Mathematical Examples of Runtime Analysis
Below table illustrates the runtime analysis of different orders of algorithms as the input size (n) increases.
n | log(n) | n | n * log(n) | n^2 | 2^n | n! |
---|---|---|---|---|---|---|
10 | 1 | 10 | 10 | 100 | 1024 | 3628800 |
20 | 2.996 | 20 | 59.9 | 400 | 1048576 | 2.432902e+1818 |
Big O Notation Tutorial – A Guide to Big O Analysis
Big O notation is a powerful tool used in computer science to describe the time complexity or space complexity of algorithms. It provides a standardized way to compare the efficiency of different algorithms in terms of their worst-case performance. Understanding Big O notation is essential for analyzing and designing efficient algorithms.
In this tutorial, we will cover the basics of Big O notation, its significance, and how to analyze the complexity of algorithms using Big O.
Table of Content
- What is Big-O Notation?
- Definition of Big-O Notation:
- Why is Big O Notation Important?
- Properties of Big O Notation
- Common Big-O Notations
- How to Determine Big O Notation?
- Mathematical Examples of Runtime Analysis
- Algorithmic Examples of Runtime Analysis
- Algorithm Classes with Number of Operations and Execution Time
- Comparison of Big O Notation, Big Ω (Omega) Notation, and Big θ (Theta) Notation
- Frequently Asked Questions about Big O Notation