Wiggle Sort II
Given an unsorted array `nums`, reorder it such that $nums[0] < nums[1] > nums[2] < nums[3] \dots$. Must be solved in $O(n)$ time with $O(1)$ extra space.
Why Interviewers Ask This
Microsoft asks Wiggle Sort II to evaluate a candidate's ability to handle complex in-place array manipulations under strict constraints. This problem specifically tests mastery of partitioning algorithms, understanding of index mapping logic, and the capacity to optimize for O(n) time and O(1) space simultaneously. It reveals whether an engineer can balance theoretical correctness with practical memory efficiency.
How to Answer This Question
Structure your solution using a three-phase logical framework: Analysis, Partitioning, and Reordering. First, analyze the constraints; explicitly state that sorting takes O(n log n), so you must find a linear-time alternative. Second, implement a median-finding algorithm like Quickselect to identify the pivot element in O(n) average time without modifying the array order globally. Third, execute the critical reordering step using a virtual index mapping technique. Instead of creating a new array, map the sorted positions to specific indices in the original array (e.g., placing larger elements at odd indices and smaller ones at even indices) using a three-way partition or a specific swap strategy. Finally, validate edge cases where duplicates exist, ensuring the wiggle property holds strictly. Throughout, verbalize your thought process regarding why standard sorting fails and how your chosen approach satisfies Microsoft's strict performance requirements.
Key Points to Cover
- Explicitly rejecting standard sorting due to O(n log n) complexity
- Correctly implementing Quickselect to find the median in O(n)
- Using virtual index mapping to achieve O(1) space complexity
- Handling duplicate elements to prevent equality violations in the wiggle pattern
- Verbalizing the trade-off between algorithmic complexity and memory usage
Sample Answer
To solve Wiggle Sort II within O(n) time and O(1) space, we cannot simply sort the array, as that would violate the time complexity constraint. My approach begins by finding the median element of the unsorted array. I wi…
Common Mistakes to Avoid
- Attempting to sort the array first, which violates the O(n) time requirement
- Creating a new auxiliary array to store the result, failing the O(1) space constraint
- Ignoring edge cases where multiple identical median values exist, causing adjacent duplicates
- Failing to explain the mathematical logic behind the virtual index mapping during the interview
Sound confident on this question in 5 minutes
Answer once and get a 30-second AI critique of your structure, content, and delivery. First attempt is free — no signup needed.