GATE CS 2020 Q.33 (CS Q.23): Hash Tables and Collision Resolution

Consider a double hashing scheme in which the primary hash function is $h_1(k) = k \bmod 23$ , and the secondary hash function is $h_2(k) = 1 + (k \bmod 19)$ . Assume that the table size is 23. Then the address returned by probe 1 in the probe sequence (assume that the probe sequence begins at probe 0) for key value $k = 90$ is _______.

Your answer

Official answer and solution

Official answer: 13
From: Official GATE 2020 answer key

Solution

Evaluate the primary and secondary hash functions and determine the bucket address for probe 1.

In double hashing, the hash probe sequence for a key $k$ at probe index $i$ is given by:

\text{hash}(k, i) = (h_1(k) + i \cdot h_2(k)) \bmod m

where $m = 23$ , and the sequence starts at probe $i = 0$ .

Evaluate the primary and secondary hash values for $k = 90$ :

$h_1(90) = 90 \bmod 23 = 90 - 3 \times 23 = 90 - 69 = 21$
$h_2(90) = 1 + (90 \bmod 19) = 1 + (90 - 4 \times 19) = 1 + (90 - 76) = 1 + 14 = 15$

Evaluate the address returned by probe 1 ( $i = 1$ ):

\text{hash}(90, 1) = (21 + 1 \times 15) \bmod 23 = 36 \bmod 23 = 13

Therefore, the address returned by probe 1 is 13.

Final answer

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

Source

Paper: GATE 2020 Computer Science and Information Technology (CS)
Question: 33 of 65, printed as CS Q.23
Section: Computer Science and Information Technology

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.

Question

Solution

Source