GATE CS 2014 Set 2 — Question 22
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Programming & Data Structures → Heaps → Heap Insert & Extract
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Question
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:
Correct answer
(A) 10, 8, 7, 3, 2, 1, 5
Solution
Initial Max-Heap (Level Order: 10, 8, 5, 3, 2):
Step 1: Insert 1
Insert 1 at the next available position (left child of 5).
Check Max-Heap property: Parent 5 > Child 1. OK.
Current Level Order: 10, 8, 5, 3, 2, 1.Step 2: Insert 7
Insert 7 at the next available position (right child of 5).
Check Max-Heap property: Parent 5 < Child 7. Violation. Swap 5 and 7.
Check Max-Heap property: Parent 10 > Child 7. OK.Final Level Order: 10, 8, 7, 3, 2, 1, 5.
10
/ \
8 5
/ \
3 2
Insert 1 at the next available position (left child of 5).
10
/ \
8 5
/ \ /
3 2 1
Check Max-Heap property: Parent 5 > Child 1. OK.
Current Level Order: 10, 8, 5, 3, 2, 1.Step 2: Insert 7
Insert 7 at the next available position (right child of 5).
10
/ \
8 5
/ \ / \
3 2 1 7
Check Max-Heap property: Parent 5 < Child 7. Violation. Swap 5 and 7.
10
/ \
8 7
/ \ / \
3 2 1 5
Check Max-Heap property: Parent 10 > Child 7. OK.Final Level Order: 10, 8, 7, 3, 2, 1, 5.
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