Understanding Big O Notation

Big O notation is a mathematical notation used to describe the limiting behavior of a function when the argument tends towards a particular value or infinity. In computer science, it's used to classify algorithms according to how their run time or space requirements grow as the input size grows.

What is Time Complexity?

Time complexity describes how the runtime of an algorithm increases as the input size grows. Common time complexities include:

**O(1)**: Constant time - the algorithm takes the same amount of time regardless of input size

**O(log n)**: Logarithmic time - binary search

**O(n)**: Linear time - simple loops

**O(n log n)**: Linearithmic time - efficient sorting algorithms

**O(n²)**: Quadratic time - nested loops

**O(2ⁿ)**: Exponential time - recursive algorithms with branching

What is Space Complexity?

Space complexity describes how much memory an algorithm uses relative to the input size. It's analyzed similarly to time complexity.

Understanding Big O notation is crucial for writing efficient code and choosing the right algorithm for your problem.