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# Sorting algorithms: Introduction to data sorting

In computer science, data sorting is an essential part of working with data in various applications. It is the process of rearranging a collection of elements in a given array or list into a specific order based on a defined criterion. Reordered elements can be sorted alphabetically, numerically, by date from smallest to largest, or vice versa. Sorted data plays a key role in efficient data processing and retrieval.

We most often load a large amount of random data into the information system, which arrives sequentially and their classification helps us to focus on the data that we currently need to process. Let’s imagine we have a large e-shop and we receive more than a thousand orders a day. The amount of our data is growing every day and without proper data categorization, order processing would be slower and slower. However, if we start sorting orders by date received, by customer ID and by processing status, after some time the order processing will be as efficient as it was at the beginning.

Thus, the appropriate arrangement of data greatly affects how quickly we can find the data we have previously stored. We use different sorting algorithms to sort the data. With them we can reduce the complexity of the problem and that is why they are indispensable tools for computer science.

As is often the case in life, there is no single universal sorting algorithm. The choice of the appropriate algorithm depends on the amount of data to be sorted, the memory available, and whether the data is already partially sorted.

In today’s article, we will learn about the characteristics of data sorting algorithms, explain the basic terms to better understand the advantages and disadvantages of the different algorithms we will introduce in the future.

## Sorting algorithms rules

Each of the sorting algorithms is governed by two basic conditions:

- The output of the algorithm has a monotonic order, that is, each of the elements is not smaller (larger) than the previous element, according to the desired order.
- The output of the algorithm is a permutation, that is, a rearrangement of the original order of the elements, with all the elements from the input present.

None is added or subtracted during the sort.

Of course, for optimal efficiency of the sorting algorithms, the input data should be placed in a data structure that allows direct access*(random access*), instead of a structure with sequential access*(sequential* access). Let us see on what criteria sorting algorithms can be classified. First, of course, we will be interested in efficiency criteria. We measure efficiency by looking at how the performance of the algorithm changes as the size of the list to be sorted increases. We are mainly interested in sorting algorithms that perform equally well as the list gets larger. In real-world applications, we are limited by the physical memory and computational power of the systems on which our programs run. This is where space and time complexity come into play, because we never want to run a function or process that exceeds the amount of space available to the system at any given time. We also don’t want our applications to get stuck and slow down. Therefore, we tend to choose the algorithm that is best suited for a particular problem and fits within our space and time limit.

## Sorting algorithms – time complexity

Although it might seem that the time consumption is the total time of the sorting algorithm, this is not quite the case, because the total time depends on a number of external factors, such as the speed of the hardware (processor, memory, disk, …), the instruction width (32 bit vs. 64 bit), the compiler used, the thread scheduler in the operating system, etc. Therefore, time complexity is defined as the number of basic operations performed in a program. Each operation is assumed to take a fixed amount of time to execute. In general, the performance of a sorting algorithm is strongly dependent on the order of the input data, so the estimation of the time complexity of the algorithm is bounded by an interval and its bounds are written with the appropriate notation. **Omega notation – notation Ω(n)**: is used to express the lower bound of the time complexity of running the algorithm. It defines the inputs where the algorithm takes minimum time, e.g. for nearly sorted inputs. **Big O notation – notation Ο(n)**: is used to express the upper bound on the interval of time complexity of running the algorithm. It defines the inputs where the algorithm takes maximum time to run, thus describing the worst cases. **Theta notation – notation θ(n)**: lies between O(n) and Ω(n) and expresses the average time complexity. We obtain it if we compute the total time for all random inputs and divide it by the total number of inputs.

## Sorting algorithms – space complexity

Spatial complexity is the total memory space required by an algorithm to execute. It is dependent on the input size and is therefore given as a function with input of size (n).

## Algorithm stability of sorting algorithms

A sorting algorithm is considered stable if the relative order of the same elements is preserved after sorting. This is important in certain applications where the original order of the same elements must be preserved. An unstable algorithm is not guaranteed to preserve this order.

## Algorithm adaptability of sorting algorithms

We consider a sorting algorithm to be adaptive if it takes advantage of existing order in the data or other information to improve sorting performance.

## Sorting method used

Sorting algorithms can use various techniques to sort elements, such as inserting elements into their correct positions, swapping elements, selecting elements, or merging different parts of a list.

## Extra space when sorting data

When available memory is limited or when data cannot be moved, an algorithm that sorts data in an existing structure and does not require additional space comes in handy. However, some algorithms need this extra space.

