My first instinct was to just count the zeros, then fill.
Clarify that the array contains only 0s and 1s, then propose a two-pointer or counting approach to achieve O(n) time and O(1) space. Walk through the algorithm step-by-step, analyze complexity, and discuss edge cases.
Pro tip: Mention that this is a special case of the Dutch National Flag problem (with only two values) and that the two-pointer approach is optimal for in-place sorting. Also, note that counting sort is simpler but requires two passes, while two-pointer does it in one pass.
Confirm the array contains only 0s and 1s, and ask whether in-place sorting is required and if extra space is allowed. This shows attention to detail and avoids misinterpretation.
Select either the two-pointer technique (one pass, in-place) or counting sort (two passes, O(1) space). Explain why the chosen method meets linear time and space constraints.
For two-pointer: initialize left at 0 and right at n-1; while left < right, move left until a 1 is found, move right until a 0 is found, then swap. For counting: count zeros, then overwrite the array with zeros followed by ones.
State time complexity O(n) and space O(1). Discuss edge cases: empty array, all zeros, all ones, already sorted, and large input.
Run through a small example like [1,0,1,0,0] to demonstrate correctness, and optionally mention potential pitfalls like infinite loops if pointers are not updated correctly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.