Consider a hash table with 9 slots. The hash function is \(h(k) = k \ mod \…

2014

Consider a hash table with 9 slots. The hash function is \(h(k) = k \ mod \ 9\). The collisions are resolved by chaining. The following 9 keys are inserted in the order: 5, 28, 19, 15, 20, 33, 12, 17, 10. The maximum, minimum, and average chain lengths in the hash table, respectively, are

  1. A.

    3, 0, and 1

  2. B.

    3, 3, and 3

  3. C.

    4, 0, and 1

  4. D.

    3, 0, and 2

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Correct answer: A

Solution: compute h(k)=k mod 9 for each key and then read off chain lengths.

  • Compute hashes: 5→5, 28→1, 19→1, 15→6, 20→2, 33→6, 12→3, 17→8, 10→1.

  • Chain lengths by slot (0 through 8): 0, 3, 1, 1, 0, 1, 2, 0, 1.

  • Maximum chain length = 3 (slot 1).

  • Minimum chain length = 0 (slots 0, 4, and 7 are empty).

  • Average chain length (over 9 slots) = total keys 9 ÷ 9 slots = 1.

Therefore the maximum, minimum, and average chain lengths are 3, 0, and 1 respectively.

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