Master Time & Space Complexity: Big-O Notation Explained (DSA Lecture 5)

Unlock the secrets of writing efficient code! 🚀

In this lecture, we dive deep into Time and Space Complexity—the most critical concept for cracking technical interviews and writing scalable software. We move beyond just memorizing formulas and focus on the "way of thinking" required to analyze algorithms.

We break down complex topics like Big-O notation, Time vs. Space trade-offs, and how to mathematically prove which approach is better using real-world examples like Sorting and Prime Number validation.

📝 What you will learn in this video:

1. Why "Time" isn't measured in seconds but in operations.
2. The difference between Big O (Worst Case), Omega (Best Case), and Theta (Average Case).
3. How to calculate complexity for loops, nested loops, and recursion.
4. Golden Rules for finding Big-O notation easily.
5. Visualizing complexity growth (Linear vs. Quadratic vs. Logarithmic).

Whether you are a beginner in DSA or preparing for coding interviews, this guide will help you choose the best algorithm every time.

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Timestamps / Chapters

[00:00] - Introduction: Why Efficiency Matters?
[00:37] - Time vs. Space Trade-off (Approach A vs. Approach B)
[03:51] - Real World Example: Bubble Sort vs. Merge Sort
[09:03] - Visualizing Complexity: The Growth Graph
[11:06] - Coding Problem: Finding Prime Numbers (Brute Force)
[13:42] - Optimizing the Prime Number Logic (Factor Pairs)
[18:40] - The Square Root Optimization (O(√n))
[24:45] - Definition of Time & Space Complexity
[29:48] - Asymptotic Notations: Big O, Omega, and Theta
[37:25] - 4 Golden Rules for Finding Big-O Complexity
[42:25] - Understanding O(log n) & Divide and Conquer
[47:19] - Nested Loops Example: Printing All Pairs (O(n²))
[52:16] - Common Complexities Cheat Sheet (Input Constraints)
[56:15] - Final Comparison Graph & Conclusion