Solution

The correct answer is _1, 3, 8, 10, 5, _

Key PointsTo insert each element into the hash table using closed hashing, we can use the given hash function (6x + 3) mod 4. Let's go through each element in the sequence and insert them into the hash table:

1. Insert 1:
   • Hash value = (6 * 1 + 3) mod 4 = 9 mod 4 = 1
   • The table becomes: _, 1, _, _, _, _, _
2. Insert 3:
   • Hash value = (6 * 3 + 3) mod 4 = 21 mod 4 = 1 (collision, linear probing)
   • The table becomes: _, 1, 3, _, _, _, _
3. Insert 8:
   • Hash value = (6 * 8 + 3) mod 4 = 51 mod 4 = 3
   • The table becomes: _, 1, 3, 8, _, _, _
4. Insert 10:
   • Hash value = (6 * 10 + 3) mod 4 = 63 mod 4 = 3 (collision, linear probing)
   • The table becomes: _, 1, 3, 8, 10, _, _
5. Insert 5:
   • Hash value = (6 * 5 + 3) mod 4 = 33 mod 4 = 1 (collision, linear probing)
   • The table becomes: _, 1, 3, 8, 10, 5, _

So, the correct answer is: 4) _, 1, 3, 8, 10, 5, _