Technology
What is Big O notation?
Big O notation is a way to describe how an algorithm's running time or memory grows as the input gets bigger. It focuses on the worst-case trend — like 'doubles when the input doubles' — so you can compare algorithms regardless of the computer.
See it, don’t just read it.
Watch a 2-minute lesson with voice + animation that explains big o notation.
Key things to understand
- 1It expresses how cost scales with input size, ignoring constant details.
- 2O(n) grows in step with the input; O(n²) grows much faster; O(log n) grows slowly.
- 3It captures the worst-case behavior for large inputs.
- 4It lets you compare algorithms' efficiency independent of hardware.
- 5Choosing a lower-order algorithm is what keeps software fast at scale.
Frequently asked questions
- What does O(n) mean?
- The work grows in direct proportion to the input size — double the data, double the time.
- Why ignore constants in Big O?
- For large inputs the growth rate dominates; whether a step takes 2 or 5 operations matters far less than whether cost grows linearly or quadratically.
- Is a lower Big O always better?
- Usually for large inputs, but for small inputs a 'worse' Big O algorithm with low overhead can actually run faster.