Q78.Marks: +2.0UGC NET Paper 2: Computer Science 26th Nov 2021
A data structure is required for storing a set of integers such that each of the following operations can be done in O(log n) time, where n is the number of elements in the set.
A. Deletion of the smallest element
B. 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?
1.A heap can be used but not a balanced binary search tree.
2.A balanced binary search tree can be used but not a heap.✓ Correct
3.Both balanced binary search tree and heap can be used.
4.Neither balanced binary search tree nor heap can be used.
Solution
The correct answer is option 2.
Explanation :
Balanced Binary Search Tree : A Balanced binary search tree is a binary search tree in which the difference between the height of left sub tree and the right sub tree is not more than 1.
Now ,to perform deletion of the smallest element ,the complexity is : O(log n)
To insert an element in balanced BST ,if it is not present in the set, we need to search the element first .To search the element the time complexity is O(log n) . To insert an element in balanced BST the complexity is O(log n).
Heap : Heap is a special case of balanced binary tree data structure where the root key is compared with its children and it has utmost two children. If we arrange Max Heap then key( a ) >= key (b),where node b is the child of node a. If we arrange Min Heap then key (a) <= key (b) ,where node b is the child of node a.
Now, ,to perform deletion of the smallest element ,the complexity is : O(log n)
To insert an element in Heap ,if it is not present in the set, we need to search the element first .To search the element the time complexity is O(n) . To insert an element in balanced BST the complexity is O(log n).