize a DP table of the same size as the grid.
- Set the starting po...
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