GATE | GATE-CS-2014-(Set-2) | Question 22

A priority queue is implemented as a Max-Heap. Initially, it has 5 elements. The level-order traversal of the heap is: 10, 8, 5, 3, 2. Two new elements 1 and 7 are inserted into the heap in that order. The level-order traversal of the heap after the insertion of the elements is:

(A) 10, 8, 7, 3, 2, 1, 5
(B) 10, 8, 7, 2, 3, 1, 5
(C) 10, 8, 7, 1, 2, 3, 5
(D) 10, 8, 7, 5, 3, 2, 1


Answer: (A)

Explanation:

Initially heap has 10, 8, 5, 3, 2
    10
   /  \ 
  8    5
 / \
3   2

After insertion of 1
     10
   /   \ 
  8     5
 / \   /
3   2 1 
No need to heapify as 5 is greater than 1.


After insertion of 7
     10
   /   \ 
  8     5
 / \   / \
3   2 1   7
Heapify 5 as 7 is greater than 5
     10
   /   \ 
  8     7
 / \   / \
3   2 1   5
No need to heapify any further as 10 is
greater than 7 


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