Consider a hash table P[0, 1, , 10] that is initially empty. The hash table is maintained using open addressing with linear probing. The hash function used is h(x) = (x + 7) 11. Consider the following sequence of insertions performed on P: 1, 13, 22, 15, 11, 24 Which of the following positions in the hash table is/are empty after these insertions are performed?

GATE CSE 2026 Session 1 Q24: Empty slots after linear-probing inserts with h(x) = (x+7) mod 11

Programming and Data Structures
1 mark
MSQ
No negative marking

Consider a hash table $P[0, 1, \ldots, 10]$ that is initially empty. The hash table is maintained using open addressing with linear probing. The hash function used is $h(x) = (x + 7) \bmod 11$ .

Consider the following sequence of insertions performed on $P$ :

1, 13, 22, 15, 11, 24

Which of the following positions in the hash table is/are empty after these insertions are performed?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

Show answer and explanation

Answer: C (official GATE 2026 final answer key)

Concept used: Linear probing: on collision try the next slot, wrapping around.

First step: Compute the home slots: 1 → 8, 13 → 9, 22 → 7, 15 → 0, 11 → 7, 24 → 9, and probe forward for collisions.

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

WhatsAppDownload image

Source: official GATE 2026 Session 1 CS question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

PracticePractise Programming and Data Structures questions →Full paperAll GATE CSE 2026 Session 1 questions →

GATE CSE 2026 Session 1 Q24: Empty slots after linear-probing inserts with h(x) = (x+7) mod 11

Question

Full step-by-step solution

More Programming and Data Structures PYQs