DFS on array
Last updated: November 7, 2025
Quick Overview
Implement a depth-first search (DFS) algorithm to traverse a given array, where each element represents the maximum number of steps that can be taken forward from that position. Your task is to determine if it is possible to reach the last index of the array starting from the first index. The function should return a boolean value: true if the last index is reachable, and false otherwise.
NVIDIA
November 7, 202527
10
4,297 solved
Implement a depth-first search (DFS) algorithm to traverse a given array, where each element represents the maximum number of steps that can be taken forward from that position. Your task is to determine if it is possible to reach the last index of the array starting from the first index. The function should return a boolean value: true if the last index is reachable, and false otherwise.
NVIDIA 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
- 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
- What is the worst-case input for your solution?
- How would your solution change if the input was sorted?
- What if the input doesn't fit in memory?
- How would you test this solution thoroughly?
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Practice DSA ProblemsSample Answer
Problem Analysis
The problem requires us to determine if we can reach the last index of an array where each element indicates the maximum steps that can be taken forward from that position. This is a classic case for ...
Approach
- Start from the first index (0) and attempt to jump to each index within the range of the maximum steps allowed by the current index's value.
- For each valid jump, recursively call the DFS functio...
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