A data structure is an organization of data items in a particular manner, together with a set of valid operations applied to this organization.

A data structure is a specialized, systematic format for organizing, storing, and managing data in computer memory so that operations can be executed efficiently.

In literature: 

Niklaus Wirth formalizes data structures::  Algorithms + Data Structures = Programs

Thomas H. Cormen et al. (Introduction to Algorithms): A data structure serves as the concrete physical implementation of an Abstract Data Type (ADT)

The following three core components describe it:

• Data Values: The set of primitive or complex values stored.

• Relationships: The logical arrangement (linear, hierarchical, or network) connecting data elements.

• Operations: The collection of algorithms permitted to manipulate and retrieve stored data.

Operations on Data Structures

• Access / Search-Locates a specific element or value within memory based on a key or index.

• Insertion-Adds a new element into a designated location within the structure.

• Deletion-Removes an existing element and reorganizes remaining memory references.

• Traversal-Accesses and processes every element in the structure sequentially or recursively exactly once.

• Sorting-Rearranges stored items into a specific order (e.g., numerical ascending or alphabetical).

• Merging-Combines elements from two separate structures into a single structure.

• Update-Replaces an existing element's value at a target reference or index.

Primitive vs. Non-Primitive

• Primitive Data Structures: Basic building blocks provided directly by programming languages (e.g., Integer, Float, Character, Boolean, Pointer).

• Non-Primitive Data Structures: Complex structures built from primitive types to aggregate multiple values (e.g., Arrays, Linked Lists, Trees).

Linear vs. Non-Linear

Linear Data Structures: Elements are linked sequentially in a single sequence, where each element connects directly to its predecessor and successor.

Array: A fixed-size, contiguous block of memory storing elements accessible via index.

Linked List: A sequence of nodes stored in non-contiguous memory connected via pointers (Singly, Doubly, or Circular).

Stack: A Last-In, First-Out (LIFO) structure where insertions (push) and deletions (pop) occur at one end.

Queue: A First-In, First-Out (FIFO) structure where items enter at the rear (enqueue) and exit at the front (dequeue).

Non-Linear Data Structures: Elements are arranged hierarchically or as a complex network rather than sequentially.

Tree: A hierarchical node-based structure consisting of a root and child subtrees (e.g., Binary Search Tree, AVL Tree, B-Tree).

Graph: A non-linear network of vertices (nodes) linked by edges, representing arbitrary relationships.

Hash Table: An associative dictionary mapping key-value pairs using a hash function for $O(1)$ average lookup time.

Heap: A specialized tree maintaining min or max heap properties for priority queue operations.

Static vs. Dynamic

• Static: Fixed memory size determined at compile time (e.g., standard Arrays).

• Dynamic: Variable memory capacity that grows or shrinks dynamically at runtime via heap allocation (e.g., Dynamic Arrays, Linked Lists).

A data type defines the kind of value that a variable can store, the amount of memory required to store it, the range of possible values, and the operations that can be performed on it

Primitive Data Types

Primitive data types are the basic built-in types a programming language provides.

char 

Character / small integer

1 byte

−128 to 127 or 0 to 255

'A'

Characters, symbols, text

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int

Integer

4 bytes

−2,147,483,648 to 2,147,483,647

100

Counting, indexing, IDs

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short

Small integer

2 bytes

−32,768 to 32,767

250

Memory-efficient integers

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long

Large integer

4/8 bytes

Implementation-dependent

100000L

Large integer values

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float

Decimal/real number

4 bytes

Approx. ±3.4 × 10³⁸

3.14f

Scientific calculations

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double

High-precision decimal

8 bytes

Approx. ±1.7 × 10³⁰⁸

3.14159

High-precision calculations

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Bool

Logical value

Implementation-dependent

0 or 1

1

True/false conditions

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void

No value

—

No value

void Functions with no return value

*Sizes and exact ranges can vary by C implementation. The ranges above are common for modern systems.

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Type Modifiers in C

C provides modifiers that change the size or range of integer types:

• signed

• unsigned

• short

• long

Examples:

• unsigned int age;

• short int marks;

• long int population;

• unsigned char code;

For example, a typical unsigned int has a range: 0 to 4,294,967,295

Non-primitive data types are built from primitive types and are generally used to represent collections or complex data structures.

Major Non-Primitive Types in C

Array -Collection of elements of the same data type

int marks[10];

Storing multiple values

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Structure-Collection of different data types under one name

struct Student

Records/entities

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Union-Different members share the same memory location

union Data

Memory-efficient representation

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Pointer-Stores the address of another variable

int *p;

Dynamic memory, linked structures

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String-Sequence of characters terminated by '\0'

char name[20];

Text processing

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User-Defined Data Types

C also supports:

• struct

• union

• enum

• typedef

Example:

struct Student {

    int rollNo;

    char name[50];

    float marks;

};

Here, Student represents a complex data entity containing different kinds of values.

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Data Types and Semantic Analysis

In semantic analysis, data types help determine whether values and operations are meaningful and valid.

For example:

int age = 20;

float marks = 85.5;

char grade = 'A';

The semantic analyzer determines:

• age → integer

• marks → floating-point value

• grade → character

• Whether assignments are type-compatible

• Whether operators are applicable

• Whether function arguments match parameter types

• Whether expressions produce valid results

Example:

int x;

float y;

x = y;   /*The semantic analysis phase checks the type compatibility between x and y.*/

Thus, data types provide the semantic meaning and constraints of values, making them fundamental to type checking, expression evaluation, symbol-table construction, and semantic analysis