ACtE07 · Chapter 7Data Structures, DBMS & Operating Systems🏛️ Past Licensure QuestionID: fc96aafe

Which array represents a min-heap (1-based index; parent ≤ children)?

Multiple Choice Options

A
[2, 1, 3, 4]
B
[1, 3, 2, 4]
✓ Correct Option
C
[3, 1, 2, 4]
D
[2, 3, 4, 1]

Detailed Technical Solution & Explanation

In a 1-based binary min-heap array $A[1 \dots n]$ , the min-heap property requires that every node's value must be less than or equal to the values of its children:

A[i] \le A[2i] \quad \text{and} \quad A[i] \le A[2i+1]

Evaluating Option B $[1, 3, 2, 4]$ :

•

For

i=1

(

A[1]=1

): Left child

A[2]=3 \ge 1

; Right child

A[3]=2 \ge 1

. (Satisfied)

•

For

i=2

(

A[2]=3

): Left child

A[4]=4 \ge 3

. (Satisfied)

Thus, $[1, 3, 2, 4]$ strictly satisfies the min-heap property.

Option Analysis:

•

Option A ([2, 1, 3, 4]): Incorrect. Root

A[1] = 2

is greater than its left child

A[2] = 1

(

2 \le 1

is false).

•

Option B ([1, 3, 2, 4]): Correct. Every parent node is smaller than or equal to its child nodes across all indices.

•

Option C ([3, 1, 2, 4]): Incorrect. Root

A[1] = 3

is greater than its children

A[2] = 1

and

A[3] = 2

•

Option D ([2, 3, 4, 1]): Incorrect. Node

A[2] = 3

is greater than its left child

A[4] = 1

Reference: Demo2 · Set 1NEC Licensure Syllabus

Which array represents a min-heap (1-based index; parent ≤ children)?

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

Want to practice this topic interactively?

Which array represents a min-heap (1-based index; parent ≤ children)?

Multiple Choice Options

Detailed Technical Solution & Explanation

Option Analysis:

Want to practice this topic interactively?