Definition of Big-O Notation
Given two functions f(n) and g(n), we say that f(n) is O(g(n)) if there exist constants c > 0 and n0 >= 0 such that f(n) <= c*g(n) for all n >= n0.
In simpler terms, f(n) is O(g(n)) if f(n) grows no faster than c*g(n) for all n >= n0 where c and n0 are constants.
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