^{What is a data structure?}

Data structure is a way of representation of relationship between logical related data elements. Data may be organized in many different ways . The logical or mathematical model of particular organization of data is called data structure.

Mathematically

In Mathematically we can define data structures

DS= organized data + Allowed operator.

In data structure, decision on the operation such as storage, retrieval and access must be carried out between the logically related data elements only.

Data structure always describe about data representation in memory.

^{Here are some examples of data structures:}

**Arrays:**Arrays are a fixed-size collection of items of the same data type. Arrays are very efficient for accessing data in a sequential order, but they can be inefficient for inserting and deleting data.**Linked lists:**Linked lists are a dynamic data structure that can grow and shrink as needed. Linked lists are efficient for inserting and deleting data, but they can be inefficient for accessing data in a sequential order.**Stacks:**Stacks are a linear data structure that follows the LIFO (Last In First Out) principle. Elements are added to the top of the stack and removed from the top of the stack. Stacks are often used to implement function calls and backtracking algorithms.**Queues:**Queues are a linear data structure that follows the FIFO (First In First Out) principle. Elements are added to the back of the queue and removed from the front of the queue. Queues are often used to implement buffers and job scheduling systems.**Trees:**Trees are a hierarchical data structure that consists of nodes and edges. Each node can have zero or more child nodes. Trees are often used to implement search trees, binary trees, and trie data structures.**Graphs:**Graphs are a non-linear data structure that consists of nodes and edges. Unlike trees, graphs can have cycles. Graphs are often used to represent networks, social media relationships, and transportation routes.**Hash tables:**Hash tables are a data structure that maps keys to values. Hash tables are very efficient for searching for data, but they can be inefficient for inserting and deleting data.

^{Why are Data Structures Important?}

^{Why are Data Structures Important?}

Data structures are important for a number of reasons:

**Efficiency:**Data structures can help to improve the efficiency of computer programs by reducing the amount of time and space required to access and manipulate data.**Scalability:**Data structures can help to make computer programs more scalable by allowing them to handle large amounts of data without sacrificing performance.**Reliability:**Data structures can help to improve the reliability of computer programs by reducing the risk of errors.**Maintainability:**Data structures can help to make computer programs more maintainable by making them easier to understand and modify.

## Applications of data structure

Compiler design

Operating system design like memory management(linked list + hash map)

Database management system( B-tree)

File systems(trees)

Statistic analysis package (data mining alogorithms)

Network data model (graph)

Electronic circuit and simulation ( graphs )

Numerical analysis

Artificial intelligence

## Type of data structure

Data structure is normally divide into two type

- Primitive data structure.
- Non primitive data structure

### Primitive data structure

These are basic data structure and are directly operated upon by the machine instruction.

Example – integer float

### Non primitive data structure

These are more sophisticated data structure these are divided from Primitive data structure.

the Non primitive data structure emphases unstructured of a group of heterogeneous and non homogenous data .

^{Examples of Data Structures in Use}

Here are some examples of how data structures are used in real-world applications:

**Arrays:**Arrays are used to store data in many different types of applications, such as web pages, databases, and video games.**Linked lists:**Linked lists are used to implement many different data structures, such as stacks, queues, and trees.**Stacks:**Stacks are used to implement function calls and backtracking algorithms.**Queues:**Queues are used to implement buffers and job scheduling systems.**Trees:**Trees are used to implement search trees, binary trees, and trie data structures.**Graphs:**Graphs are used to represent networks, social media relationships, and transportation routes.**Hash tables:**Hash tables are used to implement dictionaries and caches.