1. Introduction to the algorithm
The cardinality sorting algorithm is a non-comparative sorting algorithm that sorts according to each bit of a number. Its basic idea is to split the integer from low to high into multiple numbers according to the number of bits, and then sort them by each number, and finally get the sorting result.
The cardinality sorting algorithm can be divided into two steps: allocation and collection.
1.1 Allocation: Bucket all numbers in the array to be sorted according to the single digit value, and the same numbers are placed in the same bucket. Then rearrange the numbers in the order of the buckets.
1.2 Collection: Bucket the numbers sorted in the previous step according to the value of the ten-digit number and sort them again. Sort by analogy until sorted by the highest bit.
The time complexity of the cardinality sorting algorithm is O(d*(n+k)), where d is the number of digits of the largest number, n is the number of arrays to be sorted, and k is the number of numbers in each bucket.
The advantage of the cardinality sorting algorithm is its good stability and is suitable for a large number of sorting tasks with a small range of numbers. But its disadvantage is that it requires additional storage space to store buckets, and for cases with large numbers, it may lead to excessive buckets, which will affect performance.
2. Why learn the cardinality sorting algorithm:
2.1 Improve sorting efficiency: The cardinal sorting algorithm is a stable sorting algorithm with a time complexity of O(nk), where n is the number of elements to be sorted and k is the number of digits of the largest number. Compared with general comparison sorting algorithms such as quick sorting, merge sorting, etc., cardinality sorting can be sorted faster in some cases.
2.2 Solve specific problems: The cardinality sorting algorithm is suitable for specific types of data sorting problems, such as string sorting, telephone number sorting, etc. These problems usually require sorting the data by specific rules, and the cardinality sorting algorithm can meet these needs well.
2.3 Broaden knowledge: Learning the cardinal sorting algorithm can help us understand different sorting algorithm ideas and implementation methods, and improve our algorithm design and analysis capabilities. At the same time, learning the cardinal sorting algorithm can also provide a certain foundation for learning other sorting algorithms.
2.4 A wide range of applications: Cardinal sorting algorithms have a wide range of application scenarios in practical applications, such as computer image processing, computer vision, big data processing and other fields. Understanding and mastering cardinality sorting algorithms can help us work and research in these areas.
3. What are the practical applications of cardinality sorting algorithms in projects:
3.1 Sort by numbers: The cardinality sorting algorithm can sort numbers by number of digits, so that numbers can be sorted in the project, such as sorting student grades, salary, etc.
3.2 String sorting: The cardinality sorting algorithm can sort according to the characters of the string. In a project, you can use the cardinality sorting algorithm to sort strings, such as sorting file names, user names, etc.
3.3 Ranking calculation: In some projects, the data needs to be ranked and calculated based on some indicators. The cardinality sorting algorithm can be sorted according to the size of the indicator, so that ranking calculations can be performed conveniently in the project.
3.4 Database index establishment: In the database, in order to improve query efficiency, it is often necessary to sort a certain field and index it. The cardinality sorting algorithm can be used to sort fields in a database to facilitate indexing.
3.5 Data analysis: In data analysis projects, it is often necessary to sort and group a large amount of data. The cardinality sorting algorithm can be used to sort and group data, so as to facilitate data analysis.
