Data Structures

1. Data Structures

2. Content
1. Data Structure
2. Linear Data Structure
3. Array
4. Linked List
5. Stack
6. Queue
7. Non-Linear Data Structure
8. Tree
9. Graph

3. Data Structure
A way of organizing data in computer memory so it that can be used effectively. The
idea is to reduce time and space complexities of different operations.
Data Structure Hierarchy

4. Linear Data Structure
List of Linear Data Structures
Array
Array is data structure used to store homogeneous
elements at the contiguous locations
Linked List
A linked list is sequence of elements and each element
is separate object consist of 2 items data and reference
to next node.
Stack
A stack is an abstract data type with principle of LIFO
(last in , first out).
Queue
A queue is another ADS with principle of FIFO (first
in, first out).

5. Arrays
Array is collection of items stored at a contiguous locations. The idea is to store
multiple items of same type together.
List of Basic Operations on Array
Insertion O(n)
Adding an element at give index.
Deletion O(n)
Remove the element at given index.
Search O(n) or Sorted Array O(log n)
Searches an element using given value.
Traverse O(n)
Fetch each element one by one.
Access O(1)
Get an element value of at given index.

6. Linked List
Linked List is a sequence of nodes which contains items. Each node contains data
and link to next node.
Types of Linked List
Simple Linked List
Every node in list store next node link and last node
has NULL as link.
Doubly Linked List
Every node in list has 2 links one to the next node
and other to the previous node.
Circular Linked List
It is similar to simple linked list, except last node
link reference to first node.

7. Linked List (cont.)
List of Basic Operations on Linked List
Insertion O(1)
New Node can added as first, or at after current
reference or as last Node.
Deletion O(1)
Existing Node can deleted as first, or after current
reference or as last Node.
Search O(n)
Searches an element using given value.
Access O(n)
To get an element has to traverse from head node.
Head => 1 => 3 => NULL
Head => 0 => 1 => 3 => NULL
Head => 0 => 1 => 2 => 3 => NULL
Head => 0 => 1 => 2 => 3 => 4 => NULL
Head => A => B => C => D => E => NULL
Head => B => C => D => E => NULL
Head => B => D => E => NULL
Head => B => D => NULL

8. Stack
A Stack is Abstract Data Type (ADT) like real-world stack allows operations at one
end only or it is called as Last-In-First-Out (LIFO).
List of Basic Operations on Stack
Push O(1)
Adding an element at top of the stack.
Pop O(1)
Remove the element from top of the stack.
Access O(n)
Element can be access using top pointer.

9. Queue
A Queue is Abstract Data Type (ADT) like real-world queue allows operations at two
end or it is called as First-In-First-Out (FIFO).
List of Basic Operations on Queue
Enqueue O(1)
Adding an element at rear or end of the queue.
Dequeue O(1)
Remove the element from front of the queue.
Access O(n)
An element can be access in queue using front
or rear pointer.

10. Non-Linear Data Structure
It is a data structure in which a data element is connected to several other data
elements.
List of Non-Linear Data Structures
Tree
It is a hierarchical data structure
Graph
It is pervasive data structure

11. Tree
Type of Trees data structure
Binary Tree
It is a tree in which each node has at most 2 children
Binary Search Tree
It is similar to BT, but left child always less than parent and
right is always greater than parent
Red Black Tree
It is self-balancing BST where each node has an extra bit to
represent color.
AVL Tree
It is self-balancing BST where height of left and right
subtrees cannot be more than one.
Binary Heap
It is complete tree, with heap ordering property i.e. Root
node value is either Max or Min of its children.
Tree is a Abstract Data type (ADT), that simulates a hierarchical tree structure with root
value and subtrees of children with a parent node, represented as a set of linked node.

12. Binary Search Tree (BST)
BST, is a tree in which each node has at most 2 children and left child node key
always less than parent node and right child key is always greater than parent node
List of Basic Operations on BST
1. Insertion O(h*)
Adding an element in tree.
2. Deletion O(h*)
Remove the element from tree.
3. Search O(h*)
Search an element in a tree.
Traversal Order
1. Pre-order : Root => Left => Right
2. In-order : Left => Root => Right
3. Post-order : Left => Right => Root
4. Level-order: Level 0 => Level 1 => …Level n
* Height of the tree

13. Graph
A Graph is a non-linear data structure group of vertices and edges, where edges are used
to connect vertices. It can be seen as a cyclic tree, where the vertices(Node) maintain
complex relationship among them instead of having parent child relationship.

14. Graph (cont.)
1. Undirected Graph
(a) An undirected graph G having five vertices and seven edges. (b) An adjacency-list representation of G.
(c) The adjacency-matrix representationof G.
2. Directed Graph
(a) A directed graph G having six vertices and eight edges. (b) An adjacency-list representation of G.
(c) The adjacency-matrix representation of G.

15. Graph (cont.)
Depth First Search (DFS) Breadth First Search (BFS)
Graph Traversal

16. Questions?