使用慢排序对数组进行排序

给定一个由N 个整数组成的数组arr[] ，任务是使用慢排序按升序对给定数组进行排序。

例子：

Input: arr[] = {6, 8, 9, 4, 12, 1}
Output: 1 4 6 8 9 12

Input: arr[] = {5, 4, 3, 2, 1}
Output: 1 2 3 4 5

方法：与归并排序一样，慢排序是一种分而治之的算法。它将输入数组分成两半，称自己为两半，然后比较两半的最大元素。它将子数组的最大元素存储在子数组的顶部位置，然后递归调用没有最大元素的子数组。请按照以下步骤解决问题：

慢排序(arr[], l, r):

• 如果r >= l ，请执行以下步骤：
  • 找到数组的中间值m = (l + r) / 2 。
  • 递归调用函数SlowSort 来查找前半个元素的最大值： SlowSort(arr, l, m)
  • 递归调用函数SlowSort 求后半元素的最大值： SlowSort(arr, m + 1, r)
  • 最后将上述函数调用返回的两个最大值中的最大值存储为arr[r] = max(arr[m], arr[r])
  • 递归调用函数SlowSort，没有上一步得到的最大值： SlowSort(arr, l, r-1)

下图显示了完整的慢排序过程。例如，数组{9, 6, 8, 4, 1, 3, 7, 2} 。从图中可以看出，数组被递归分成两半，直到大小变为1。一旦大小变为1，比较过程就开始了。

慢排序

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to swap two elements
void swap(int* xp, int* yp)
{
    int temp = *xp;
    *xp = *yp;
    *yp = temp;
}
 
// Function to sort the array using
// the Slow sort
void slow_sort(int A[], int i, int j)
{
    // Recursion break condition
    if (i >= j)
        return;
 
    // Store the middle value
    int m = (i + j) / 2;
 
    // Recursively call with the
    // left half
    slow_sort(A, i, m);
 
    // Recursively call with the
    // right half
    slow_sort(A, m + 1, j);
 
    // Swap if the first element is
    // lower than second
    if (A[j] < A[m]) {
        swap(&A[j], &A[m]);
    }
 
    // Recursively call with the
    // array excluding the maximum
    // element
    slow_sort(A, i, j - 1);
}
 
// Function to print the array
void printArray(int arr[], int size)
{
    int i;
    for (i = 0; i < size; i++)
        cout << arr[i] << " ";
    cout << endl;
}
 
// Driver Code
int main()
{
    // Given Input
    int arr[] = { 6, 8, 9, 4, 12, 1 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    // Function Call
    slow_sort(arr, 0, n - 1);
 
    // Print the sorted array
    printArray(arr, n);
 
    return 0;
}

Java

// Java program for the above approach
class GFG{
 
// Function to sort the array using
// the Slow sort
static void slow_sort(int A[], int i, int j)
{
     
    // Recursion break condition
    if (i >= j)
        return;
 
    // Store the middle value
    int m = (i + j) / 2;
 
    // Recursively call with the
    // left half
    slow_sort(A, i, m);
 
    // Recursively call with the
    // right half
    slow_sort(A, m + 1, j);
 
    // Swap if the first element is
    // lower than second
    if (A[j] < A[m])
    {
        int temp = A[j];
        A[j] = A[m];
        A[m] = temp;
    }
 
    // Recursively call with the
    // array excluding the maximum
    // element
    slow_sort(A, i, j - 1);
}
 
// Function to print the array
static void printArray(int arr[], int size)
{
    int i;
    for(i = 0; i < size; i++)
        System.out.print(arr[i] + " ");
         
    System.out.println();
}
 
// Driver code
public static void main(String[] args)
{
    int arr[] = { 6, 8, 9, 4, 12, 1 };
    int n = arr.length;
 
    // Function Call
    slow_sort(arr, 0, n - 1);
 
