## Introduction

Sorting algorithms are an essential software development tool for organizing data in a structured way. In order to get the best performance from sorting algorithms it is important to utilize the best algorithm that has the best time complexity.

## What Is Time Complexity

Time complexity is a way of measuring how efficient an algorithm is in terms of time. It describes how the complexity of an algorithm grows as the size of the input data increases. The best algorithms have a better asymptotic runtime complexity, meaning the bigger the task, the less time it takes to run.

## What Is Asymptotic Runtime Complexity

Asymptotic runtime complexity is the measure of the amount of memory or time needed for an algorithm to run, relative to the size of the input data. It is a way of measuring how the time taken for an algorithm to run increases with the size of the dataset. This can be further divided into two main types, “best-case” and “worst-case”.

### Best-Case Asymptotic Runtime Complexity

The best-case asymptotic runtime complexity is when the algorithm completes the task in the least amount of time. Best-case asymptotic runtime complexity is determined by examining the relationship between the number of elements in the input data, and the time taken to complete the task.

### Worst-Case Asymptotic Runtime Complexity

The worst-case asymptotic runtime complexity is when the algorithm takes the longest amount of time to complete the task. It is determined by examining the relationship between the number of elements in the input data, and the time taken to complete the task.

## Best Sorting Algorithm

The best sorting algorithm for a good asymptotic runtime complexity is the **Quick Sort Algorithm**. QuickSort is the most widely used sorting algorithm and is a comparison-based algorithm. It is a recursive algorithm that works by splitting the array into subarrays, and then sorting each subarray.

### How The Quick Sort Algorithm Works

- Choose one element, called the
**pivot**, from the array. - Reorder the array so that all elements with values less than the pivot come before the pivot, while all elements with values greater than the pivot come after it (equal values can go either way).
- After this partitioning, the pivot is in its final position.
- Recursively apply the above steps to the sub-array of elements with smaller values and separately to the sub-array of elements with greater values.

## Pros and Cons

The main advantage of Quick Sort is that it is very efficient and has relatively good complexity (Ω(n log n) for Average and Worst-case). It also requires very little extra space and is very adaptive. One of the disadvantages is that it is not a stable algorithm, meaning elements that have the same values may not have their original order preserved.

## Summary

The Quick Sort algorithm is the most widely used sorting algorithm and the best algorithm for achieving a good asymptotic runtime complexity. It is an efficient algorithm with relatively good complexity and requires very little extra space. However, it is not a stable algorithm which can be an issue in some cases.

## FAQ

##### What Is Time Complexity?

Time complexity is a way of measuring how efficient an algorithm is in terms of time. It describes how the complexity of an algorithm grows as the size of the input data increases.

##### What Is Asymptotic Runtime Complexity?

Asymptotic runtime complexity is the measure of the amount of memory or time needed for an algorithm to run, relative to the size of the input data. It is a way of measuring how the time taken for an algorithm to run increases with the size of the dataset.

##### What Is The Best Sorting Algorithm?

The best sorting algorithm for achieving a good asymptotic runtime complexity is the Quick Sort Algorithm. It is an efficient algorithm with relatively good complexity and requires very little extra space.

##### Are There Any Disadvantages To Quick Sort?

The main disadvantage of Quick Sort is that it is not a stable algorithm, meaning elements that have the same values may not have their original order preserved.