# Heap Tree

 Question 1
Let A be a priority queue for maintaining a set of elements. Suppose A is implemented using a max-heap data structure. The operation Extract-Max(A) extracts and deletes the maximum element from A. The operation Insert(A,key) inserts a new element key in A. The properties of a max-heap are preserved at the end of each of these operations.
When A contains n elements, which one of the following statements about the worst case running time of these two operations is TRUE?
 A Both Extract-Max(A) and Insert(A,key) run in O(1). B Both Extract-Max(A) and Insert(A,key) run in O(log(n)). C Extract-Max(A) runs in O(1) whereas Insert(A,key) runs in O(n). D Extract-Max(A) runs in O(1) whereas Insert(A,key) runs in O(log(n)).
GATE CSE 2023   Data Structure
Question 1 Explanation:
 Question 2
Which one of the following sequences when stored in an array at locations A, . . . , A forms a max-heap?
 A 23, 17, 10, 6, 13, 14, 1, 5, 7, 12 B 23, 17, 14, 7, 13, 10, 1, 5, 6, 12 C 23, 17, 14, 6, 13, 10, 1, 5, 7, 15 D 23, 14, 17, 1, 10, 13, 16, 12, 7, 5
GATE CSE 2023   Data Structure
Question 2 Explanation:

 Question 3
Let H be a binary min-heap consisting of n elements implemented as an array. What is the worst case time complexity of an optimal algorithm to find the maximum element in H?
 A $\Theta (1)$ B $\Theta (\log n)$ C $\Theta ( n)$ D $\Theta (n \log n)$
GATE CSE 2021 SET-2   Data Structure
Question 3 Explanation:
 Question 4
Consider the array representation of a binary min-heap containing 1023 elements. The minimum number of comparisons required to find the maximum in the heap is ___________.
 A 512 B 511 C 1022 D 10
GATE CSE 2020   Data Structure
Question 4 Explanation:
 Question 5
Consider the following statements:

I. The smallest element in a max-heap is always at a leaf node.
II. The second largest element in a max-heap is always a child of the root node.
III. A max-heap can be constructed from a binary search tree in $\Theta (n)$ time.
IV. A binary search tree can be constructed from a max-heap in $\Theta (n)$ time.

Which of the above statements is/are TRUE?
 A I, II and III B I, II and IV C I, III and IV D II, III and IV
GATE CSE 2019   Data Structure
Question 5 Explanation:

There are 5 questions to complete.

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1. Please give question no 20 first then 19.
It will be in sequence