# Big-O Notation

## Algorithms are usually compared on the basis of two dimensions Memory space and Time taken. Time taken is usually considered more important. The actual run time on a particular computer is not a good basis for comparison since it depends heavily on the computer. Big-O notation tells the number of steps an algorithm takes to carry out a task for the given input size. Big-O notation finds out an algorithm’s performance when the input size increases. This is called growth rate. The growth rate determines the performance of an algorithm with respect to the input size. Any change in the input size which affects the algorithm’s performance is depicted by its growth rate. Big-O of an algorithm specifies the upper bound of its performance. Big-O notation is very useful for comparing the performance of two or more algorithms. Big-O notation is a mathematical formula that describes an algorithm’s performance. It is the bounding function of the input size and time required by an algorithm. It specifies the upper bound of an algorithm’s performance.

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• Q1

What is time complexity?

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It refers to the time required by an algorithm to complete the task for the given input size.

• Q2

What specifies the performance of an algorithm with respect to the input size?

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The growth rate of an algorithm specifies the performance of the algorithm with respect to the input size.

• Q3

How is time complexity of an algorithm depicted?

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Using Big-O notation, we can depict the time complexity of an algorithm.

• Q4

How can we compare two algorithms without actually running them on a computer?

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Using Big-O notation, we can compare two algorithms, without actually running them on a computer.

• Q5

Name the dimensions on the basis of which algorithms are compared.

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