Remove Zero Sum Consecutive Nodes from Linked List
Given the head of a linked list, repeatedly delete consecutive sequences of nodes that sum to 0 until there are no such sequences. Use a Hash Map to track cumulative sums.
Why Interviewers Ask This
Amazon asks this question to evaluate a candidate's mastery of prefix sums and hash map utilization for optimizing linked list traversals. It tests the ability to identify redundant computations and solve complex in-place manipulation problems with O(N) time complexity, reflecting their leadership principle of 'Insist on the Highest Standards' through algorithmic efficiency.
How to Answer This Question
1. Clarify the problem constraints: confirm if the list can be modified in-place or if a new list is required, and verify edge cases like null heads or lists containing only zeros.
2. Propose the optimal strategy: Explain that a brute-force approach checking every subarray is O(N^2), but using a cumulative sum hash map allows us to detect zero-sum sequences in a single pass.
3. Detail the two-pass logic: Describe how the first pass populates the map with running sums and nodes, while the second pass reconstructs the list by skipping nodes between duplicate sums.
4. Discuss space-time trade-offs: Explicitly state the O(N) time and O(N) space complexity, noting why this is acceptable for Amazon's scale.
5. Walk through a dry run: Use a concrete example like [1, -1, 3] to demonstrate how the cumulative sum resets and how pointers are adjusted to remove the sequence.
Key Points to Cover
- Explicitly mention the O(N) time complexity requirement expected by Amazon engineers
- Demonstrate understanding of how cumulative sums mathematically prove a zero-sum subarray
- Address the specific challenge of modifying the linked list structure during traversal
- Propose a dummy head node to simplify edge case handling for head removal
- Explain the logic clearly rather than just writing code, showing architectural thinking
Sample Answer
To solve this efficiently, I would leverage the concept of prefix sums combined with a hash map to achieve O(N) time complexity. The core insight is that if we encounter the same cumulative sum at two different nodes, th…
Common Mistakes to Avoid
- Attempting a brute-force O(N^2) solution by checking every possible subarray, which fails performance standards
- Failing to use a dummy node, leading to complex pointer logic when the head of the list needs to be removed
- Not considering that removing a zero-sum sequence might create a new zero-sum sequence requiring iteration
- Confusing the hash map key as the node value instead of the cumulative running sum
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