I proposed a data structure combining a dynamic array and a hash map. The array would store the values, while the hash map would keep track of the indices. I explained how the insert operation could add a new element to the end of the array and update the hash map, achieving O(1) time complexity for insert and delete operations. However, the delete operation required careful handling to maintain O(1) performance during element removal, which involves swapping the element to be deleted with the last element before removing it.

The interviewer seemed engaged initially and asked follow-up questions about handling duplicate entries and resizing the array. I clarified how I would maintain a count of duplicates in the hash map, which led to further queries about edge cases and memory considerations. Although I felt confident in articulating my approach, I stumbled a bit on the specifics of resizing the array, which may have impacted their perception of my practical implementation skills. Overall, I sensed that my theoretical understanding was solid, but the practical execution fell short in some areas.