gen-briefly-explain-asymptotic-big-o-complexity-and-one-common-m-123f

Briefly explain asymptotic (big-O) complexity and one common misconception about it.

# Asymptotic (Big-O) Complexity **Big-O notation** describes how an algorithm's resource requirements (usually time or space) grow as input size increases. It focuses on the dominant term and ignores constants. For example: - **O(1)**: constant time (array access) - **O(n)**: linear time (scanning a list) - **O(n²)**: quadratic time (nested loops) - **O(log n)**: logarithmic time (binary search) ## Common Misconception **"O(n) is always faster than O(n²)"** This is false for small inputs or when constants differ significantly. An O(n²) algorithm with a tiny constant factor might outperform an O(n) algorithm with a large constant for practical input sizes. Example: An O(n²) algorithm taking 0.001·n² microseconds will be faster than an O(n) algorithm taking 1000·n microseconds when n < 1,000,000. Big-O describes *asymptotic* behavior—what happens as n approaches infinity—not necessarily real-world performance for your specific use case.