Programming and Data Structures · Binary Heaps

Official IIT answer key · IISc Bangalore · Audited Aug 2026

GATE CSE 2016 Set 2 Q34 · NAT · 2 marks

A complete binary min-heap is made by including each integer in $[1, 1023]$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _________.

Numerical answer

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Key concept

Binary Heaps

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Binary Heaps

Binary heaps are tested frequently in GATE CS with a strong focus on structural and array properties (complete binary tree indexing), operation trace (insertion bubbling up and bottom-up build-heap sift-down), and extreme value locations (finding maximum in min-heap or minimum in max-heap). Questions vary from direct index/leaf counting formulas and tree height calculations to asymptotic complexities of priority queue operations. Recent years exhibit an increased prevalence of NAT and MSQ questions testing index ranges and structural properties.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

Programming and Data Structures · Binary Heaps

Official IIT answer key · IISc Bangalore · Audited Aug 2026

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GATE CSE 2016 Set 2 Q34 · NAT · 2 marks

A complete binary min-heap is made by including each integer in $[1, 1023]$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _________.

Numerical answer

Enter a value to check

Key concept

Binary Heaps

Step-by-step verified solution

Examiner trap & misconception

Topic notes

How GATE tests Binary Heaps

Full Binary Heaps guide →

More on Binary Heaps

All 15 questions on Binary Heaps →

Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.

A complete binary min-heap is made by including each integer in $[1, 1023]$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _________.

Step-by-step verified solution

Check you can still solve Binary Heaps under a clock

More from GATE CSE 2016 Set 2

More on Binary Heaps

A complete binary min-heap is made by including each integer in $[1, 1023]$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _________.

Step-by-step verified solution

Check you can still solve Binary Heaps under a clock

More from GATE CSE 2016 Set 2

More on Binary Heaps

A complete binary min-heap is made by including each integer in [1,1023][1, 1023][1,1023] exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _________.

Step-by-step verified solution

Check you can still solve Binary Heaps under a clock

More from GATE CSE 2016 Set 2

More on Binary Heaps

Share this solution

A complete binary min-heap is made by including each integer in [1,1023][1, 1023][1,1023] exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _________.

Step-by-step verified solution

Check you can still solve Binary Heaps under a clock

More from GATE CSE 2016 Set 2

More on Binary Heaps

Share this solution

A complete binary min-heap is made by including each integer in $[1, 1023]$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _________.

A complete binary min-heap is made by including each integer in $[1, 1023]$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth 0. The maximum depth at which integer 9 can appear is _________.