**Data structures Notes B.Tech 3rd Sem**: are ways of organizing and storing data so that they can be accessed and modified efficiently. They are fundamental to designing efficient algorithms and play a critical role in software development.

## Arrays

**Definition: **A collection of elements identified by index or key.

**Data Structures Notes B.Tech 3rd Sem**

Characteristics:

- Fixed size.
- Elements of the same type.
- Indexed access (0-based in most programming languages).

Operations:

Data Structures Notes B.Tech 3rd Sem

- Access: O(1)
- Insertion: O(n) (at worst case, when inserting at the beginning or middle)
- Deletion: O(n) (at worst case, when deleting from the beginning or middle)
- Applications: Used in situations where data size is known and doesn’t change, like lookup tables.

## Linked Lists

Definition: A linear collection of data elements, called nodes, where the linear order is given by means of pointers.

Types:

- Singly Linked List: Each node points to the next node.
- Doubly Linked List: Each node points to both the next and previous nodes.
- Circular Linked List: The last node points to the first node.

Operations:

- Access: O(n)
- Insertion: O(1) (at the beginning)
- Deletion: O(1) (at the beginning)
- Applications: Useful in scenarios where the size of data is unknown or changes frequently, like in dynamic memory allocation.

## Stacks | Data Structures Notes B.Tech 3rd Sem

Definition: A collection of elements that follows the Last In First Out (LIFO) principle.

Operations:

- Push (insert element): O(1)
- Pop (remove element): O(1)
- Peek/Top (access top element): O(1)
- Applications: Used in recursion, undo mechanisms in text editors, and expression evaluation.

## Queues | Data Structures Notes B.Tech 3rd Sem

Definition: A collection of elements that follows the First In First Out (FIFO) principle.

Types:

- Simple Queue: Basic FIFO structure.
- Circular Queue: The last position is connected back to the first position.
- Priority Queue: Elements are dequeued based on priority.

Operations:

- Enqueue (insert element): O(1)
- Dequeue (remove element): O(1)
- Peek/Front (access front element): O(1)
- Applications: Used in scheduling algorithms, buffering data streams, and handling requests in web servers.

## Trees

Definition: A hierarchical data structure with nodes connected by edges.

Types:

- Binary Tree: Each node has at most two children.
- Binary Search Tree (BST): A binary tree with the left child node having values less than the parent and the right child node having values greater than the parent.
- AVL Tree: A self-balancing binary search tree.
- B-tree: A self-balancing search tree for database and file systems.

Operations: Data Structures Notes B.Tech 3rd Sem

- Search: O(log n) for balanced trees.
- Insertion: O(log n) for balanced trees.
- Deletion: O(log n) for balanced trees.
- Applications: Used in hierarchical data representation, database indexing, and network routing algorithms.

## Graphs

Definition: A collection of nodes (vertices) and edges connecting pairs of nodes.

Types:

- Undirected Graph: Edges have no direction.
- Directed Graph (Digraph): Edges have a direction.
- Weighted Graph: Edges have weights.

Representation:

- Adjacency Matrix
- Adjacency List

Operations:

- Traversal (BFS, DFS): O(V + E)
- Shortest Path (Dijkstra’s, Floyd-Warshall): Varies based on the algorithm.
- Applications: Used in network analysis, social networks, and finding shortest paths in maps.

## Hash Tables | Data Structures Notes B.Tech 3rd Sem

Definition: A data structure that maps keys to values using a hash function.

Operations:

- Insertion: O(1) (average case)
- Deletion: O(1) (average case)
- Search: O(1) (average case)

Collision Handling:

- Chaining: Store multiple elements in the same bucket using a linked list.
- Open Addressing: Find the next open slot using a probing sequence.
- Applications: Used in implementing associative arrays, database indexing, and caches.

## Heaps

Definition: A special tree-based data structure that satisfies the heap property.

Types:

- Max-Heap: The key of each node is greater than or equal to the keys of its children.
- Min-Heap: The key of each node is less than or equal to the keys of its children.

Operations: Data Structures Notes B.Tech 3rd Sem

- Insertion: O(log n)
- Deletion: O(log n)
- Peek (Max or Min): O(1)
- Applications: Used in priority queues, heap sort, and graph algorithms (like Prim’s and Dijkstra’s).

Conclusion | Data Structures Notes B.Tech 3rd Sem

Data structures are essential tools for organizing and managing data efficiently. Understanding their characteristics, operations, and applications is crucial for solving complex problems and designing efficient algorithms. Whether it’s for basic programming tasks or advanced computing systems, the right choice of data structure can significantly impact performance and scalability.

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