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Data Structures & Algorithms - Data Structures Basics

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📌 1. Basic Concepts in Data Structures

1.1 Data

  • Raw facts, figures, or symbols that can be processed to generate meaningful information.
  • Example:
    • Numbers: 1, 2, 3, 4
    • Characters: ‘A’, ‘B’, ‘C’

1.2 Data Structure

  • A way of organizing and storing data efficiently.
  • Example: Arrays, Linked Lists, Trees, Graphs.

1.3 Data Type

  • Classification of data into predefined types.
  • Types:
    • Primitive Data Types: int, char, float, bool.
    • Derived Data Types: array, pointer, structure, union.

1.4 Abstract Data Type (ADT)

  • A mathematical model for a data structure that defines operations but hides implementation details.
  • Example: Stack, Queue, List.

📌 2. Operations on Data Structures

2.1 Insertion

  • Adding a new element to a data structure.
  • Example: Inserting an element in an array at index 2.

2.2 Deletion

  • Removing an element from a data structure.
  • Example: Deleting an element from a linked list.

2.3 Traversal

  • Visiting and processing each element in a data structure.
  • Example: Printing all elements in a linked list.

2.4 Searching

  • Finding an element in a data structure.
  • Example: Binary Search, Linear Search.

2.5 Sorting

  • Arranging elements in a particular order (ascending or descending).
  • Example: Quick Sort, Merge Sort.

📌 3. Complexity Analysis

3.1 Time Complexity

  • The time taken by an algorithm as a function of input size.
  • Example: O(n), O(log n), O(n²).

3.2 Space Complexity

  • The amount of memory used by an algorithm.
  • Example: O(1) for constant space, O(n) for linear space.

3.3 Big O Notation (O)

  • Represents the worst-case scenario of an algorithm.
  • Example: O(n²) for Bubble Sort.

3.4 Omega Notation (Ω)

  • Represents the best-case scenario of an algorithm.

3.5 Theta Notation (Θ)

  • Represents the average-case scenario of an algorithm.

📌 4. Types of Data Structures

4.1 Linear Data Structures

  • Elements are arranged sequentially.
  • Example: Arrays, Linked Lists, Stacks, Queues.

4.2 Non-Linear Data Structures

  • Elements are connected in a hierarchical manner.
  • Example: Trees, Graphs.

4.3 Static Data Structures

  • Size is fixed during compilation.
  • Example: Arrays.

4.4 Dynamic Data Structures

  • Size changes during execution.
  • Example: Linked Lists.

📌 5. Terms Related to Arrays

5.1 Index

  • Position of an element in an array, starting from 0.

5.2 One-Dimensional Array

  • Elements stored in a single row.

5.3 Multi-Dimensional Array

  • Arrays with more than one row/column.

📌 6. Terms Related to Linked Lists

6.1 Node

  • A unit containing data and a pointer to the next node.

6.2 Head

  • The first node in a linked list.

6.3 Tail

  • The last node in a linked list (points to NULL).

6.4 Singly Linked List

  • Each node has a pointer to the next node.

6.5 Doubly Linked List

  • Each node has pointers to both previous and next nodes.

6.6 Circular Linked List

  • The last node connects back to the first node.

📌 7. Terms Related to Stack

7.1 LIFO (Last In, First Out)

  • The last inserted element is removed first.

7.2 Push

  • Adds an element to the stack.

7.3 Pop

  • Removes the top element from the stack.

7.4 Peek (Top Element)

  • Retrieves the top element without removing it.

📌 8. Terms Related to Queue

8.1 FIFO (First In, First Out)

  • The first inserted element is removed first.

8.2 Enqueue

  • Adds an element to the queue.

8.3 Dequeue

  • Removes an element from the queue.

8.4 Circular Queue

  • The last position connects to the first position.

8.5 Priority Queue

  • Elements are dequeued based on priority.

📌 9. Terms Related to Trees

9.1 Root

  • The topmost node in a tree.

9.2 Parent and Child Nodes

  • A node that has sub-nodes is a parent, and sub-nodes are children.

9.3 Leaf Node

  • A node with no children.

9.4 Depth

  • Distance from the root node to a specific node.

9.5 Height

  • Maximum depth of a tree.

9.6 Binary Tree

  • Each node has at most two children.

9.7 Binary Search Tree (BST)

  • A binary tree where left child < parent < right child.

9.8 AVL Tree

  • A self-balancing BST.

9.9 Heap (Min-Heap, Max-Heap)

  • A complete binary tree with heap properties.

📌 10. Terms Related to Graphs

10.1 Vertex (Node)

  • A fundamental unit of a graph.

10.2 Edge

  • A connection between two vertices.

10.3 Degree of a Vertex

  • The number of edges connected to a vertex.

10.4 Adjacency Matrix

  • Matrix representation of a graph.

10.5 Adjacency List

  • List representation of a graph.

10.6 Directed vs Undirected Graph

  • Directed Graph: Edges have directions.
  • Undirected Graph: Edges do not have directions.

10.7 Weighted Graph

  • Edges have weights/costs.

10.8 DFS (Depth-First Search)

  • A graph traversal algorithm using a stack.

10.9 BFS (Breadth-First Search)

  • A graph traversal algorithm using a queue.

📌 11. Hashing and Hash Tables

11.1 Hash Function

  • A function that maps data to a fixed-size value.

11.2 Collision

  • When two inputs produce the same hash value.

11.3 Chaining

  • A technique to handle collisions using linked lists.

11.4 Open Addressing

  • A collision handling method where another empty slot is found.
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