Question $1$

A data structure is required for storing a set of integers such that each of the following operations can be done in $O(logn)$ time, where n is the number of

elements in the set.

Deletion of the smallest element

Insertion of an element if it is not already present in the set

Which of the following data structures can be used for this purpose?

A heap can be used but not a balanced binary search tree

A balanced binary search tree can be used but not a heap

Neither balanced search tree nor heap can be used

Both balanced binary search tree and heap can be used