I knew what a bitonic array was but blanked on the cleanest approach under pressure.
First, clarify the definition of a bitonic array and whether it's guaranteed to be bitonic. Then, explain that the most efficient approach is to find the peak element using binary search, then sort each half (which are monotonic) using an efficient sorting algorithm like merge sort or by merging the two sorted halves. Emphasize the time complexity and why this is optimal.
Pro tip: Mention that if the array is already bitonic, you can sort it in O(n) time by merging the increasing and decreasing sequences, but if the array is not guaranteed to be bitonic, you must first check or sort it. Also, discuss edge cases like all increasing or all decreasing arrays.
Ask the interviewer to define a bitonic array and confirm whether the input is guaranteed to be bitonic. Also, clarify if the array can have duplicates and what the expected output is (e.g., sorted in ascending order).
Explain that a bitonic array increases then decreases, so there is a single peak. Use binary search to find the peak element in O(log n) time.
The elements before the peak are in increasing order, and the elements after the peak are in decreasing order. Reverse the second half to make it increasing, then merge the two sorted halves to produce a fully sorted array in O(n) time.
State that the overall time complexity is O(n) because merging two sorted arrays of total size n takes linear time, and finding the peak takes O(log n). Space complexity is O(n) for the merged array, but can be O(1) if sorting in place is allowed and we use a clever in-place merge.
Mention that if the array is not bitonic, you would need to sort it with a general algorithm like quicksort or mergesort (O(n log n)). Also, handle edge cases: empty array, single element, all increasing, all decreasing, and duplicates.
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