Big O Notation: Mastering Time and Space Complexity
Unlock the power of Big O notation to analyze and optimize algorithm performance, enabling you to write efficient and scalable code.
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Introduction to Big O Notation
Unit 1: Understanding Big O Basics
What is Big O?
Time vs. Space
Asymptotic Analysis
Meet the Complexity Crew
Big O Isn't Timing!
Common Complexity Classes and Algorithm Analysis
Unit 1: Constant and Logarithmic Complexity
O(1): Constant Time
O(log n): Logarithmic
Logarithmic Examples
Space Complexity of O(log n)
Logarithmic Gotchas
Unit 2: Linear and Linearithmic Complexity
O(n): Linear Time
O(n) Examples
O(n log n): Linearithmic
Merge Sort Analysis
Quicksort and O(n log n)
Unit 3: Quadratic, Exponential, and Factorial Complexity
O(n^2): Quadratic Time
Bubble Sort Analysis
O(2^n): Exponential Time
Fibonacci Sequence
O(n!): Factorial Time
Unit 4: Dominant Terms and Scenario Analysis
Dominant Term
Simplifying Expressions
Best-Case Scenario
Worst-Case Scenario
Average-Case Scenario
Big O Notation and Data Structures
Unit 1: Arrays, Linked Lists, Stacks, and Queues
Arrays: Performance
Linked Lists: Analysis
Stack it Up: Big O
Queues: Performance
When to use Which?
Unit 2: Hash Tables
Hash Tables: The O(1)?
Collision Resolution
Hash Functions Matter
Load Factor & Rehashing
Hash Table Use Cases
Unit 3: Trees and Graphs
Trees: Traversal
Balanced vs Unbalanced
Graph Representations
Graph Traversal
Shortest Path Algorithms
Unit 4: Space Complexity Deep Dive
Auxiliary Space
Ints, Floats, and Strings
Booleans and Pointers
Data Structure Overhead
Space Optimization Tips
Advanced Big O Concepts and Applications
Unit 1: Recursive Algorithm Analysis
Recursion and Big O
Substitution Method
Master Theorem Intro
Master Theorem Cases
Limitations of Master
Unit 2: Space Complexity Deep Dive
Auxiliary Space Intro
Why Auxiliary Matters
Data Type Footprint
Object Space
Space Complexity Tips
Unit 3: Big O in Real-World Applications
Sorting Showdown
Searching Algorithms
Graph Traversal
Pathfinding Big O
Real World Impact
Unit 4: Amortized Analysis
Amortized Intro
Aggregate Method
Accounting Method
Potential Method
When to Use Amortized