Time complexity to get min elements from max-heap

Question

I was asked in an interview:

What is the best time complexity in getting the min element(s) from a max-heap?

I replied as O(1) a

Answer 1

Best complexity is O(n).

Rather than, not wrote here a lot about that,
The min element in MAX-heap, and the MAX element in min-heap
Can be also at the (lowest level - 1) and not always in lowest level.

explain:
because in heap there is an option of missing nodes from the right side of the lowest level, it could be not a balancing (fully) tree, what makes it to have leafs also in (lower level -1).

what means that there are n/2 to check. so in big O term it's equal to O(n).

Examples for situation like that:

• MAX-heap[10,9,1,8,7] (1 is the smaller value, but didnt apear in lowest level)
  
• min-heap [8,10,20,17,15] (20 is the max value, but didnt apear in lowest level)