10 Best Sorting Algorithms Explained, with Examples

This article explores in-depth sorting algorithms, a basic tool in computer science for efficient organization of data and provides practical insights through sample codes of various algorithm types. The article contains technical analysis of the sorting algorithm, using the large O notation to analyze its time and space complexity, and also provides a high-level overview for the public to understand. The article comprehensively explores the sorting algorithm, discusses its importance, different types and main algorithms that need to be understood, focusing on practical applications and algorithm comparisons.

Key Points

1. Basics and Practicality: This article explores in-depth sorting algorithms, a must-have tool in computer science for efficient organization of data and provides practical insights through sample code of various algorithm types.
2. Technical Analysis and Accessibility: It includes technical inspections of sorting algorithms, analyzing its time and space complexity using large O notation, and also provides a high-level overview for easy understanding.
3. Comprehensive coverage: This article comprehensively explores the sorting algorithm, discusses its importance, different types and main algorithms that need to be understood, focusing on practical applications and algorithm comparisons.

What is the sorting algorithm?

Essentially, a sorting algorithm is a computer program that organizes data into specific orders, such as alphabetical or numerical order, usually in ascending or descending order.

What is the purpose of the sorting algorithm?

Sorting algorithms are mainly used to rearrange large amounts of data in an efficient way to make it easier to search and manipulate them. They are also used to increase the efficiency of other algorithms such as search and merging that rely on sorted data to operate.

Why is the sorting algorithm so important?

Sorting algorithms are used to organize data in a specific order, which makes it easier to search, access, and analyze data. In many applications, sorting is a key part of the data processing flow, and the efficiency of the sorting algorithm can have a significant impact on the overall performance of the system.

• In the database: Sort is used to retrieve records in a specific order, such as by date, alphabetical or numerical order. This allows users to quickly find the data they need without manually searching for large amounts of unsorted data.
• In search engines: Sort search results in relevance order. By sorting the results this way, users can quickly find the information they are looking for without filtering irrelevant or irrelevant results.
• In many scientific and engineering applications: Researchers can run data analysis and simulations to gain insight into complex systems and make more accurate predictions about future behavior.

Different types of sorts in data structures

A variety of sorts are available. The choice of sorting algorithms depends on a variety of factors, such as the size of the data set, the type of data being sorted, and the time and space complexity required.

Comparison-based sorting algorithm

These algorithms compare elements of the dataset and determine their order based on the results of the comparison. Examples of comparison-based sorting algorithms include bubble sort, insert sort, quick sort, merge sort, and heap sort.

Non-comparison-based sorting algorithm

These algorithms do not directly compare elements, but use other properties of the dataset to determine their order. Examples of non-comparison-based sorting algorithms include count sorting, cardinality sorting, and bucket sorting.

In-place sorting algorithm

These algorithms sort datasets in-situ, meaning they do not require extra memory to store intermediate results. Examples of in-situ sorting algorithms include bubble sorting, insert sorting, quick sorting, and hill sorting.

Stable sorting algorithm

These algorithms retain the relative order of elements such as the dataset. Examples of stable sorting algorithms include insert sort, merge sort, and Timsort.

Adaptive sorting algorithm

These algorithms utilize any existing order in the dataset to improve their efficiency. Examples of adaptive sorting algorithms include insert sorting, bubble sorting, and Timsort.

Top ten sorting algorithms that need to be known

Now let's take a look at the top ten sorting algorithms that you need to pay attention to when selecting a sorting algorithm.

Bubblestone

Bubblestone is a simple sorting algorithm that iterates over and over the given list of items, compares each pair of adjacent items, and swaps them if they are incorrect in order. The algorithm continues until it traverses the entire list without exchanging any items. Bubble sorting is sometimes called "sinking sorting".

History of bubble sort

The origin of bubble sort dates back to the late 1950s, and Donald Knut popularized it in his 1968 classic The Art of Computer Programming. Since then, it has been widely used in a variety of applications, including the sorting algorithms of compilers, the sorting of elements in databases, and even the sorting of playing cards.

Pros and disadvantages of bubble sorting

Bubblestone is considered to be a relatively inefficient sorting algorithm because its average and worst-case complexity are O(n^2). This makes it much less efficient than most other sorting algorithms, such as quick sort or merge sort.

Technical Description: O(n^2) complexity means that the time required for the algorithm to complete is proportional to the square of the input size. This means that a larger input size will cause the algorithm to complete much longer.

For example, if you consider an algorithm that sorts an array of numbers, it might take one second to sort an array of ten numbers, but it might take four seconds to sort an array of 20 numbers. This is because the algorithm has to compare each element in the array with every other element, so it has to compare a larger array 20 times and a smaller array only 10 times.

However, it is very easy to understand and implement and is often used as an introduction to sorting and building blocks for more complex algorithms. But now it is rarely used in practice.

User case for bubble sorting

Bubblestone is a simple algorithm that can be used to sort lists or arrays of small elements. It is easy to implement and understand, so it can be used in situations where simplicity and clarity are more important than performance.

