## About Data Structures

- Data structures are fundamental components of computer science and programming.
- They are used to store, organize, and manage data efficiently, allowing for quick retrieval, modification, and processing of information.
- Data structures serve as the building blocks for various algorithms and applications, enabling developers to solve complex problems and optimize software performance.

## Definition

Data structures are collections of data elements or values that are organized and stored in a specific way to facilitate various operations such as insertion, deletion, searching, and traversal.

## Purpose

- Data structures are used to manage and manipulate data in memory or on storage devices.
- They play a crucial role in designing and implementing algorithms, data storage, and data retrieval.

## Types Of Data Structures

**Primitive Data Types**: These are the basic data types provided by programming languages, like integers, floating-point numbers, characters, and booleans.**Arrays**: Ordered collections of elements of the same data type, accessed by an index.**Linked Lists**: A sequence of elements where each element points to the next one. Linked lists can be singly or doubly linked.**Stacks**: A linear data structure that follows the Last-In-First-Out (LIFO) principle, often used for managing function calls, undo operations, and more.**Queues**: A linear data structure that follows the First-In-First-Out (FIFO) principle, commonly used for task scheduling, order processing, and more.**Trees**: Hierarchical structures with a root element and child nodes. Types include binary trees, binary search trees, and AVL trees.**Graphs**: Non-linear data structures consisting of nodes connected by edges. Graphs can be directed or undirected and are used to represent relationships between data points.**Hash Tables**: Data structures that map keys to values for efficient retrieval, insertion, and deletion of data.**Heaps**: Specialized trees that satisfy the heap property, often used in priority queues and sorting algorithms.

## Operations On Data Structures

**Insertion:**Adding data to the structure.**Deletion:**Removing data from the structure.**Search:**Finding specific data within the structure.**Update:**Modifying existing data.**Traversal:**Visiting all elements in a structured manner.**Sorting:**Arranging elements in a specific order.**Access:**Retrieving data at a specific location.

## Selection Of Data Structures

Choosing the appropriate data structure depends on the specific requirements of your application, including the frequency of data operations, memory constraints, and the type of data being stored.

## Time & Space Complexity

Data structures have associated time and space complexities for each operation, and it’s crucial to select the right structure to optimize your application’s performance.

## Implementation

Data structures can be implemented in various programming languages using classes, structs, or built-in language features.

## Linear Data Structures

- Linear data structures are a type of data structure in computer science that organize and store data elements in a sequential manner, where each element has a distinct predecessor and successor, except for the first and last elements.
- These structures are used to represent and manipulate data in a linear or one-dimensional fashion.

## Types Of Linear Data Structures

**Arrays**: An array is a collection of elements of the same data type stored at contiguous memory locations. Elements in an array can be accessed by their index, making it easy to retrieve and manipulate data. However, the size of an array is typically fixed.**Linked Lists**: Linked lists consist of nodes where each node contains data and a reference (or a pointer) to the next node in the sequence. There are several variations of linked lists, including singly linked lists (each node points to the next node), doubly linked lists (each node has references to both the next and previous nodes), and circular linked lists (the last node points back to the first node).**Stacks**: A stack is a linear data structure that follows the Last-In-First-Out (LIFO) principle. You can think of it as a collection of items stacked on top of each other. Elements are added or removed from the top of the stack. Stacks are commonly used for function call management, expression evaluation, and other applications.**Queues**: A queue is a linear data structure that follows the First-In-First-Out (FIFO) principle. It’s like a line of people waiting, where the first person in line is the first to be served. Queues are used for tasks such as process scheduling, print job management, and more. Common variations include priority queues and double-ended queues (deque).**Vectors (Dynamic Arrays)**: Vectors are similar to arrays but can dynamically resize themselves as elements are added or removed. They combine the benefits of arrays and linked lists, allowing for efficient random access like arrays while also providing flexibility.**Tuples**: Tuples are ordered collections of elements, often of different data types. They are typically used to group related data together. Tuples are generally immutable, meaning their elements cannot be changed after creation.**Lists (Python-specific)**: In Python, a list is a versatile linear data structure that can hold elements of different data types. It is implemented as an array list, providing dynamic resizing and various methods for element manipulation.**Strings**: Strings are sequences of characters, making them a linear data structure. They are often used to represent text and can be manipulated using various string operations.