4. Implementation and explanation of cardinality sorting algorithm:
4.1 Implementation of cardinality sorting algorithm
// Get the largest number in the array static int GetMax(int[] arr, int n)
{
int max = arr[0];
for (int i = 1; i < n; i++)
{
if (arr[i] > max)
{
max = arr[i];
}
}
return max;
}
// Sort the array by specified number of digits using count sort static void CountSort(int[] arr, int n, int exp)
{
int[] output = new int[n]; //Storing the sorted results int[] count = new int[10]; // Store the number of times each number appears
// Initialize the count array to 0 for (int i = 0; i < 10; i++)
{
count[i] = 0;
}
// Statistics the number of times each number appears for (int i = 0; i < n; i++)
{
count[(arr[i] / exp) % 10]++;
}
// Calculate the position of each number in the sorted array for (int i = 1; i < 10; i++)
{
count[i] += count[i - 1];
}
// Put the number into the output array according to the calculated position for (int i = n - 1; i >= 0; i--)
{
output[count[(arr[i] / exp) % 10] - 1] = arr[i];
count[(arr[i] / exp) % 10]--;
}
// Copy the elements in the output array into the original array arr for (int i = 0; i < n; i++)
{
arr[i] = output[i];
}
}
// Sort arrays using the radix sorting algorithm static void RadixSortAlgorithm(int[] arr, int n)
{
int max = GetMax(arr, n);
// Count and sort the single digits, ten digits, hundreds digits, etc. of each number for (int exp = 1; max / exp > 0; exp *= 10)
{
CountSort(arr, n, exp);
}
}4.2 Explanation of cardinality sorting algorithm
In the above code, we implement the cardinality sorting algorithm. Here is a detailed explanation of the code:
4.2.1 First, we define aRadixSortclass, and a cardinality sorting algorithm is implemented in it.
4.2.2 GetMaxThe function is used to get the maximum value in an array, it takes an integer array and the length of the array as a parameter, and returns the maximum value in the array.
4.2.3 CountSortFunctions are the core part of the radix sorting algorithm, which uses count sorting to sort the array by specified number of bits. The function takes an integer array, the length and number of bits as parameters.
4.2.4 inCountSortIn the function, we first create aoutputArray to store sorted results, and acountArray to store the number of occurrences of each number.
4.2.5 We willcountThe array is initialized to 0, and then iterates through the entire array using a loop to count the number of occurrences of each number.
4.2.6 Next, we use a loop to calculate the position of each number in the sorted array.
4.2.7 Finally, we use another loop to put the number into the calculated position.outputIn the array, andoutputCopy elements in the array to the original arrayarrmiddle.
4.2.8 RadixSortAlgorithmFunctions are implementations of cardinality sorting algorithms, which receive an integer array and the length of the array as parameters.
4.2.9 inRadixSortAlgorithmIn the function, we first get the maximum value in the array.
4.2.10 Then, we count and sort the single digits, ten digits, hundreds digits, etc. of each number.
5. What should be noted in the cardinality sorting algorithm:
5.1 Select the appropriate cardinality: The cardinality sorting algorithm is sorted according to different digits of the element, so it is necessary to select the appropriate cardinality. Generally speaking, the cardinality can be a decimal number or other binary number. The specific cardinality selection needs to be determined based on the sorted data set.
5.2 Determine the number of sorting: The cardinality sorting algorithm needs to sort by the number of bits of the element, so it needs to determine the number of sorting. The number of sorts is equal to the maximum number of digits of the element, and you can get the maximum number of digits by traversing the dataset.
5.3 Determine the order of sorting: In the cardinality sorting algorithm, each sorting is sorted according to a certain number of elements, so the order of sorting needs to be determined. Generally speaking, it can be sorted from low to high, or from high to low.
5.4 Methods to determine sorting: The cardinality sorting algorithm can be sorted using stable sorting algorithms, such as insertion sorting, counting sorting, etc. Each sorting requires sorting by a certain single-digit number of the element, which can be achieved using a stable sorting algorithm.
5.5 Determine the use of auxiliary space: The cardinal sorting algorithm needs to use auxiliary space to store temporary sorting results, so it is necessary to determine the use of auxiliary space. A two-dimensional array can be used to represent auxiliary space, where each row represents the sorting result of a certain one-digit number.
5.6 The situation of dealing with negative numbers: The cardinality sorting algorithm is generally applicable to the sorting of non-negative integers, and special processing is required for the sorting of negative numbers. Negative numbers can be converted to positive numbers for sorting, and then the result can be converted back.
5.7 Determine the stability of sorting: The cardinality sorting algorithm can be a stable sorting algorithm, that is, the same elements remain in the relative order in the sorted results. Ensuring the stability of the sort can be achieved by using a stable sorting algorithm in each sort.
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