GATE CS 2015 Set 2 — Question 50
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Programming & Data Structures → Hashing → Hash Functions
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Question
Which one of the following hash functions on integers will distribute keys most uniformly over 10 buckets numbered 0 to 9 for ranging from 0 to 2020?
Correct answer
(B) h(i) = i³ mod 10
Solution
We analyze the distribution of values modulo 10 for each function:(A) : The quadratic residues modulo 10 are . The values are never produced. This is not uniform.(B) : The cubic residues modulo 10 map as follows:
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This is a permutation of digits . Since the input range to covers the cycle many times uniformly, this function distributes keys very uniformly.(C) . Same as (A), not uniform.(D) . This produces only even numbers . Not uniform.Therefore, (B) is the correct answer.
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This is a permutation of digits . Since the input range to covers the cycle many times uniformly, this function distributes keys very uniformly.(C) . Same as (A), not uniform.(D) . This produces only even numbers . Not uniform.Therefore, (B) is the correct answer.
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