Hash Table and Linear Probing: Examining Table Entries During a Search

How many table entries will be examined during a search of key 29 in a Hash Table with the given conditions?

Note: This is an unsuccessful search since the key is not in the table.

Answer:

In a Hash Table of size m=11, with hash function h(x)=x%11 and Linear Probing used for collision resolution, during an unsuccessful search for the key 29, all 11 table entries would be examined.

The question revolves around a Hash Table that stores positive integers, with its size being m=11. The hash function here is h(x)=x%11 and Linear Probing is used for collision resolution.

In the scenario described, several keys (namely 18, 46, 9, 58, 30, 27, 101, 74) are inserted into the Hash Table. We are to determine how many table entries will be examined during a lookup of the key 29. Note this is an unsuccessful search since the key is not in the table.

The hash value of 29 using the given hash function is h(29)=29%11=7. Starting from entry 7 in the hash table, we continue to the right due to Linear Probing. We stop when we find an empty spot or reach the end and loop back to the start, until we've checked all 11 spots. Hence, for the search key 29, all 11 table entries would have been examined, as the search is unsuccessful.