Hash/hash value can be
used to uniquely identify secret information. This requires that the hash function is collision resistant, which
means that it is very hard to find data that generate the same hash value.
Hash function is any function that can be used to map data of arbitrary size to
data of fixed size. The values returned by a hash function are called hash
values/hash codes/ hashes.
Hash
functions accelerate table or database lookup by detecting duplicated records
in a large file.
Majorly used hash
function: Division
The hash function is: f_{D} (x) = x %
M This gives bucket address that range from 0 to M1, where M
= the table size.
Hashing
Hashing
is the process of mapping large amount of data item to a smaller table with the
help of a hashing function. The essence of hashing is to facilitate
the next level searching method when compared with the linear or binary
search. The advantage of this searching method is its efficiency to hand vast
amount of data items in a given collection.
Loading density
The identifier density of a hash table is the ratio n/T, where n
is the number of identifiers in the table. The loading density or
loading factor of a hash table is a=n /(sb).
Collision:
When hash function generates same hash for two different values is
known as collision. Because when be store the data in bucket than there will be
more than one value in bucket.
Linear probing is a scheme in
computer programming for resolving hash collisions of values of hash functions
by sequentially searching the hash table for a free location.
stepSize = probes.
newLocation = (startingValue + stepSize) %
arraySize
Linear probing function (H(x, i)):
H(x, i) = (H(x) + i) (mod n), Here ordinary
hash function H(x).
Here H(x) is the starting value, n the size of
the hash table, and the stepsize is i in this case.
Often, the step size is one; that is, the array
cells that are probed are consecutive in the hash table. Double hashing is a
variant of the same method in which the step size is itself computed by a hash
function.
Chained Hashing/Chaining
Instead of storing the data item directly in the
hashtable, each hashtable entry contains a reference to a datastructure, e.g. a
linked list (chain), or a balanced search tree. We compute the hash
value v of the data item d and then store d in the
data structure referred to from the hashtable entry at index v.
Chaining using linked list:
Hash table (hash
map) is a data structure used to implement an
associative array, a structure that can map
keys to values. A hash table uses a hash function to compute an index into
an array of buckets or slots, from which the desired value can be found.
Ideally, the hash function will assign each key
to a unique bucket, but it is possible that two keys will generate an identical
hash causing both keys to point to the same bucket. Instead, most hash table
designs assume that hash collisions—different keys that are assigned by the
hash function to the same bucket—will occur and must be accommodated in some
way.

Average

Worst case

Space

O(n)

O(n)

Search

O(1)

O(n)

Insert

O(1)

O(n)

Delete

O(1)

O(n)
