GATE CS 2026 Set 2 Q.30: Hash Tables and Collision Resolution

The keys 5, 28, 19, 15, 26, 33, 12, 17, 10 are inserted into a hash table using the hash function $h(k) = k \bmod 9$ . The collisions are resolved by chaining. After all the keys are inserted, the length of the longest chain is __________. (answer in integer)

Your answer

Official answer and solution

Official answer: 3
From: Official GATE 2026 answer key

Solution

Compute $k \bmod 9$ for each of the 9 keys and find the maximum bucket count.

Computing $h(k) = k \bmod 9$ for each key:

$5 \bmod 9 = 5$
$28 \bmod 9 = 1$
$19 \bmod 9 = 1$
$15 \bmod 9 = 6$
$26 \bmod 9 = 8$
$33 \bmod 9 = 6$
$12 \bmod 9 = 3$
$17 \bmod 9 = 8$
$10 \bmod 9 = 1$

Bucket counts:

Bucket $1$ : $\{28, 19, 10\}$ (length $3$ )
Bucket $3$ : $\{12\}$ (length $1$ )
Bucket $5$ : $\{5\}$ (length $1$ )
Bucket $6$ : $\{15, 33\}$ (length $2$ )
Bucket $8$ : $\{26, 17\}$ (length $2$ )

The length of the longest chain is $3$ .

Final answer

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 2 (CS2)
Question: 30 of 65
Section: Computer Science and Information Technology

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