1. Introduction to the algorithm
Counting Sort is a sorting algorithm with linear time complexity, suitable for situations where the range of elements to be sorted is small. The core idea of this algorithm is to count the number of occurrences of each element and then reconstruct an ordered sequence based on the number of times.
The specific implementation steps are as follows:
1.1 Statistics the number of times each element in the element to be sorted and save it as an array.
1.2 Accumulate the statistical results to obtain the index of the last position of each element in the ordered sequence.
1.3 Traverse the elements to be sorted and place the elements in the corresponding position according to the statistical results.
1.4 After putting the element in the corresponding position, decrement its count in the statistical results by one.
The time complexity of count sorting is O(n+k), where n is the number of elements to be sorted and k is the range of elements to be sorted. Since additional space is needed to store statistical results and sort results, its spatial complexity is O(n+k).
The characteristics of counting sorting are good stability and have certain restrictions on the value of elements, which are suitable for situations where the range of elements to be sorted is small. However, since additional space is needed to store statistical results and sorting results, when the range of elements to be sorted is large, the spatial complexity of count sorting will also increase accordingly.
2. Why learn counting and sorting algorithm:
2.1 Familiar with sorting algorithms: Count sorting is a common sorting algorithm. Mastering the counting sorting algorithm can help you better understand and learn other sorting algorithms, such as insertion sorting, bubble sorting, quick sorting, etc.
2.2 Efficient time complexity: The time complexity of the counting sorting algorithm is O(n+k), where n represents the number of elements to be sorted, and k represents the value range of elements to be sorted. Compared with other common sorting algorithms, the time complexity of counting sorting algorithms is relatively low, so in some scenarios, the counting sorting algorithm can provide more efficient sorting efficiency.
2.3 Can handle large-scale data: the counting and sorting algorithm can process large-scale data without significantly degrading the algorithm performance due to the increase in data scale. Therefore, in scenarios where a large amount of data is needed, the count sorting algorithm is a good choice.
2.4 Not affected by the number of comparisons: The counting sorting algorithm does not involve comparison operations, but completes the sorting by counting the number of times each element appears. Therefore, the performance of the count sorting algorithm is independent of the number of comparisons between elements to be sorted. This makes the count sorting algorithm perform well in some special cases, such as when the elements to be sorted have a certain regularity or a large number of repetitive elements.
3. What are the practical applications of counting and sorting algorithms in projects:
3.1 String sorting: The count sorting algorithm can be used to sort a set of strings. You can count the number of times each character appears, and then generate a sorted string array based on the counting results in the order of characters.
3.2 Frequency statistics: In some projects, it is necessary to count the frequency of each element in a set of data. The counting sorting algorithm can be used to perform frequency statistics on a set of data, and can count the number of times each element appears, and then generate the corresponding frequency statistics result based on the counting results.
3.3 Sorting with limited data range: The count sorting algorithm is suitable for sorting problems with limited data range, such as sorting a set of integers. If you know that the range of integers is within a smaller interval, you can use the count sorting algorithm. In this case, the time complexity of the counting and sorting algorithm can reach a linear level and is more efficient.
3.4 Data deduplication: The counting sorting algorithm can also be used to deduplicate a set of data. You can count the number of occurrences of each element, and then generate a deduplicated data array based on the counting results.
4. Implementation and explanation of counting and sorting algorithm:
4.1 Implementation of Counting and Sorting Algorithm
public static void Main(string[] args)
{
int[] inputArray = { 4, 2, 2, 8, 3, 3, 1 };
("Original array:");
PrintArray(inputArray);
int[] sortedArray = CountingSortAlgorithm(inputArray);
("Sorted array:");
PrintArray(sortedArray);
}// Counting sorting algorithm static int[] CountingSortAlgorithm(int[] inputArray)
{
// Find the maximum value in the input array int max = inputArray[0];
for (int i = 1; i < ; i++)
{
if (inputArray[i] > max)
max = inputArray[i];
}
// Create a count array, initialize to 0 int[] countArray = new int[max + 1];
// Statistics the number of times each number appears for (int i = 0; i < ; i++)
{
countArray[inputArray[i]]++;
}
// Build the sorted array based on the counted array int[] sortedArray = new int[];
int index = 0;
for (int i = 0; i < ; i++)
{
while (countArray[i] > 0)
{
sortedArray[index++] = i;
countArray[i]--;
}
}
return sortedArray;
}
// Print array static void PrintArray(int[] array)
{
for (int i = 0; i < ; i++)
{
(array[i] + " ");
}
();
}4.2 Explanation of counting and sorting algorithm
4.2.1 First, inMainThe algorithm is tested in the method.
4.2.2 inMainIn the method, we define an input arrayinputArray, it contains a set of unsorted integers.
4.2.3 We callPrintArrayMethod prints out the original array.
4.2.4 Next, we callCountingSortAlgorithmMethod to count sorting.
4.2.5 InCountingSortAlgorithmIn the method, we first find the maximum value in the input arraymax, used to create a count array.
4.2.6 Let's create acountArray, its length ismax + 1, and initialize with 0.
4.2.7 Then, we loop through the input array, count the number of occurrences of each number, and store it incountArraymiddle.
4.2.8 Next, we willcountArrayBuild the sorted array. Let's create asortedArray, used to store sorted results.
4.2.9 Let's define aindexvariable and initialize it to 0. Then, we go throughcountArray, fill in each number in order according to the number of occurrencessortedArraymiddle.
4.2.10 Finally, we return the sorted arraysortedArray。
4.2.11 We call againPrintArrayMethod, print out the sorted array.
5. What should be noted in the counting and sorting algorithm:
5.1 The size of the counting array: The size of the counting array should be greater than or equal to the maximum value in the array to be sorted, otherwise it will cause the array to be out of bounds error.
5.2 Initialization of counting array: The counting array needs to be initialized to 0, which is used to count the number of each element.
5.3 Accumulation of counting arrays: The counting array should perform the accumulation operation so that each element represents the number of less than or equal to the element.
5.4 The traversal order of counting arrays: When placing elements in the correct position, the counting array should be traversed from behind to front, so that stability can be maintained.
5.5 Update of counting array: After placing elements in the correct position, the number of corresponding elements in the counting array needs to be updated.
5.6 Negative numbers processing: The count sorting algorithm is only suitable for the sorting of non-negative integers. Special treatment is required for the processing of negative numbers, such as the negative number can be converted into positive numbers to handle.
5.7 Processing of repeat elements: The counting sorting algorithm requires special attention to the processing of repeat elements. An additional array can be used to store the location of the element.
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