• Educational purpose. It is often used as an example of simple sorting algorithms in computer science courses. Students can learn basic sorting techniques and understand how algorithms work by learning bubble sorting.
• Sort small datasets. It can be used to sort small datasets with up to a few hundred elements. In situations where performance is not a critical issue, bubbling sorting can be a quick and easy way to sort small lists.
• Pre-sorted data. It can be used as a preliminary step in more complex sorting algorithms. For example, if the data has been partially sorted, the data can be further sorted using bubble sort before running a more complex algorithm.
• Sort data with limited resources. It is useful in situations where resources are limited, such as in embedded systems or microcontrollers, as it requires very little memory and processing power.
• Building blocks for more complex algorithms. It is often used with merge sorting or quick sorting, as well as sorting small subarrays using insert sorting, as these other algorithms can achieve better performance on larger datasets.

Implementation of bubble sorting

1. Iterate through the project using nested loops.
2. Compare adjacent items in the list.
3. If the project order is wrong, exchange the project.
4. Continue until the list is sorted.

Bubbling sort in Python

<code class="language-python">def bubble_sort(items):
    for i in range(len(items)):
        for j in range(len(items)-1-i):
            if items[j] > items[j+1]:
                items[j], items[j+1] = items[j+1], items[j]
    return items

items = [6,20,8,19,56,23,87,41,49,53]
print(bubble_sort(items))</code>

Bubbling sorting in JavaScript

<code class="language-javascript">function bubbleSort(items) {
  let swapped;
  do {
    swapped = false;
    for (let i = 0; i < items.length - 1; i++) {
      if (items[i] > items[i + 1]) {
        let temp = items[i];
        items[i] = items[i + 1];
        items[i + 1] = temp;
        swapped = true;
      }
    }
  } while (swapped);
  return items;
}

let items = [6, 20, 8, 19, 56, 23, 87, 41, 49, 53];
console.log(bubbleSort(items));</code>

(Due to space limitations, only the algorithm name and brief description will be retained. Please refer to the original text for the complete code and detailed explanation)

Insert sort

Insert sort is a simple algorithm that builds a final sorted array at a time, and is named so because of how smaller elements are inserted into the correct position in the sorted array.

Quick sort

Quick sort is a popular divide-and-conquer sorting algorithm based on the principle of dividing an array into two subarrays—one containing an element smaller than the "pivot" element and the other containing an element larger than the pivot element. Then recursively sort the two subarrays.

Bucket sort

Bucket sorting is a useful algorithm for sorting evenly distributed data, which can be easily parallelized for improved performance.

Hill sort

Hill sort uses the insert sorting algorithm, but instead of sorting the entire list at once, it divides the list into smaller sublists. These sublists are then sorted using the insert sort algorithm, thereby reducing the number of swaps required to sort the list.

Merge sort

The basic idea of ​​merge sort is to divide the input list into two halves, sort each halve recursively using merge sort, and then merge the two sorted halves together.

Select sort

Select Sort repeatedly select the smallest element from the unsorted part of the list and swap it with the first element of the unsorted part. This process continues until the entire list is sorted.

Black sort

The basic idea of ​​cardinality sorting is to sort the data by grouping each number of a number or character, from right to left or from left to right.

Comb sort

Comb sort compares pairs of elements that are a certain distance apart, and if they are incorrect in order, swap them.

Timsort

The Timsort algorithm works by dividing the input data into smaller subarrays and then sorting these subarrays using insert sort.

(Timsort implementation code is omitted due to length reasons)

Comparison of all sorting algorithms

Please note that the time complexity and spatial complexity listed in the table are worst case complexity, and actual performance may vary depending on the specific implementation and input data.

算法	时间复杂度	空间复杂度	原地排序	稳定排序	自适应排序
冒泡排序	O(n^2)	O(1)	是	是	否
快速排序	O(n log n)	O(log n)	是	否	是
桶排序	O(n k)	O(n k)	否	是	否
希尔排序	O(n log n)	O(1)	是	否	否
合并排序	O(n log n)	O(n)	否	是	否
选择排序	O(n^2)	O(1)	是	否	否
基数排序	O(w·n)	O(w n)	否	是	否
梳排序	O(n^2)	O(1)	是	否	是
Timsort	O(n log n)	O(n)	是	是	是

What is the most commonly used sorting algorithm?

The most commonly used sorting algorithm may be quick sorting. It is widely used in many programming languages ​​(including C, C, Java, and Python), as well as in many software applications and libraries. Quick sorting is favored for its efficiency and versatility in handling different types of data and is often used as the default sorting algorithm in programming languages ​​and software frameworks. However, other sorting algorithms such as merge sort and Timsort are also widely used in various applications due to their efficiency and unique capabilities.

(The remaining content, such as summary, FAQ, etc., has been omitted due to space limitations.)

The above is the detailed content of 10 Best Sorting Algorithms Explained, with Examples. For more information, please follow other related articles on the PHP Chinese website!