Final answer:
An open addressing hash table with linear probing is a data structure for storing integers, where collisions are resolved by checking subsequent slots. Implementations require methods for insertion, deletion, and searching, considering boundary conditions, and maintaining table integrity.
Step-by-step explanation:
Open Addressing Hash Table with Linear Probing
An open addressing hash table is a data structure used to store keys (in this case, integers), where collisions are handled by placing the colliding item in the next available space in the array. When dealing with collisions in an open addressing hash table, linear probing is a systematic method for finding the next available slot. It works by checking the next slot in the array, incrementing the index by a fixed step (usually 1) until an empty slot is found.
To insert an integer, you hash it to get an index and place it at that index in the table. If the slot is already occupied due to a collision, you probe forward in the table, visiting each slot in turn until you find an empty slot to occupy. For deletion, you would search for the item using the same probing sequence used during insertion, and upon finding it, you can remove it and then rehash any subsequent elements in the probe sequence to maintain the table's integrity. The search operation involves applying the hash function to the target value and checking the resulting index, then using linear probing until the value is found or an empty slot is encountered.
Proper implementation of a hash table using open addressing and linear probing requires careful consideration of boundary conditions (such as wrapping around to the beginning of the table when you reach the end) and load factors (to determine when the table should be resized to maintain efficiency).