Linear probing is a collision resolution technique for hash tables that uses open addressing. When a collision occurs by inserting a key-value pair, linear probing searches through consecutive table indices to find the next empty slot. This provides constant expected time for search, insertion, and deletion when using a random hash function. However, linear probing can cause clustering where many elements are stored near each other, degrading performance.

1. LINEAR PROBING
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2. HASHING
Hashing is the transformation of a string of
characters into a usually shorter fixed-length
value or key that represents the original string.
 Hashing is used to index and retrieve items in a
database because it is faster to find the item
using the shorter hashed key than to find it using
the original value

3. Hashing is nothing but by implementing a hash
function
Hashing is a technique used for performing
insertions, deletions and finds in constant average
time
Hash table
Hash table ADT which supports only a subset of the
operations allowed by binary search trees. Hash
table structure is merely an array of some fixed
size, containing the items

4. Openaddressing
 In an open addressing hashing system, all the data go
inside the table
 In open addressing,
 Unlike separate chaining, all the keys are stored inside
the hash table.
 No key is stored outside the hash table
There are three common collision resolution strategies:
 Linear Probing
 Quadratic probing
 Double hashing

5. Linearprobing
Linear probing is s technique for resolving hash
collisions of values of hash function.
Linear probing is a scheme in computer
programming for resolving collisions in hash
tables, data structures for maintaining a collection
of key–value pairs and looking up the value
associated with a given key.
 Linear probing can provide high performance
because of its good locality of reference, but is more
sensitive to the quality of its hash function than some
other collision resolution schemes.

6.  Linear probing is a component of open
addressing schemes for using a hash table to solve
the dictionary problem.
The linear probing hash table is a fairly simple
structure where data items are stored directly
inside the hash element array. It gets its name by
the way it handles the unique problems that exist
when storing the data items in the table directly.
 It takes constant expected time per search,
insertion, or deletion when implemented using a
random hash function

7. insertion
To insert a key–value pair (x,v) into the table (possibly
replacing any existing pair with the same key), the
insertion algorithm follows the same sequence of cells
that would be followed for a search, until finding either
an empty cell or a cell whose stored key is x.The new
key–value pair is then placed into that cell
If the insertion would cause the load factor of the table
(its fraction of occupied cells) to grow above some
preset threshold, the whole table may be replaced by a
new table, larger by a constant factor, with a new hash
function, as in a dynamic array.

9. Insert Operation
 Hash function is used to compute the hash value for
a key to be inserted.
 Hash value is then used as an index to store the key
in the hash table.
 In case of collision,
 Probing is performed until an empty bucket is
found.
 Once an empty bucket is found, the key is inserted.
 Probing is performed in accordance with the
technique used for open addressing.

10. Search Operation
 To search any particular key,
 Its hash value is obtained using the hash function
used.
 Using the hash value, that bucket of the hash table
is checked.
 If the required key is found, the key is searched.
 Otherwise, the subsequent buckets are checked
until the required key or an empty bucket is found.
 The empty bucket indicates that the key is not
present in the hash table.

11. Advantage
 It is easy to compute.
Disadvantage
 The main problem with linear probing
is clustering.
 Many consecutive elements form
groups.
 Then, it takes time to search an
element or to find an empty bucket.

12.  Linear Probing has the best cache
performance but suffers from
clustering.
 Quadratic probing lies between the
two in terms of cache performance
and clustering.
 Double caching has poor cache
performance but no clustering.