GATE CS 2026 Set 1 Q.24: Hash Tables and Collision Resolution

Consider a hash table $P[0, 1, \dots, 10]$ 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?

Official answer and solution

Official answer: C
From: Official GATE 2026 answer key

Solution

Insert each key sequentially using $h(x) = (x + 7) \bmod 11$ and linear probing $(h(x) + i) \bmod 11$ .

Tracing each insertion into $P[0..10]$ :

$x = 1$ : $h(1) = (1 + 7) \bmod 11 = 8 \implies P[8] = 1$ .
$x = 13$ : $h(13) = (13 + 7) \bmod 11 = 9 \implies P[9] = 13$ .
$x = 22$ : $h(22) = (22 + 7) \bmod 11 = 7 \implies P[7] = 22$ .
$x = 15$ : $h(15) = (15 + 7) \bmod 11 = 0 \implies P[0] = 15$ .
$x = 11$ : $h(11) = (11 + 7) \bmod 11 = 7$ (occupied) $\rightarrow 8$ (occupied) $\rightarrow 9$ (occupied) $\rightarrow 10$ (empty) $\implies P[10] = 11$ .
$x = 24$ : $h(24) = (24 + 7) \bmod 11 = 9$ (occupied) $\rightarrow 10$ (occupied) $\rightarrow 0$ (occupied) $\rightarrow 1$ (empty) $\implies P[1] = 24$ .

Occupied positions are $\{0, 1, 7, 8, 9, 10\}$ , and empty positions are $\{2, 3, 4, 5, 6\}$ . Among the given options, only position 2 is empty.

Final answer

Option (C)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 1 (CS1)
Question: 24 of 65
Section: Computer Science and Information Technology

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