对双调数组进行排序

给定一个双音数组arr[]任务是对给定的双音数组进行排序。

A Bitonic Sequence is a sequence of numbers that is first strictly increasing then after a point strictly decreasing.

例子：

Input: arr[] = {5, 10, 15, 25, 20, 3, 2, 1} 
Output: 1 2 3 5 10 15 20 25
Input: arr[] = {5, 20, 30, 40, 36, 33, 25, 15, 10} 
Output: 5 10 15 20 25 30 33 36 40

方法：

• 这个想法是将变量K初始化为数组大小的2的最高幂，例如比较相距K远的元素。
• 如果元素不按递增顺序交换元素。
• 将K减半并重复该过程直到K变为零。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
using namespace std;
 
// Function to Sort a Bitonic array
// in constant space
void sortArr(int a[], int n)
{
    int i, k;
 
    // Initialse the value of k
    k = (int)log2(n);
    k = pow(2, k);
 
    // In each iteration compare elements
    // k distance apart and swap if
    // they are not in order
    while (k > 0) {
        for (i = 0; i + k < n; i++)
            if (a[i] > a[i + k])
                swap(a[i], a[i + k]);
 
        // k is reduced to half
        // after every iteration
        k = k / 2;
    }
 
    // Print the array elements
    for (i = 0; i < n; i++) {
        cout << a[i] << " ";
    }
}
 
// Driver Code
int main()
{
    // Given array arr[]
    int arr[] = { 5, 20, 30, 40, 36, 33, 25, 15, 10 };
    int n = sizeof(arr) / sizeof(arr[0]);
 
    // Function Call
    sortArr(arr, n);
 
    return 0;
}

Java

// Java program for the above approach
import java.io.*;
 
class GFG{
     
// Function to Sort a Bitonic array
// in constant space
static void sortArr(int a[], int n)
{
    int i, k;
 
    // Initialse the value of k
    k = (int)(Math.log(n) / Math.log(2));
    k = (int) Math.pow(2, k);
 
    // In each iteration compare elements
    // k distance apart and swap if
    // they are not in order
    while (k > 0)
    {
        for(i = 0; i + k < n; i++)
            if (a[i] > a[i + k])
            {
                int tmp = a[i];
                a[i] = a[i + k];
                a[i + k] = tmp;
            }
 
        // k is reduced to half
        // after every iteration
        k = k / 2;
    }
 
    // Print the array elements
    for(i = 0; i < n; i++)
    {
        System.out.print(a[i] + " ");
    }
}
     
// Driver code
public static void main (String[] args)
{
     
    // Given array arr[]
    int arr[] = { 5, 20, 30, 40, 36,
                  33, 25, 15, 10 };
    int n = arr.length;
     
    // Function call
    sortArr(arr, n);
}
}
 
// This code is contributed by offbeat

Python3

# Python3 program for the
# above approach
import math
 
# Function to sort bitonic
# array in constant space
def sortArr(a, n):
 
    # Initialize thevalue of k
    k = int(math.log(n, 2))
    k = int(pow(2, k))
 
    # In each iteration compare elements
    # k distance apart and swap it
    # they are not in order
    while(k > 0):
        i = 0
        while i + k < n:
            if a[i] > a[i + k]:
                a[i], a[i + k] = a[i + k], a[i]
            i = i + 1
             
        # k is reduced to half after
        # every iteration
        k = k // 2
     
    # Print the array elements    
    for i in range(n):
        print(a[i], end = " ")
 
# Driver code
 
# Given array
a = [ 5, 20, 30, 40, 36, 33, 25, 15, 10 ]
n = len(a)
 
# Function call
sortArr(a, n)
 
# This code is contributed by virusbuddah_

C#

// C# program for the above approach
using System;
 
class GFG{
     
// Function to Sort a Bitonic array
// in constant space
static void sortArr(int []a, int n)
{
    int i, k;
 
    // Initialse the value of k
    k = (int)(Math.Log(n) / Math.Log(2));
    k = (int) Math.Pow(2, k);
 
    // In each iteration compare elements
    // k distance apart and swap if
    // they are not in order
    while (k > 0)
    {
        for(i = 0; i + k < n; i++)
            if (a[i] > a[i + k])
            {
                int tmp = a[i];
                a[i] = a[i + k];
                a[i + k] = tmp;
            }
 
        // k is reduced to half
        // after every iteration
        k = k / 2;
    }
 
    // Print the array elements
    for(i = 0; i < n; i++)
    {
        Console.Write(a[i] + " ");
    }
}
     
// Driver code
public static void Main(String[] args)
{
     
    // Given array []arr
    int []arr = { 5, 20, 30, 40, 36,
                  33, 25, 15, 10 };
    int n = arr.Length;
     
    // Function call
    sortArr(arr, n);
}
}
 
// This code is contributed by amal kumar choubey

Javascript

 
// Java script program for the above approach
     
// Function to Sort a Bitonic array
// in constant space
function sortArr(a,n)
{
    let i, k;
 
    // Initialse the value of k
    k = parseInt(Math.log(n) / Math.log(2));
    k = parseInt( Math.pow(2, k));
 
    // In each iteration compare elements
    // k distance apart and swap if
    // they are not in order
    while (k > 0)
    {
        for(i = 0; i + k < n; i++)
            if (a[i] > a[i + k])
            {
                let tmp = a[i];
                a[i] = a[i + k];
                a[i + k] = tmp;
            }
 
        // k is reduced to half
        // after every iteration
        k = k / 2;
    }
 
    // Print the array elements
    for(i = 0; i < n; i++)
    {
        document.write(a[i] + " ");
    }
}
     
// Driver code
 
     
    // Given array arr[]
    let arr = [ 5, 20, 30, 40, 36,
                33, 25, 15, 10 ];
    let n = arr.length;
     
    // Function call
    sortArr(arr, n);
 
// This code is contributed by sravan kumar

输出：

5 10 15 20 25 30 33 36 40

时间复杂度： O(N*log N)
辅助空间： O(1)

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