GATE CS 2014 Set 1 — Question 50
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Programming & Data Structures → Hashing → Chaining
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Question
Consider a hash table with 9 slots. The hash function is . 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
Correct answer
(A) 3, 0, and 1
Solution
The hash function is . The keys are inserted into slots 0 to 8.Insertions:
Slot 0: 0
Slot 1: 3 (28, 19, 10)
Slot 2: 1 (20)
Slot 3: 1 (12)
Slot 4: 0
Slot 5: 1 (5)
Slot 6: 2 (15, 33)
Slot 7: 0
Slot 8: 1 (17)Maximum chain length = 3 (Slot 1)
Minimum chain length = 0 (Slots 0, 4, 7)
Average chain length = Thus, the values are 3, 0, and 1.
- Slot 5: [5]
- Slot 1: [28]
- Slot 1: [28, 19] (Collision)
- Slot 6: [15]
- Slot 2: [20]
- Slot 6: [15, 33] (Collision)
- Slot 3: [12]
- Slot 8: [17]
- Slot 1: [28, 19, 10] (Collision)
Slot 0: 0
Slot 1: 3 (28, 19, 10)
Slot 2: 1 (20)
Slot 3: 1 (12)
Slot 4: 0
Slot 5: 1 (5)
Slot 6: 2 (15, 33)
Slot 7: 0
Slot 8: 1 (17)Maximum chain length = 3 (Slot 1)
Minimum chain length = 0 (Slots 0, 4, 7)
Average chain length = Thus, the values are 3, 0, and 1.
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