# Complexity Notations

Contents

## Introduction

In this article, let’s have a look at complexity notations like Big Theta, Big Omega, and Big O notation.

Complexity notations are mathematical notations used to describe the performance of algorithms in terms of their time and space requirements. These notations allow us to compare the efficiency of different algorithms for solving the same problem, and to choose the most efficient algorithm for a given application.

## Types of Notations:

The most common complexity notation is Big O notation, which gives an upper bound on the time or space required by an algorithm as a function of the size of the input. For example, an algorithm with a time complexity of O(n) means that its running time grows linearly with the size of the input.

Other common complexity notations include Big Theta notation, which gives both an upper and lower bound on the time or space required by an algorithm, and Big Omega notation, which gives a lower bound on the time or space required by an algorithm.

By using complexity notations, we can compare the performance of different algorithms and choose the most efficient one for a given application. This can help us write efficient and scalable programs that can handle large inputs without running out of time or space. Try again.

## Big oh notation (O):

Big O notation is a mathematical notation used to describe the performance of an algorithm in terms of its time or space complexity. It gives an upper bound on the number of steps or the amount of space required by the algorithm to solve a problem of size n.

For example, an algorithm with a time complexity of O(n) means that its running time grows linearly with the size of the input. This means that if the input size is doubled, the running time of the algorithm will also be roughly doubled. On the other hand, an algorithm with a time complexity of O(log n) means that its running time grows logarithmically with the size of the input. This means that if the input size is doubled, the running time of the algorithm will only increase by a constant amount.

Big O notation is commonly used to compare the efficiency of different algorithms for solving the same problem. By choosing algorithms with lower time or space complexity, we can ensure that our programs will run quickly and efficiently, even on large inputs.

## Big Theta notation (Θ) :

Big Theta notation is a mathematical notation used to describe the performance of an algorithm in terms of its time or space complexity. It gives both an upper and lower bound on the number of steps or the amount of space required by the algorithm to solve a problem of size n.

For example, an algorithm with a time complexity of Θ(n) means that its running time grows linearly with the size of the input. This means that if the input size is doubled, the running time of the algorithm will also be roughly doubled. On the other hand, an algorithm with a time complexity of Θ(log n) means that its running time grows logarithmically with the size of the input. This means that if the input size is doubled, the running time of the algorithm will only increase by a constant amount.

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Big Theta notation is commonly used to compare the efficiency of different algorithms for solving the same problem. By choosing algorithms with lower time or space complexity, we can ensure that our programs will run quickly and efficiently, even on large inputs. Unlike Big O notation, which only gives an upper bound on the time or space required by an algorithm, Big Theta notation provides a more precise analysis of an algorithm’s performance.

## Big Omega notation (Ω) :

Big Omega notation is a mathematical notation used to describe the performance of an algorithm in terms of its time or space complexity. It gives a lower bound on the number of steps or the amount of space required by the algorithm to solve a problem of size n.

For example, an algorithm with a time complexity of Ω(n) means that its running time grows linearly with the size of the input. This means that if the input size is doubled, the running time of the algorithm will also be roughly doubled. On the other hand, an algorithm with a time complexity of Ω(log n) means that its running time grows logarithmically with the size of the input. This means that if the input size is doubled, the running time of the algorithm will only increase by a constant amount.

Big Omega notation is commonly used to compare the efficiency of different algorithms for solving the same problem. By choosing algorithms with lower time or space complexity, we can ensure that our programs will run quickly and efficiently, even on large inputs. Unlike Big O notation, which only gives an upper bound on the time or space required by an algorithm, Big Omega notation provides a more precise analysis of an algorithm’s performance by providing a lower bound on its time or space complexity.

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## Conclusion

That’s it for this article. In the next article, we will learn the differences between stack and heap memory.

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