The naive approach jumps to mind immediately and that's the problem.
Use two separate binary searches: one to find the leftmost occurrence of the target and another to find the rightmost occurrence. Modify the standard binary search to continue searching even after finding the target, adjusting the search space based on whether you're looking for the first or last position. This ensures O(log n) time complexity.
Pro tip: Clarify with the interviewer whether the array can contain duplicates and if the target is guaranteed to be present. Also, mention that you can optimize by first finding any occurrence and then expanding, but that would be O(n) in the worst case, so the two-binary-search approach is optimal.
Confirm the array is sorted, may contain duplicates, and the target may or may not be present. Discuss edge cases like empty array, target smaller than all elements, or larger than all elements.
Modify binary search to find the leftmost index: when nums[mid] == target, record the index and continue searching in the left half (high = mid - 1) to find an earlier occurrence.
Similarly, modify binary search to find the rightmost index: when nums[mid] == target, record the index and continue searching in the right half (low = mid + 1) to find a later occurrence.
Implement both searches, initializing result to [-1, -1]. If the first search fails, return [-1, -1] immediately; otherwise, run the second search and return the results.
State that each binary search takes O(log n) time, so overall O(log n) time and O(1) space. Walk through test cases like target at boundaries, single element, and duplicates.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.