1. APPLICATION OF TRIES

2. Why Trie Data Structure?
• Searching trees in general favor keys which are of
fixed size since this leads to efficient storage
management.
• However in case of applications which are retrieval
based and which call for keys varying length, tries
provide better options.
• Tries are also called as Lexicographic Search
trees.

3. Definition For Trie:
• A trie of order m may be empty.
• If not empty, then it consists of an ordered
sequence of exactly m tries of order m.
• The branching at any level of the trie is
determined only by the portion and not by the
whole word.
• Alphabetic keys require a trie of order 27(26 letters
of the alphabet + a blank) for their storage and

4. Representation Of Trie
• The trie have two category of node structures.
▫ Branch node
▫ Information node
• A branch node is merely a collection of LINK fields
each pointing either to a branch node or to an
information node.
• An information node holds the keys that is to be
stored in the trie.

5. Operations In Trie
• The three operations in the trie data Structure
are
• Searching a trie
• Insertion
• Deletion

6. Example
• Construct a Trie for the keys
001,100,111,011,010
STEP 1:
Insert (001,100)
0 1
001 100

7. Example
• STEP 2: 0 1
Insert(111)
0 1
001
100 111

8. Example
• STEP 3:
Insert(011) 0 1
0 1 0 1
001 011 100 111

9. Example
• STEP 4:
Insert(010) 0 1
0 1 0 1
001 100 111
010 011

10. INSERTION
• To Insert a key K into the trie we begin as we
would to search for the key k, possibly moving
down the trie.
• At the point where the LINK field of the branch
node leads to NIL, the key k is inserted as an
information node.

11. Insertion
• In the Above constructed trie INSERT A KEY
101. 0 1
0 1 0 1
001 111
010 011 100 101

12. Deletion
• The deletion of a key K from a trie proceeds as one
would to search for the key.
• On reaching the information node(node l)holding k, the
same is deleted.
▫ It need to be ensured the branch node to which node l
is linked accommodates other information node as well!
 If there is more than1 information node/if there is at
least one LINK field/or both ,then deletion id done.
 If it leaves the branch node with just one more key
,we delete the branch node and push the node to a
higher level
 If the situation leads to node being the only non
empty node , once again we delete the branch node
and push node to a higher level.

13. Deletion
• Delete 010: 0 1
0 1 0 1
001 111
010 011 100 101

14. Performance Of trie
• The performance of search trees is determined by the
number of keys that form the tree.
• The complexities of the search ,delete and insert
operations were given by O(h) where the height h is
dependent on the number of keys represented in the
search tree.
• In contrast, the performance of the trie is dependent on
the length of the key-The number of characters forming
the key rather than the number of keys itself.

15. APPLICATIONS OF TRIE DATA
STRUCTURES

16. TRIES IN AUTO COMPLETE
• Since a trie is a tree-like data structure in which each
node contains an array of pointers, one pointer for each
character in the alphabet.
• Starting at the root node, we can trace a word by
following pointers corresponding to the letters in the
target word.
• Starting from the root node, you can check if a word
exists in the trie easily by following pointers
corresponding to the letters in the target word.

17. AUTO COMPLETE
• Auto-complete functionality is used widely over
the internet and mobile apps. A lot of websites
and apps try to complete your input as soon as
you start typing.
• All the descendants of a node have a common
prefix of the string associated with that node.

19. AUTO COMPLETE IN GOOGLE SEARCH

20. WHY TRIES IN AUTO COMPLETE
• Implementing auto complete using a trie is easy.
• We simply trace pointers to get to a node that
represents the string the user entered. By
exploring the trie from that node down, we can
enumerate all strings that complete user’s input.

21. CRIMINOLOGY
• Suppose that you are at the scene of a crime and
observe the first few characters CRX on the
registration plate of the getaway car. If we have a
trie of registration numbers, we can use the
characters CRX to reach a subtrie that contains all
registration numbers that begin with CRX. The
elements in this subtrie can then be examined to
see which cars satisfy other properties that might
have been observed.

