Wiggle Sort II

Wiggle Sort II

What is this problem about?

"Wiggle Sort II" is a stricter version of the wiggle sort problem. The condition is nums[0] < nums[1] > nums[2] < nums[3]... (strictly less/greater, no equality). Furthermore, the input might contain many duplicate elements, making a simple greedy swap approach insufficient because adjacent equal elements would violate the strict inequality.

Why is this asked in interviews?

This is a "Medium" to "Hard" level problem at Microsoft and Meta because it pushes the boundaries of array partitioning. To solve it in O(N) time and O(1) extra space, you need advanced techniques like finding the Median and using a virtual indexing trick. It tests your knowledge of Quickselect and three-way partitioning.

Algorithmic pattern used

The standard pattern involves:

1. Finding the Median of the array (using Quickselect in O(N)).
2. Using a Three-way Partition (similar to the Dutch National Flag problem) to group elements smaller than the median, equal to the median, and larger than the median.
3. Mapping the indices such that larger elements go to odd positions and smaller elements go to even positions.

Example explanation

Array: [1, 1, 2, 2, 3, 3]. Median is 2.

1. Small elements: [1, 1].
2. Median elements: [2, 2].
3. Large elements: [3, 3]. We place Large elements in odd spots (1, 3, 5) and Small elements in even spots (0, 2, 4). Result: [2, 3, 1, 3, 1, 2]. (Note: Exact placement depends on the specific partitioning).

Common mistakes candidates make

• Handling duplicates: Not accounting for cases like [4, 5, 5, 6] where two 5s might end up adjacent if not placed carefully.
• O(N log N) solution: Most candidates sort and then interleave, which is O(N log N). Interviewers will often ask for the O(N) version.
• High space complexity: Using a temporary array to store the result instead of an in-place virtual mapping.

Interview preparation tip

Master the Quickselect algorithm. It is the backbone for finding medians or the Kth largest element in O(N). Also, practice the "Dutch National Flag" partitioning as it appears in many array reordering problems.