An algorithm’s efficiency often depends on the amount of time, storage, and other resources to execute the algorithm. But, when you calculate the complexity of an algorithm, it does not provide the exact amount of resources required. Therefore, developers often measure the complexity in a general form (notation), and the expressions are known as asymptotic notations. This article at GeeksforGeeks explains the concept of asymptotic analysis and various notations used to analyze any algorithm.
What is Asymptotic Analysis?
When a developer writes an algorithm for a particular computational problem, they design it in such a way that it gives the best results, especially in terms of time and memory used. Furthermore, coders must ensure that:
- The algorithm should be machine-independent.
- It must be general and not programming language specific.
- It must work on all possible inputs.
Here, asymptotic analysis plays a crucial role in finding any algorithm’s efficiency. Additionally, the notation can also help developers identify the behavior of an algorithm on a given input or when the input size changes.
Types of Asymptotic Analysis
This notation is often used for the worst-case analysis of an algorithm. “The Big-O notation is useful when we only have an upper bound on the time complexity of an algorithm. Many times we easily find an upper bound by simply looking at the algorithm,” says the author. Here are some stepwise procedures for Big-O runtime analysis:
- Identify what the input is.
- Express the maximum number of operations.
- Check the quality of the compiler or interpreter.
- Remove all the constant factors.
Big Omega Notation
Commonly denoted by Ω, this notation indicates the best case analysis of an algorithm. The best case Ω of an algorithm describes that the function can never get any better than the specified value. Additionally, Big Omega notation demonstrates the minimum time required by an algorithm for all input values. Ω notation can be helpful when you have a lower bound on the time complexity of an algorithm.
Big Theta Notation
Theta notation, denoted by Θ, is an asymptotic analysis that defines the exact asymptotic behavior and encloses a function from above and below. Since it represents an algorithm’s upper and lower bound of the running time, programmers use it for analyzing the average-case complexity. Take note of the following points:
- The best case in Θ is not used.
- Θ in the worst case describes asymptotic bounds for the worst-case combination of input values.
- Simply writing Θ indicates the worst case.
To read the original article, click on https://www.geeksforgeeks.org/analysis-of-algorithms-set-3asymptotic-notations/.