22. AUTOMATIC COMMAND COMPLETION
• When using an operating system such as Unix or
DOS, we type in system commands to accomplish
certain tasks. For example, the Unix and DOS
command cd may be used to change the current
directory.

23. Commands that have the prefix “ps”
• ps2ascii ps2pdf psbook psmandup psselect
• ps2epsi ps2pk pscal psmerge pstopnm
• ps2frag ps2ps psidtopgm psnup pstops
• ps2gif psbb pslatex psresize pstruct
• Figure 10 Commands that begin with "ps"
We can simply the task of typing in commands by providing a command
completion facility which automatically types in the command suffix once the
user has typed in a long enough prefix to uniquely identify the command.
For instance, once the letters psi have been entered, we know that the
command must be psidtopgm because there is only one command that has
the prefix psi. In this case, we replace the need to type in a 9 character
command name by the need to type in just the first 3 characters of the
command!

24. LONGEST PREFIX MATCHING
• Longest prefix match (also called Maximum prefix length match)
refers to an algorithm used by routers in Internet Protocol (IP)
networking to select an entry from a routing table .
• Because each entry in a routing table may specify a network, one
destination address may match more than one routing table entry.
The most specific table entry — the one with the highest subnet
mask — is called the longest prefix match. It is called this because it
is also the entry where the largest number of leading address bits in
the table entry match those of the destination address.

25. For example, consider this IPv4 routing table (CIDR
notation is used):
192.168.20.16/28
192.168.0.0/16
When the address 192.168.20.19 needs to be looked
up, both entries in the routing table "match". That is, both
entries contain the looked up address. In this case, the
longest prefix of the candidate routes is
192.168.20.16/28, since its subnet mask (/28) is higher
than the other entry's mask (/16), making the route more
specific.

26. • A network browser keeps a history of the URLs of
sites that you have visited. By organizing this history
as a trie, the user need only type the prefix of a
previously used URL and the browser can complete
the URL.

28. SPELL CHECKERS
• Spell checkers are ubiquitous. Word
processors have spell checkers, as
do browser-based e-mail clients.
They all work the same way: a
dictionary is stored in some data
structure, then each word of input is
submitted to a search in the data
structure, and those that fail are
flagged as spelling errors

29. SPELL CHECKERS
• There are many appropriate data structures to
store the word list, including a sorted array
accessed via binary search, a hash table, or a
bloom filter. In this exercise you are challenged
to store the word list character-by-character in a
trie.

30. Spell Check..

31. Spell Check..
a bc… 0 p …z
0
a e i u
1
a g s pug
page 2 pig
peg pest

32. PHONE BOOK SEARCH..
• Trie data structure are mostly used to search for
a contact on phone book.
• Prefix Matching
a = a*

33. Example
a bc… r s …z Contacts in Phone book
0 alberto
t ram
a sankar
alberto ram 1 star
stella
a e
sanka 2
r
star stella

34. PHONE BOOK SEARCH..
• Suffix Matching
• Can be used to index all E
suffixes in a text in order to
carry out fast full text
searches.

35. TRIES IN T9
• T9 is a technology used on many mobile phones to
make typing text messages easier.
• The idea is simple - each number of the phone's keypad
corresponds to 3-4 letters of the alphabet.
• Many phones will notice when you type in a word that is
not in its dictionary, and will add that word. Others keep
track of the frequency of certain words and favor those
words over other words that have the same sequence of
keypresses.

36. TRIES IN T9
• How does a T9 dictionary work?
• It can be implemented in several ways, one of
them is Trie. The route is represented by the
digits and the nodes point to collection of words.
• T9 works by filtering the possibilities down
sequentially starting with the first possible
letters.

37. TRIES IN T9
• It can be implemented using nested hash tables
as well, the key of the hash table is a letter and
on every digit the algorithm calculates all
possible routes (O(3^n) routes).
• For example, If we type '4663' we get 'good'
when we press down button we get 'gone' then
'home' etc..