## Recursion

It classifies algorithms based on whether recursion is used.

## Serial or parallel sorting

Algorithms can use a single processor core (thread) for serial sorting, or they can use multi-core processors for parallel sorting.

## Practical applications using data sorting

Data sorting is used in virtually all areas of computer science. **Databases: data** classification is an essential part for efficient access and organization of data in databases. Sorting helps in faster searching and improves the performance of queries (SQL queries). **Search services:** web browser algorithms use complex sorting algorithms to process our searches as optimally as possible and display the result, often in a fraction of a second. **Internet shopping:** When we shop online and sort products by price, rating or popularity, sorting algorithms work to make our shopping experience smoother and more efficient. **Data analysis:** Sorting also plays an important role in analytical tasks such as identifying trends, generating reports and extracting insights from data. **Financial Markets:** Exchanges use sorting algorithms to organize buy and sell orders, which play an important role in determining market prices. **Graphics processing:** It is used in rendering graphics, especially in rendering objects depending on the depth or distance from the observer. It also ensures proper texturing of objects and smoothing of the image.

## Advantages of sorting algorithms

### Efficiency

Sorting algorithms help in arranging the data in a specific order, making it easier and faster to search, retrieve and analyze information.

### Increased performance

By organizing the data, algorithms can perform operations more efficiently, leading to increased performance in a variety of applications.

### Simplified data analysis

Sorting makes it easier to identify patterns and trends in the data.

### Reduced memory consumption

Sorting can help reduce memory usage by removing duplicate elements.

### Improved data visualisation

Sorted data can be visualised more effectively in tables and graphs.

## Sorting algorithms disadvantages

### Time complexity

Sorting algorithms can have high time complexity, especially for large data sets.

### Spatial complexity

Some sorting algorithms require additional memory space to perform their operations.

### Stability

Some sorting algorithms do not preserve the original order of the same elements.

### Algorithm selection

Choosing the most appropriate sorting algorithm for a given dataset can be challenging.

## Sorting algorithms – quick overview and comparison

Repeatedly compares and swaps two adjacent out-of-order elements until the output is sorted. **Method:** exchange, **Time complexity:** O(n²), **Memory complexity:** O(1), **Stability:** yes

It improves the algorithm of element exchange by allowing them to be exchanged over a longer distance (ridge). **Method:** exchange, **Time complexity:** O(n²), **Memory complexity:** O(1), **Stability:** no

Repeatedly removes the smallest element from the unsorted part and moves it to the sorted part. **Method:** selection, **Time complexity:** O(n²), **Memory complexity:** O(1), **Stability:** no

It successively takes elements from the input and inserts them in such a place that their relative order is always preserved. **Method:** insertion, **Time complexity:** O(n²), **Memory complexity:** O(1), **Stability:** yes

When sorting, it finds out how many different elements there are and uses this information to calculate the order of each element. **Method:** counting, **Time complexity:** O(n+k), **Memory complexity:** O(k), **Stability:** yes

It creates a maximum heap from the input, from which it gradually cuts off the current largest elements. After removing an element, the heap is rearranged. **Method:** selection, **Time complexity:** O(n log n), **Memory complexity:** O(n), **Stability:** no

Gradually divides the input into two parts, (those into further parts) until they can no longer be divided. The sorted output is created by joining the parts in reverse order. **Method:** merging, **Time complexity:** O(n log n), **Memory complexity:** O(1), **Stability:** yes

The input field is rearranged and split into two parts using a pivot element. These steps are repeated until the parts consist of a single element **Method:** splitting, **Time complexity:** O(n log n), **Memory complexity:** O(log n), **Stability:** no

Based on the hash function, it divides the input elements into individual buckets that have specified ranges. Each bucket is then sorted individually using an appropriate sorting method. **Method:** distribution, **Time complexity:** O(n+k), **Memory complexity:** O(n+k), **Stability:** possible

The algorithm processes and sorts elements based on individual digits or characters. There are two variants, either from least significant digit (LSD) right-to-left or most significant digit (MSD) left-to-right. **Method:** counting and distribution , **Time complexity:** O(n*k), **Memory complexity:** O(n+k), **Stability:** yes

## Summary

Sorting helps us efficiently organize clumps of messy data so that we can access it more quickly later when we process it. We have explained the principles of sorting and the characteristics of sorting algorithms so that we can compare specific algorithms for sorting data, which next time we will introduce in turn, explain their working principle and program them in Java.

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