Hashing types

1. HASHING

2. DEFN.,
 Hashing in the data structure is a technique of
mapping a large chunk of data into small
tables using a hashing function.
 It is also known as the message digest function.
 It is a technique that uniquely identifies a specific
item from a collection of similar items

4. HASH FUNCTION
 A hash function is a function that takes a set of
inputs of any arbitrary size and fits them into a
table or other data structure that contains fixed-
size elements.
 The table or data structure generated is usually
called a hash table.

6. SEPARATE CHAINING/OPEN HASHING
 To handle the collision,
 This technique creates a linked list to the slot for
which collision occurs.
 The new key is then inserted in the linked list.
 These linked lists to the slots appear like chains.
 That is why, this technique is called as separate
chaining.

8.  Advantages:
1) Simple to implement.
2) Hash table never fills up, we can always add more
elements to the chain.
3) Less sensitive to the hash function or load factors.
4) It is mostly used when it is unknown how many and
how frequently keys may be inserted or deleted.
 Disadvantages:
1) Cache performance of chaining is not good as keys
are stored using a linked list. Open addressing provides
better cache performance as everything is stored in the
same table.
2) Wastage of Space (Some Parts of hash table are
never used)
3) If the chain becomes long, then search time can
become O(n) in the worst case.
4) Uses extra space for links.

9. DISADVANTAGE OF SEPARATE CHAINING

10. OPEN ADDRESSING/CLOSED HASHING
LINEAR PROBING
 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.
 In these schemes, each cell of a hash table stores
a single key–value pair.
 h´(𝑥) = 𝑥 𝑚𝑜𝑑 𝑚
 ℎ(𝑥, 𝑖) = (ℎ´(𝑥) + 𝑖)𝑚𝑜𝑑 𝑚
 The value of i| = 0, 1, . . ., m – 1. So we start from i
= 0

12. DRAWBACKS OF LINEAR PROBING

13. QUADRATIC PROBING
 Quadratic probing operates by taking the original
hash index and adding successive values of an
arbitrary quadratic polynomial until an open slot is
found.
 h´ = (𝑥) = 𝑥 𝑚𝑜𝑑 𝑚
 ℎ(𝑥, 𝑖) = (ℎ´(𝑥) + 𝑖2)𝑚𝑜𝑑 𝑚
 We can put some other quadratic equations also
using some constants
 The value of i = 0, 1, . . ., m – 1. So we start from i =
0, and increase this until we get one free space.

19. PROPERTIES OF QUADRATIC PROBING

21. DOUBLE HASHING
 Double hashing uses the idea of applying a second
hash function to key when a collision occurs. is size
of hash table.
 First hash function is typically
 hash1(key) = key % TABLE_SIZE
 A popular second hash function is :
 hash2(key) = PRIME – (key % PRIME) where
PRIME is a prime smaller than the TABLE_SIZE.

29. REHASHING
 Rehashing is the process of re-calculating the
hashcode of already stored entries (Key-Value
pairs), to move them to another bigger size
hashmap when the threshold is reached/crossed.
Rehashing of a hash map is done when the number
of elements in the map reaches the maximum
threshold value.

32. EXTENDIBLE HASING
 Extendible hashing is a dynamically updateable
disk-based index structure which implements a
hashing scheme utilizing a directory.
 The index is used to support exact match queries,
i.e., find the record with a given key.
 Overflows are handled by doubling the directory
which logically doubles the number of buckets.

33. CONTENT BEYOND SYLLABUS
 RED BLACK TREES
Red Black Tree is a Binary Search Tree in which every node is
colored either RED or BLACK.
 Rules That Every Red-Black Tree Follows:
 Every node has a colour either red or black.
 The root of the tree is always black.
 There are no two adjacent red nodes (A red node cannot have
a red parent or red child).
 Every path from a node (including root) to any of its
descendants NULL nodes has the same number of black
nodes.
 http://www.btechsmartclass.com/data_structures/red-black-
trees.html

34.  THANK YOU !