GATE CS 2024 Set 1 — Question 41
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Programming & Data Structures → Heaps → Heapify & Build-Heap
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Question
An array is heapified. Which one of the following options represents the first three elements in the heapified array?
Correct answer
(D) 131, 111, 90
Solution
The problem asks for the first three elements of the array after it has been heapified. Since the options suggest the root is 131 (the maximum element in the input), we assume a Max-Heap is constructed using the standard bottom-up
Indices: to . Size .The
Check subtree at index 3: Parent , Children . is larger. No further swap.
Check subtree at index 1: Parent , Children . Max child is . Swap and .
Array:
Check subtree at index 4: Parent , Child . Max child is . Swap and .
Array: Final Heapified Array: The first three elements are 131, 111, 90.
build-heap algorithm.Input Array: Indices: to . Size .The
build-heap process starts from the last non-leaf node, which is at index , and iterates down to .1.Index 4 (): Child is . Since , no swap needed.
Array: 2.Index 3 (): Children are and . Max child is . Swap and .
Array: 3.Index 2 (): Children are and . is larger than both. No swap.
Array: 4.Index 1 (): Children are and . Max child is . Swap and .
Array: Check subtree at index 3: Parent , Children . is larger. No further swap.
5.Index 0 (): Children are and . Max child is . Swap and .
Array: Check subtree at index 1: Parent , Children . Max child is . Swap and .
Array:
Check subtree at index 4: Parent , Child . Max child is . Swap and .
Array: Final Heapified Array: The first three elements are 131, 111, 90.
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