Dynamic Programming on array
Last updated: November 10, 2025
Quick Overview
Given an array of integers, write a function to find the maximum sum of non-adjacent elements using dynamic programming. The function should take an array as input and return an integer representing the maximum sum. Ensure your solution has a time complexity of O(n).
HashiCorp
November 10, 202538
12
1,772 solved
Given an array of integers, write a function to find the maximum sum of non-adjacent elements using dynamic programming. The function should take an array as input and return an integer representing the maximum sum. Ensure your solution has a time complexity of O(n).
HashiCorp uses this problem in the Take-home Project 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?
- What happens if the input contains duplicates?
- How would your solution change if the input was sorted?
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Practice DSA ProblemsSample Answer
Problem Analysis
This problem can be classified under dynamic programming because we need to make optimal decisions based on previously computed results. The specific pattern here is the 'maximum sum of non-adjacent e...
Approach
We will use a dynamic programming approach to solve this problem. The idea is to maintain two states: incl (the maximum sum including the current element) and excl (the maximum sum excluding the c...
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