Lecture Notes on Data Structures and Algorithms

Introduction

• Core concepts for upcoming video tutorials.
• Importance of data structures:
  • Organizes data efficiently for access, querying, and updating.
  • Essential for fast algorithms.
  • Creates cleaner, more understandable code.

Data Structures

Definition

• Data structure: Way of organizing data for efficient usage.

Importance

• Essential for powerful algorithms.
• Helps manage data naturally.
• A key factor differentiating good programmers from excellent ones.

Abstract Data Types

Definition

• Abstract Data Type (ADT): Abstraction of a data structure providing only the interface.
• Example: Modes of transportation from A to B.
  • Walking, biking, and trains analogous to data structures.

Computational Complexity

Big O Notation

• Standardizes time and space complexity analysis.
• Focuses on worst-case scenarios.
• Common complexities:
  • Constant time: O(1)
  • Logarithmic time: O(log n)
  • Linear time: O(n)
  • Quadratic time: O(n²)
  • Exponential time: O(2^n)

Properties

• Big O cares about performance as input size increases.
• Ignore constants and less significant terms.

Arrays

Definition

• Static array: Fixed-length, indexable container of elements.

Usage

• Used in various programming scenarios.
• Common operations:
  • Access: O(1)
  • Search: O(n)
  • Insert/Delete: O(n) for static, O(1) amortized for dynamic arrays.

Linked Lists

Definition

• Singly and doubly linked lists: Sequential list of nodes holding data.

Characteristics

• Nodes contain pointers to next (and previous) nodes.
• Common usage in implementing lists, stacks, queues, etc.

Stacks

Definition

• Stack: Last In, First Out (LIFO) data structure.

Operations

• Push: Add to stack.
• Pop: Remove from top of stack.

Applications

• Used in function calls, backtracking algorithms, etc.

Queues

Definition

• Queue: First In, First Out (FIFO) data structure.

Operations

• Enqueue: Add to back.
• Dequeue: Remove from front.

Applications

• Used in scheduling tasks, breadth-first search in graphs, etc.

Priority Queues

Definition

• Abstract data type where each element has a priority.

Operations

• Insert, pull highest priority, update priorities.

Applications

• Used in Dijkstra's algorithm, scheduling processes, etc.

Hash Tables

Definition

• A data structure mapping keys to values using a hash function.

Operations

• Insertion, deletion, and searching.

Collision Resolution

• Separate chaining: Uses linked lists for collisions.
• Open addressing: Probes for next empty slot.

Summary of Existing Data Structures

• Arrays, linked lists, stacks, queues, priority queues, trees: Each with specific use cases and complexities.
• Importance of choosing the right data structure for the task at hand.

Conclusion

• Data structures are foundational for efficient algorithms.
• Understanding how to implement and use them is crucial for programming success.