Asymptotic notation is a mathematical tool used to describe the behavior of algorithms as the input size grows. It is used to classify algorithms according to how fast they grow or how much memory they use.
There are three main properties of asymptotic notation:
- Time complexity: This refers to how long an algorithm takes to run as the input size increases. Time complexity is usually expressed in terms of the number of basic operations the algorithm performs.
- Space complexity: This refers to how much memory an algorithm uses as the input size increases. Space complexity is usually expressed in terms of the number of variables the algorithm needs to store.
- Asymptotic behavior: This refers to how the time or space complexity of an algorithm grows as the input size increases. There are three main categories of asymptotic behavior:
- O(1), which means the algorithm has a constant time or space complexity and does not depend on the input size.
- O(n), which means the algorithm has a linear time or space complexity and grows linearly with the input size.
- O(n^c), where c is a constant, which means the algorithm has a polynomial time or space complexity and grows faster than O(n) but slower than O(n^2).