A trie is a tree-like data structure that stores strings and words by structuring nodes to represent letters. Each node contains branches for the letters of the alphabet, allowing words to be retrieved by traversing down the branches. Tries are efficient for storing and retrieving sets of words because no hash function is needed, unlike hash tables, though tries use more memory due to empty nodes. Common uses of tries include phone books, search engines, dictionaries, linguistics, and programming command completion.

1. Tries : A Brief Analysis
ADITYA NIHAL KUMAR SINGH
2015UGCS061

2. What is a trie?
A trie is a tree-like data structure whose nodes store the letters of an alphabet. By
structuring the nodes in a particular way, words and strings can be retrieved from the
structure by traversing down a branch path of the tree.
There are a handful of different ways to represent something as seemingly simple as a set
of words. For example, a hash or dictionary is one that we’re probably familiar with, as is
as hash table.
But there’s another structure that was created to solve the very problem of representing a
set of words: a trie. The term “trie” comes from the word retrieval, and is usually
pronounced “try”, to distinguish it from other “tree” structures.

3. How does a trie
look like?

4. Where do the
letters of
different words
live if the root
node doesn’t
house them all?

5. Giving Trie
traversal a try

6. Pseudo code to check whether a single word
exists in a dictionary of words or not
boolean check(String s) {
for(every char in String s) {
if(child node is null) {
return false;
}
}
return true;
}

7. How do we insert the letters into their correct places?

8. Pseudo code for insertion into a tire
void insert(String s) {
for(every char in string s) {
if(child node belonging to current char is null) {
child node=new Node();
}
current_node=child_node;
}
}

11. HASH TABLE
Array + Linked List
Hash function is needed
Memory is not wasted as much
TRIE
Array + Pointers
No hash function is required
Takes up a lot of memory with
empty or null pointers
Hash Tables Vs Tries

12. How a trie changes as it grows?
As trie grows in size, less work must be done to add a value,
since the “intermediate nodes”, or the branches of the trie
have already been build up.
Each time we add a word’s letter, we need to look at 26
references, since there are only 26 possibilities in the
alphabet. This number never changes in the context of our
trie, so it is a constant value.

13. Big O notation of a Trie
The worst case runtime of creating a trie structure is
dependent on how many words the trie contains, and how
long they might potentially be. This is known as O(m.n)
time, where m is the longest word and n is the total number
of words.
The time of searching, inserting & deleting from a trie
depends on length of the word a and total number of words
: O(a.n)

14. Uses of Tries
Phone Book
Google search
T9 dictionary
Criminology
Linux commands completion
And many more…

15. Resources
Digit-based sorting and data structures, Professor Avrim Blum
Lecture Notes on Tries, Professor Frank Pfenning
Algorithms: Tries, Robert Sedgewick and Kevin Wayne
Tries, Brilliant Learning
Tries, Daniel Ellard
Tries, Harvard CS50

16. Thank you.