![]() ![]() Resolution sequences for different elements are different even if the first hash function hashes the elements to the same field.Compared to linear probing access becomes inefficient at a higher load factor. ![]() With Double hashing, insert the following elements in the given order.Ĩ9, 18, 49, 58 and 69 are inserted into a hash table Primary hash function is H1(key) = key mod 10, and secondary hash function is H2(key)=7-(key mod 7). Hash1(key) = Key % table size. A popular secondary hash function is: Hash 2(key) = R - ( key % R ) where R is a prime number that is smaller than the size of the table. Primary hash function is similar to direct hashing.This c is added to the home address to produce an overflow addresses: if occupied, proceed by adding c to the overflow address, until an empty slot is found. The primary hash function determines the home address. If the home address is occupied, apply a second hash function to get a number c (c relatively prime to N).Double hashing uses the idea of applying a second hash function to the key when a collision occurs.Double hashing requires that the size of the hash table is a prime number.Disadvantage of Chaining: Too many linked lists (overhead of linked lists).Advantages of Chaining: Unbounded elements can be stored (No bound to the size of table).There is no need to search for empty cells in the array or table.If M is too small, then chains are too long.If M is too large, then too many empty chains.For any t > 1, probability that list length > t α is exponentially small in t. Theorem: Let α = N / M > 1 be average length of list.Average length = N / M, where N is size of array and M is the number of linked lists.Cost is proportional to length of list.Other items that hash to the same index are simply added to the linked list.A data item’s key is hashed to the index in simple hashing, and the item is inserted into the linked list at that index.Using the chaining, insert the following elements into the hash table. Example: Assume a table has 8 slots (m=8).A linked list is created at each index in the hash table.A chain is simply a linked list of all the elements with the same hash key.Open Addressing (Linear probing, Quadratic probing, Random probing), etc.Handling the Collisions: The following techniques can be used to handle the collisions.Collision: No matter what the hash function, there is the possibility that two different keys could resolve to the same hash address.Example: Addresses from 0 to 99, key = 453 in base 11 = 382.Transform the number into another base and then divide by the maximum address. ![]()
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