An Overview of Big-O

Big-O notation is a mathematical notation that is used to describe the performance or complexity of an algorithm, specifically how long an algorithm takes to run as the input size grows. Understanding Big-O notation is essential for software engineers, as it allows them to analyze and compare the efficiency of different algorithms and make informed decisions about which one to use in a given situation. In this guide, we will cover the basics of Big-O notation and how to use it to analyze the performance of algorithms.

What is Big-O?

Big-O notation is a way of expressing the time (or space) complexity of an algorithm. It provides a rough estimate of how long an algorithm takes to run (or how much memory it uses), based on the size of the input. For example, an algorithm with a time complexity of  means that the running time increases linearly with the size of the input.

What is time complexity?

Time complexity is a measure of how long an algorithm takes to run, based on the size of the input. It is expressed using Big-O notation, which provides a rough estimate of the running time. An algorithm with a lower time complexity will generally be faster than an algorithm with a higher time complexity.

What is space complexity?

Space complexity is a measure of how much memory an algorithm requires, based on the size of the input. Like time complexity, it is expressed using Big-O notation. An algorithm with a lower space complexity will generally require less memory than an algorithm with a higher space complexity.

Examples of time complexity

Here are some examples of how different time complexities are expressed using Big-O notation:

• O(1): Constant time. The running time is independent of the size of the input.
• O(n): Linear time. The running time increases linearly with the size of the input.
• O(n^2): Quadratic time. The running time is proportional to the square of the size of the input.
• O(log(n)): Logarithmic time. The running time increases logarithmically with the size of the input.
• O(2^n): Exponential time. The running time increases exponentially in the size of the input.

Famous Time Complexities

Big-O notation uses mathematical notation to describe the upper bound of an algorithm’s running time. It provides a way to compare the running time of different algorithms, regardless of the specific hardware or implementation being used.

It’s important to note that Big-O notation only provides an upper bound on the running time of an algorithm. This means that an algorithm with a time complexity of O(n)  could potentially run faster than an algorithm with a time complexity of O(log(n))  in some cases, depending on the specific implementation and hardware being used.

Additionally, Big-O notation only considers the dominant term in the running time equation. For example, an algorithm with a running time of O(n^2+n)  would be simplified to O(n^2).

Famous Big-O Notations with Examples.