Data structures are methods for organizing and storing data in computer memory for efficient access and modification, including arrays, linked lists, stacks, queues, trees, and graphs. Their efficiency is assessed through time and space complexity, which measures how performance and memory usage scale with data size. Common operations on data structures include insertion, access, search, deletion, updating, traversal, and sorting.

1. Introduction to
Data Structures

2. Data Structures
• Data structures are ways of organizing and storing data in
computer memory so that they can be accessed and
modified efficiently.
• They are essentially containers that hold data in a specific
layout.
• Examples include arrays, linked lists, stacks, queues, trees,
and graphs.

3. Data Structures - Applications
• Arrays: Used in applications that require indexed access to
elements, such as image processing where each pixel needs to be
accessed using an index (or indices).
• Stacks: Used in undo functionality in software like text editors or
going back in a web browser, etc.
• Queues: Used in task scheduling systems.
• Trees: Used in databases and file systems to store hierarchical
data.
• Graphs: Used in social networks to represent connections between
users and in GPS (or navigation systems) to find the shortest path.

4. Efficiency of Data Structures
• Data structures are ways of organizing and storing data to
facilitate efficient operations.
• The efficiency of a data structure is evaluated based on how
quickly and effectively it supports various operations like
accessing, inserting, deleting, updating, and searching for
data.
• Typically, efficiency is divided into
• Time complexity
• Space complexity

5. Efficiency of Data Structures
• Time Complexity: Measures how the time to perform
operations changes with the size of the data.
• Example
• Array: Accessing an element by index is O(1) (constant time),
but inserting an element in the beginning can be O(n) (linear
time) due to shifting.

6. Efficiency of Data Structures
• Space Complexity: Measures the amount of memory used
by a data structure as it scales with the size of the data it
contains.
• Examples
• Array: An array with n elements typically has a space
complexity of O(n), as the memory usage grows linearly with
the number of elements.
• Linked List: A linked list generally has a space complexity of
O(n) because each node requires some memory to store the
data and a pointer to the next node.

7. Common operations on Data
Structures
• Some of the common operations performed on some data
structures are:
• Insertion
• Access
• Search
• Deletion
• Updation
• Traversal
• Sorting