Performance of Open Addressing

Like Chaining, the performance of hashing can be evaluated under the assumption that each key is equally likely to be hashed to any slot of the table (simple uniform hashing) 

m = Number of slots in the hash table

n = Number of keys to be inserted in the hash table

 Load factor α = n/m  ( < 1 )

Expected time to search/insert/delete < 1/(1 – α) 

So Search, Insert and Delete take (1/(1 – α)) time

Related Articles: Hashing | Set 1 (Introduction), Hashing | Set 2 (Separate Chaining) 

Open Addressing is a method for handling collisions. In Open Addressing, all elements are stored in the hash table itself. So at any point, the size of the table must be greater than or equal to the total number of keys (Note that we can increase table size by copying old data if needed). This approach is also known as closed hashing. This entire procedure is based upon probing. We will understand the types of probing ahead:

• Insert(k): Keep probing until an empty slot is found. Once an empty slot is found, insert k. 
• Search(k): Keep probing until the slot’s key doesn’t become equal to k or an empty slot is reached. 
• Delete(k): Delete operation is interesting. If we simply delete a key, then the search may fail. So slots of deleted keys are marked specially as “deleted”. 
  The insert can insert an item in a deleted slot, but the search doesn’t stop at a deleted slot.