An array [82, 101, 90, 11, 111, 75, 33, 131, 44, 93] is heapified. Which one…

2024

An array [82, 101, 90, 11, 111, 75, 33, 131, 44, 93] is heapified. Which one of the following options represents the first three elements in the heapified array?

  1. A.

    82, 90, 101

  2. B.

    82, 11, 93

  3. C.

    131, 11, 93

  4. D.

    131, 111, 90

Attempted by 234 students.

Show answer & explanation

Correct answer: D

Key insight: build a max-heap (largest element becomes the root) using the standard bottom-up heapify.

  • Start with the array: [82, 101, 90, 11, 111, 75, 33, 131, 44, 93].

  • Heapify index 3: swap 11 and 131 → [82, 101, 90, 131, 111, 75, 33, 11, 44, 93].

  • Heapify index 1: swap 101 and 131 → [82, 131, 90, 101, 111, 75, 33, 11, 44, 93].

  • Heapify index 0: swap 82 and 131 → [131, 82, 90, 101, 111, 75, 33, 11, 44, 93]. Then fix index 1 by swapping 82 and 111 → [131, 111, 90, 101, 82, 75, 33, 11, 44, 93], and finally swap 82 and 93 → [131, 111, 90, 101, 93, 75, 33, 11, 44, 82].

Final heapified array: [131, 111, 90, 101, 93, 75, 33, 11, 44, 82]. The first three elements are 131, 111, 90.

A video solution is available for this question — log in and enroll to watch it.

Explore the full course: Gate Guidance By Sanchit Sir