Time Complexity
Domain: Algorithms
🎯 Motivation
How the running time of an algorithm grows as the input size increases. This determines whether an algorithm is practical for large inputs.
📋 Concrete Example
A linear search through 100 items takes 100 steps. Through 1,000,000 items takes 1,000,000 steps. It scales as O(n). Binary search takes only about 20 steps for 1,000,000 items — O(log n).
🔗 Analogy
Time to find a book by scanning every shelf (O(n), linear) vs. using the catalogue to jump to the right shelf (O(log n), logarithmic). The catalogue scales far better as the library grows.