If the values 1372, 1111, 1574, 6992, 1968, 5712, 1263, 1418 are to be stored using the hash function number mod 10. then when would the collision occur?

The correct answer is Option 2.

Key Points

• The hash function given in the problem is number mod 10, which means the remainder when the number is divided by 10 is used as the hash value.
• Let us calculate the hash values for the given numbers:
  • 1372 mod 10 = 2
  • 1111 mod 10 = 1
  • 1574 mod 10 = 4
  • 6992 mod 10 = 2
  • 1968 mod 10 = 8
  • 5712 mod 10 = 2
  • 1263 mod 10 = 3
  • 1418 mod 10 = 8
• Now, observe the hash values:
  • 1372, 6992, and 5712 all have the same hash value of 2.
  • Hence, a collision occurs when storing 6992 and 5712, as they share the same hash value (2) and the same storage location.
• Therefore, the collision occurs while storing 6992 and 5712, which corresponds to Option 2.

Additional Information

• A collision in hashing occurs when two distinct keys hash to the same index in the hash table.
• Collisions can be handled using techniques such as chaining (linked lists) or open addressing (linear probing, quadratic probing, etc.).
• Modular arithmetic (e.g., number mod 10) is a common and simple hash function, but it can lead to collisions if the data set is not evenly distributed.
• Choosing a good hash function and an appropriate table size can minimize collisions and improve efficiency.