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Which of the following scenarios leads to linear running time for a random search hit in a linear-probing hash table?

(a) All keys hash to same index

(b) All keys hash to different indices

(c) All keys hash to an even-numbered index

(d) All keys hash to different even-numbered indices

The question was posed to me in an internship interview.

I'd like to ask this question from Hashing techniques topic in division Indexing and Hashing of Database Management

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The correct choice is (a) All keys hash to same index

Easiest explanation - If all keys hash to the same location then the i-th inserted key would need i lookups to be found. The probability of looking up i-th key is 1/n (since it’s random). If you know some probability it’s trivial to show that such lookups have linear time.

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