Time and Space Complexity
Every programmer eventually comes across the terms time complexity and space complexity . These concepts are critical in writing efficient programs and are fundamental in coding interviews. In this post, we’ll dive deep into Big O , Big Ω , and Big Θ , understand how to analyze algorithms, and illustrate everything with diagrams and examples. 1. Why Do We Need Complexity Analysis? Imagine two algorithms solving the same problem. One takes 1 second for 1000 inputs, while the other takes 10 seconds . As input size grows, the difference becomes massive. Complexity analysis gives us a way to predict performance without running the program on all possible inputs. Diagram: Growth Rates Input size (n) → O(1): ■■■■■■■■■ (constant) O(log n): ■■■■■■■■■■■■■■ (slow growth) O(n): ■■■■■■■■■■■■■■■■■■■■■ (linear growth) O(n²): ■■■■■■■■■■■■■■■■■■■■■■■■■■■■■ (steep) O(2^n): skyrockets! 2. Big O, Big ...