    // Print the sorted array
    printArray(arr, n);
}
}
 
// This code is contributed by abhinavjain194

Python3

# Python3 program for the above approach
 
# Function to sort the array using
# the Slow sort
def slow_sort(A, i, j):
     
    # Recursion break condition
    if (i >= j):
        return
         
    # Store the middle value
    m = (i + j) // 2
     
    # Recursively call with the
    # left half
    slow_sort(A, i, m)
 
    # Recursively call with the
    # right half
    slow_sort(A, m + 1, j)
 
    # Swap if the first element is
    # lower than second
    if (A[j] < A[m]):
        temp = A[m]
        A[m] = A[j]
        A[j] = temp
 
    # Recursively call with the
    # array excluding the maximum
    # element
    slow_sort(A, i, j - 1)
 
# Function to print the array
def printArray(arr, size):
     
    for i in range(size):
        print(arr[i], end = " ")
 
# Driver Code
if __name__ == '__main__':
     
    arr = [ 6, 8, 9, 4, 12, 1 ]
    n = len(arr)
     
    # Function Call
    slow_sort(arr, 0, n - 1)
     
    # Print the sorted array
    printArray(arr, n)
 
# This code is contributed by SoumikMondal

C#

// C# implementation of the approach
using System;
 
class GFG
{
   
// Function to sort the array using
// the Slow sort
static void slow_sort(int[] A, int i, int j)
{
     
    // Recursion break condition
    if (i >= j)
        return;
 
    // Store the middle value
    int m = (i + j) / 2;
 
    // Recursively call with the
    // left half
    slow_sort(A, i, m);
 
    // Recursively call with the
    // right half
    slow_sort(A, m + 1, j);
 
    // Swap if the first element is
    // lower than second
    if (A[j] < A[m])
    {
        int temp = A[j];
        A[j] = A[m];
        A[m] = temp;
    }
 
    // Recursively call with the
    // array excluding the maximum
    // element
    slow_sort(A, i, j - 1);
}
 
// Function to print the array
static void printArray(int[] arr, int size)
{
    int i;
    for(i = 0; i < size; i++)
        Console.Write(arr[i] + " ");
         
    Console.WriteLine();
}
 
    // Driver code
    public static void Main()
    {
    int[] arr = { 6, 8, 9, 4, 12, 1 };
    int n = arr.Length;
 
    // Function Call
    slow_sort(arr, 0, n - 1);
 
    // Print the sorted array
    printArray(arr, n);
    }
}
 
// this code is contributed by sanjoy_62.

Javascript

 
    // JavaScript program for the above approach
     
    // Function to sort the array using
    // the Slow sort
    function slow_sort(A, i, j)
    {
 
        // Recursion break condition
        if (i >= j)
            return;
 
        // Store the middle value
        let m = parseInt((i + j) / 2, 10);
 
        // Recursively call with the
        // left half
        slow_sort(A, i, m);
 
        // Recursively call with the
        // right half
        slow_sort(A, m + 1, j);
 
        // Swap if the first element is
        // lower than second
        if (A[j] < A[m])
        {
            let temp = A[j];
            A[j] = A[m];
            A[m] = temp;
        }
 
        // Recursively call with the
        // array excluding the maximum
        // element
        slow_sort(A, i, j - 1);
    }
 
    // Function to print the array
    function printArray(arr, size)
    {
        let i;
        for(i = 0; i < size; i++)
            document.write(arr[i] + " ");
 
        document.write("</br>");
    }
     
    let arr = [ 6, 8, 9, 4, 12, 1 ];
    let n = arr.length;
  
    // Function Call
    slow_sort(arr, 0, n - 1);
  
    // Print the sorted array
    printArray(arr, n);
     

输出：

1 4 6 8 9 12

最佳案例时间复杂度： $O(N^{\frac{log_2 N}{2 + e}})$ , 其中 e > 0
平均案例时间复杂度： $O(N^{\frac{log_2 N}{2}})$
辅助空间： O(1)

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