The naive approach works but they clearly wanted something better.
Use the Dutch National Flag algorithm (three-pointer approach) to partition the array into three sections: red, white, and blue. Maintain three pointers: low for the boundary of red, mid for the current element, and high for the boundary of blue. Iterate through the array, swapping elements to place them in the correct section, achieving O(n) time and O(1) space.
Pro tip: Emphasize that this is a one-pass solution with constant space, which is optimal for large datasets. Mention that the algorithm is stable in terms of color grouping but not necessarily preserving original order within colors, which is acceptable here.
Confirm that the array contains only three distinct values (e.g., 0, 1, 2) and that sorting must be in-place. Ask if stability within colors is required (usually not).
Select the Dutch National Flag algorithm (three-pointer approach) as it optimally solves the problem in O(n) time and O(1) space.
Set low = 0, mid = 0, and high = n-1. These pointers divide the array into four regions: red (0 to low-1), white (low to mid-1), unknown (mid to high), and blue (high+1 to n-1).
While mid <= high, examine the element at mid. If it's red (0), swap with low and increment both low and mid. If white (1), just increment mid. If blue (2), swap with high and decrement high (do not increment mid).
After the loop, the array is sorted. Explain that each element is examined at most once, giving O(n) time, and only a few pointers are used, giving O(1) space.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.