## Non-Linear Data Structures

- Non-linear data structures are data structures in computer science that do not organize their elements in a linear, sequential manner like arrays or linked lists. In a non-linear data structure, elements are interconnected in a more complex fashion, often forming hierarchies, networks, or relationships that do not follow a simple, one-after-another order.
- These structures are used to represent more complex relationships and data organization in various applications.

## Types Of Non-Linear Data Structures

**Trees****Binary Tree:**A tree structure where each node has at most two child nodes.**Binary Search Tree (BST):**A binary tree where the left child is smaller, and the right child is greater than the parent node.**AVL Tree:**A self-balancing binary search tree where the height difference between left and right subtrees is limited.**Red-Black Tree:**A type of self-balancing binary search tree with rules governing the coloring of nodes.**B-Tree:**A tree structure used in databases and file systems for efficient searching and sorting.**Trie (Prefix Tree):**A tree-like structure used for storing a dynamic set of strings, often used in text processing.

**Graphs****Directed Graph (DiGraph):**A graph in which edges have a direction, i.e., they go from one node to another.**Undirected Graph:**A graph in which edges have no direction, meaning they connect two nodes without a specific start or end.**Weighted Graph:**A graph where each edge has an associated weight or cost.**Directed Acyclic Graph (DAG):**A directed graph with no cycles, commonly used in topological sorting and optimization problems.**Bipartite Graph:**A graph whose vertices can be divided into two disjoint sets such that no two vertices within the same set are connected by an edge.

**Heaps****Binary Heap:**A binary tree that satisfies the heap property, either in the form of a max-heap or min-heap.**Priority Queue:**An abstract data type that supports efficient retrieval of the highest-priority element.

**Hash Tables****Hash Map:**A data structure that uses a hash function to map keys to values, providing fast lookup and insertion.**Hash Set:**A data structure that stores a set of unique elements using a hash function.**Hash Table with Open Addressing or Separate Chaining:**Variants of hash tables that handle collisions in different ways.

**Skip List:**A data structure that allows for efficient search, insertion, and deletion operations by maintaining multiple layers of linked lists.**Quadtree and Octree:**Tree structures used for spatial partitioning in two and three dimensions, respectively, often in computer graphics and geographic information systems (GIS).**Radix Tree:**A tree structure used for storing and searching for strings with keys that can be represented as sequences of characters.

## Abstract Data Type

- An Abstract Data Type (ADT) is a high-level mathematical model for representing data and the operations that can be performed on that data.
- It defines a set of values and a set of operations that can be performed on those values, without specifying how these operations are implemented.
- ADTs are used to abstractly describe the behavior of data structures, focusing on what the data structure does rather than how it does it.

## Key Characteristics Of An Abstract Data Type

**Data and Operations**: An ADT encapsulates both data and the operations that can be performed on that data. It defines a set of operations that can be be used to manipulate the data but doesn’t concern itself with the internal details of how these operations are implemented.**Encapsulation**: ADTs provide encapsulation, meaning that the data and the operations are bundled together into a single unit. This allows for the hiding of the internal details of the data structure, exposing only the necessary interfaces to interact with it.**Information Hiding**: The internal representation of the data is hidden from the user of the ADT. Users of the ADT don’t need to know how the data is stored or manipulated internally. They only need to understand the specified interface and behavior.**Data Integrity**: ADTs often come with a set of constraints and invariants that should be maintained. The ADT’s operations are responsible for ensuring that these constraints are upheld.**Reusability**: ADTs are designed to be reusable. They can be implemented in various programming languages and used in different applications without modification to the underlying code, as long as the interface remains consistent.**Abstraction**: ADTs provide an abstraction layer that separates the logical view of data from its physical implementation. This abstraction allows for modular and more maintainable software design.

## Examples Of Common ADTs include

**Stack**: An ADT that represents a last-in, first-out (LIFO) data structure with operations like push and pop.**Queue**: An ADT that represents a first-in, first-out (FIFO) data structure with operations like enqueue and dequeue.**List**: An ADT that represents a collection of items with operations like insertion, deletion, and retrieval.**Dictionary (or Map)**: An ADT that stores key-value pairs with operations for adding, removing, and retrieving values associated with specific keys.**Set**: An ADT that represents a collection of unique elements with operations for adding, removing, and testing for membership.