GATE CS 2022 Set 1 — Question 16
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Programming & Data Structures → Hashing → Hash Functions
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Question
Suppose we are given keys, hash table slots, and two simple uniform hash functions and . Further suppose our hashing scheme uses for the odd keys and for the even keys. What is the expected number of keys in a slot?
Correct answer
(B) (n)/(m)
Solution
Let be the total number of keys and be the number of slots.
Let be the number of odd keys and be the number of even keys, such that .For any specific slot :
The probability that a specific odd key hashes to slot using is (simple uniform hashing).
The expected number of odd keys in slot is .The probability that a specific even key hashes to slot using is (simple uniform hashing).
The expected number of even keys in slot is .The total expected number of keys in slot is:
.
Let be the number of odd keys and be the number of even keys, such that .For any specific slot :
The probability that a specific odd key hashes to slot using is (simple uniform hashing).
The expected number of odd keys in slot is .The probability that a specific even key hashes to slot using is (simple uniform hashing).
The expected number of even keys in slot is .The total expected number of keys in slot is:
.
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