When it comes to sorting algorithms, there are various options to choose from. One of the advanced sorting algorithms that you might come across is the Quicksort algorithm.

The Quicksort algorithm is an efficient divide-and-conquer algorithm that sorts an array by selecting a pivot element and partitioning the other elements into sub-arrays, according to whether they are less than or greater than the pivot. The sub-arrays are then sorted recursively.

Here's an example implementation of the Quicksort algorithm in Java:

1// Quicksort algorithm
2
3public class Quicksort {
4  public static void quicksort(int[] arr, int low, int high) {
5    if (low < high) {
6      int pivotIndex = partition(arr, low, high);
7      quicksort(arr, low, pivotIndex - 1);
8      quicksort(arr, pivotIndex + 1, high);
9    }
10  }
11
12  public static int partition(int[] arr, int low, int high) {
13    int pivot = arr[high];
14    int i = low - 1;
15
16    for (int j = low; j < high; j++) {
17      if (arr[j] < pivot) {
18        i++;
19        swap(arr, i, j);
20      }
21    }
22
23    swap(arr, i + 1, high);
24    return i + 1;
25  }
26
27  public static void swap(int[] arr, int i, int j) {
28    int temp = arr[i];
29    arr[i] = arr[j];
30    arr[j] = temp;
31  }
32
33  public static void main(String[] args) {
34    int[] arr = {12, 4, 5, 6, 7, 3, 1, 15};
35
36    System.out.println("Original array:");
37    for (int num : arr) {
38      System.out.print(num + " ");
39    }
40    System.out.println();
41
42    quicksort(arr, 0, arr.length - 1);
43
44    System.out.println("Sorted array:");
45    for (int num : arr) {
46      System.out.print(num + " ");
47    }
48    System.out.println();
49  }
50}

In this example, we have an array of integers that we want to sort using the Quicksort algorithm. The quicksort function takes in the array, the starting index, and the ending index. It partitions the array based on a pivot element and recursively sorts the sub-arrays. The partition function helps in selecting the pivot element and partitioning the array.

Understanding advanced sorting algorithms like Quicksort can be beneficial in cases where you need to efficiently sort large datasets or optimize the performance of your code. It is widely used in practice due to its average-case time complexity of O(n log n) and its ability to handle large amounts of data.

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}

// Quicksort algorithm

​

public class Quicksort {

  public static void quicksort(int[] arr, int low, int high) {

    if (low < high) {

      int pivotIndex = partition(arr, low, high);

      quicksort(arr, low, pivotIndex - 1);

      quicksort(arr, pivotIndex + 1, high);

    }

  }

​

  public static int partition(int[] arr, int low, int high) {

    int pivot = arr[high];

    int i = low - 1;

​

    for (int j = low; j < high; j++) {

      if (arr[j] < pivot) {

        i++;

        swap(arr, i, j);

      }

    }

​

    swap(arr, i + 1, high);

    return i + 1;

  }

​

  public static void swap(int[] arr, int i, int j) {

    int temp = arr[i];

    arr[i] = arr[j];