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IBM Data Structures & Algorithms Data Structures & Algorithms Medium

Following keys are inserted into a hash table: 6, 29, 20, 16, 21, 33, 12, 17, 13, 41, 30...

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Following keys are inserted into a hash table:
6, 29, 20, 16, 21, 33, 12, 17, 13, 41, 30

using h(k) = k mod 7 hash function.

If collisions are resolved using chaining then max chain length will be.

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Show answer & explanation
Answer: B. 3

Computing h(k) = k mod 7 for each key maps them to hash table slots. Multiple keys hash to the same slot, forming chains. Slot 6 contains the longest chain with three keys (6, 20, 41), making the maximum chain length 3.

Step-by-step Derivation:
Calculate h(k) for each key:

  • h(6) = 6 mod 7 = 6
  • h(29) = 29 mod 7 = 1
  • h(20) = 20 mod 7 = 6
  • h(16) = 16 mod 7 = 2
  • h(21) = 21 mod 7 = 0
  • h(33) = 33 mod 7 = 5
  • h(12) = 12 mod 7 = 5
  • h(17) = 17 mod 7 = 3
  • h(13) = 13 mod 7 = 6
  • h(41) = 41 mod 7 = 6
  • h(30) = 30 mod 7 = 2

Chains formed:

  • Slot 0: [21] → length 1
  • Slot 1: [29] → length 1
  • Slot 2: [16, 30] → length 2
  • Slot 3: [17] → length 1
  • Slot 4: [] → length 0
  • Slot 5: [33, 12] → length 2
  • Slot 6: [6, 20, 13, 41] → length 4

Wait, recalculating slot 6: 6, 20, 13, 41 all map to 6, giving length 4. Let me verify: h(41) = 41 mod 7 = 6. Yes, the maximum chain length is 4.