Hash tables

In the majority of computer languages, set data and map structures are implemented using hash tables. Both hash table Python and Go come with pre-implemented dictionaries and maps, whereas C++ and Java include them in their standard libraries.

  • Hash tables store data by associating keys with values in a non-ordered set.

Hash tables provide an efficient mix of lookup, insert, and delete operations. Arrays and linked lists both fail in this regard.

  • A lookup in an unsorted array has a worst-case complexity that is linear.
  • Binary search works extremely quickly for looking for items in a sorted array but is slow and wasteful when adding new items to the array.
  • In a linked list, insertions may be performed efficiently, however lookups need linear time.

A hash table is an associative data structure that keeps track of information. In a hash table, data is kept in an array format with a unique index value for each data item. If we know the id of the needed data, data access becomes extremely quick.

As a result, regardless of the data quantity, search and hash table insertion operations may be performed quickly using this data structure. This type of table employs an array as its store medium and employs the hash method to build an index for inserting or locating an entry.


In computing, hashing is a method through which an array’s key values may be translated into a sequence of indexes. To get a set of admissible values, you should utilize the modulo operator. Consider a 20-byte hash table in which the following values are to be kept. Items are formatted as (keys and values).

Basic Procedures

Here are the major fundamental operations of a hash table:

  • Search a hash table for an element.
  • The Hash table Insert function  is used to insert an element into a hash table.
  • Delete removes an entry from the hash table.

Hash Collision

Hash collision happens when the hash function produces the same index for several keys.

We may resolve this by using one of the following methods:

  1. Resolution of collisions through chaining; or
  2. Open Addressing.

Resolution of Collisions through Chaining

If a hash function generates the same index for numerous items during chaining, these elements are kept in the same index utilizing a doubly-linked list.

If j represents a slot for several items, it includes a reference to the list’s head. If no element is available, j contains NIL.

Open Addressing

Open addressing, unlike chaining, does not store multiple components in the same slot. Each slot is either populated with a single key or is left empty.

The following strategies are used in open addressing:

  • Linear Probing

In linear probing, collisions are addressed by examining the next slot.

h(k, i) = (h′(k) + i) mod m

where i = 0, 1,…

h'(k) is a new hash function

If there is a collision at h(k, 0), then h(k, 1) is examined. In this manner, the quantity of i is linearly increased.

When using linear probing, a group of neighboring slots is filled all at once. When introducing a new element, the cluster must be visited in its entirety. This increases the time necessary to conduct hash table operations.

  • Quadratic Probing

The following relation expands the space between slots beyond the conventional value of one, allowing for a comparable function to linear probing.

h (k, i) =  (h(k) + c1 i + c2 i2) mod m

where c1 and c2 are positive constants,

i = 0, 1,…

  • Double Hashing

After applying h(k), if an impact occurs, a new hash function is computed to determine where to place k.

h (k, i) = (h1 (k) + ih2 (k)) mod m

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Constant Amortized Time Resizing

Hash tables perform optimally when their sizes are proportionate to the number of records they contain. Table resizing is required whenever lists get too big if the expected number of records is unknown.

  • A bigger table is designated;
  • The previous table is being emptied one record at a time;
  • And added to the brand-new table.

This technique provides compounded consistent time performance for inserts if the table size is expanded by a constant factor at each resize, for example, by doubling its size.