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Consider a hash table with 11 slots. The hash functionis h(k) = k mod 11. The collisions are resolved byopen Hashing(Chaining). The following 11 keys are inserted in theorder: 28, 19, 15, 20, 33, 30, 42, 63, 60, 32, 43. Themaximum, minimum, and average chain lengths in thehash table, respectively, are-

Question

Consider a hash table with 11 slots. The hash functionis h(k) = k mod 11. The collisions are resolved byopen Hashing(Chaining). The following 11 keys are inserted in theorder: 28, 19, 15, 20, 33, 30, 42, 63, 60, 32, 43. Themaximum, minimum, and average chain lengths in thehash table, respectively, are-

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Solution

To answer this question, we first need to understand how a hash table works. A hash table is a data structure that implements an associative array abstract data type, a structure that can map keys to values. A hash table uses a hash function to compute an index into an array of buckets or slots, from which the desired value can be found.

The hash function given is h(k) = k mod 11. This means that we divide the key by 11 and the remainder is the index of the slot where we store the value. If two keys map to the same slot, a collision occurs, and we resolve it by chaining, which means we create a linked list of keys at that slot.

Let's insert the keys one by one:

  1. 28 mod 11 = 6. So, 28 goes to slot 6.
  2. 19 mod 11 = 8. So, 19 goes to slot 8.
  3. 15 mod 11 = 4. So, 15 goes to slot 4.
  4. 20 mod 11 = 9. So, 20 goes to slot 9.
  5. 33 mod 11 = 0. So, 33 goes to slot 0.
  6. 30 mod 11 = 8. So, 30 goes to the same slot as 19, slot 8.
  7. 42 mod 11 = 9. So, 42 goes to the same slot as 20, slot 9.
  8. 63 mod 11 = 3. So, 63 goes to slot 3.
  9. 60 mod 11 = 5. So, 60 goes to slot 5.
  10. 32 mod 11 = 10. So, 32 goes to slot 10.
  11. 43 mod 11 = 10. So, 43 goes to the same slot as 32, slot 10.

Now, let's calculate the chain lengths:

  • Slot 0, 1, 2, 7, and 11: Chain length is 1.
  • Slot 3, 4, 5, and 6: Chain length is 1.
  • Slot 8: Chain length is 2 (19, 30).
  • Slot 9: Chain length is 2 (20, 42).
  • Slot 10: Chain length is 2 (32, 43).

So, the maximum chain length is 2, the minimum chain length is 1, and the average chain length is (17 + 24) / 11 = 1.36 (rounded to two decimal places).

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