Consider a 13 element hash table for which f(key)=key mod 13 is used with integer keys. Assuming linear probing is used for collision resolution, at which location would the key 103 be inserted, if the keys 661, 182, 24 and 103 are inserted in that order?Select one:a. 1b. 12c. 11d. 0
Question
Consider a 13 element hash table for which f(key)=key mod 13 is used with integer keys. Assuming linear probing is used for collision resolution, at which location would the key 103 be inserted, if the keys 661, 182, 24 and 103 are inserted in that order?Select one:a. 1b. 12c. 11d. 0
Solution
To solve this problem, we need to follow these steps:
- Calculate the hash value for each key using the hash function f(key) = key mod 13.
- If a collision occurs, use linear probing to find the next available slot.
Let's do this step by step:
- For key 661, the hash value is 661 mod 13 = 8. So, 661 would be inserted at location 8.
- For key 182, the hash value is 182 mod 13 = 0. So, 182 would be inserted at location 0.
- For key 24, the hash value is 24 mod 13 = 11. So, 24 would be inserted at location 11.
- For key 103, the hash value is 103 mod 13 = 12. However, since linear probing is used for collision resolution, we need to check if location 12 is available. If it is, 103 would be inserted at location 12. If it's not, we would move to the next location (wrapping around to the beginning of the table if necessary) until we find an available slot.
Without information about the initial state of the hash table or the keys that might already be in it, we can't definitively say where 103 would be inserted. But based on the information given, the answer would be 12 (option b).
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