Rearrange array such that difference of adjacent elements is in descending order

Given an array a[] with n integers the task is to rearrange the elements of the array in such a way that the differences of the adjacent elements are in descending order.
Examples: 
 

Input : arr[] = {1, 2, 3, 4, 5, 6} 
Output : 6 1 5 2 4 3
Explanation:
For first two elements the difference is abs(6-1)=5
For next two elements the difference is abs(1-5)=4
For next two elements the difference is abs(5-2)=3
For next two elements the difference is abs(2-4)=2
For next two elements the difference is abs(4-3)=1
Hence, difference array is 5, 4, 3, 2, 1.

Input : arr[] = {7, 10, 2, 4, 5}
Output : 10 2 7 4 5 
Explanation:
For first two elements the difference is abs(10-2)=8
For next two elements the difference is abs(2-7)=5
For next two elements the difference is abs(7-4)=3
For next two elements the difference is abs(4-5)=1
Hence, difference array is 8, 5, 3, 1.

Approach:
To solve the problem mentioned above we have to sort the array and then print the elements in the following order for the even-sized array :
 

a[n], a[1], a[n-1], a[2] ..... a[(n/2)], [(n/2)+1] 

And for odd-sized array, we have to print array elements in the following order:
 

a[n], a[1], a[n-1], a[2] ..... a[(n/2)+1]

Below is the implementation of the above approach: 
 

// C++ implementation to Rearrange array
// such that difference of adjacent
// elements is in descending order

#include <bits/stdc++.h>
using namespace std;

// Function to print array in given order
void printArray(int* a, int n)
{
    // Sort the array
    sort(a, a + n);
    int i = 0;
    int j = n - 1;

    // Check elements till the middle index
    while (i <= j) {
        // check if length is odd
        // print the middle index at last
        if (i == j) {
            cout << a[i] << " ";
        }
        // Print the remaining elements
        // in the described order
        else {
            cout << a[j] << " ";
            cout << a[i] << " ";
        }
        i = i + 1;
        j = j - 1;
    }
    cout << endl;
}

// Driver code
int main()
{

    // array declaration
    int arr1[] = { 1, 2, 3, 4, 5, 6 };

    // size of array
    int n1 = sizeof(arr1) / sizeof(arr1[0]);

    printArray(arr1, n1);
}

// Java implementation to Rearrange array
// such that difference of adjacent
// elements is in descending order
import java.util.*;

class GFG {
    
// Function to print array in given order
static void printArray(int []a, int n)
{
    
    // Sort the array
    Arrays.sort(a);
    
    int i = 0;
    int j = n - 1;
    
    // Check elements till the 
    // middle index
    while (i <= j)
    {
        
        // Check if length is odd print
        // the middle index at last
        if (i == j)
        {
            System.out.print(a[i] + " ");
        }
        
        // Print the remaining elements
        // in the described order
        else 
        {
            System.out.print(a[j] + " ");
            System.out.print(a[i] + " ");
        }
        i = i + 1;
        j = j - 1;
    }
    System.out.println();
}
    
// Driver code
public static void main (String[] args) 
{
    
    // Array declaration
    int arr1[] = { 1, 2, 3, 4, 5, 6 };
    
    // Size of array
    int n1 = arr1.length;
    
    printArray(arr1, n1);
}    
}

// This code is contributed by AnkitRai01

# Python3 implementation to rearrange  
# array such that difference of adjacent 
# elements is in descending order 

# Function to print array in given order 
def printArray(a, n): 
    
    # Sort the array 
    a.sort();
    
    i = 0; 
    j = n - 1; 

    # Check elements till the middle index 
    while (i <= j):
        
        # Check if length is odd print
        # the middle index at last 
        if (i == j):
            print(a[i], end = " "); 
            
        # Print the remaining elements 
        # in the described order 
        else :
            print(a[j], end = " ");
            print(a[i], end = " "); 
        
        i = i + 1; 
        j = j - 1; 

    print();

# Driver code 
if __name__ == "__main__" : 

    # Array declaration 
    arr1 = [ 1, 2, 3, 4, 5, 6 ]; 

    # Size of array 
    n1 = len(arr1); 

    printArray(arr1, n1); 

# This code is contributed by AnkitRai01

// C# implementation to rearrange array
// such that difference of adjacent
// elements is in descending order
using System;

class GFG {
        
// Function to print array in given order
static void printArray(int []a, int n)
{
        
    // Sort the array
    Array.Sort(a);
        
    int i = 0;
    int j = n - 1;
        
    // Check elements till the 
    // middle index
    while (i <= j)
    {
            
        // Check if length is odd print
        // the middle index at last
        if (i == j)
        {
            Console.Write(a[i] + " ");
        }
            
        // Print the remaining elements
        // in the described order
        else
        {
            Console.Write(a[j] + " ");
            Console.Write(a[i] + " ");
        }
        i = i + 1;
        j = j - 1;
    }
    Console.WriteLine();
}
        
// Driver code
public static void Main (string[] args) 
{
        
    // Array declaration
    int []arr1 = { 1, 2, 3, 4, 5, 6 };
        
    // Size of array
    int n1 = arr1.Length;
        
    printArray(arr1, n1);
}     
}

// This code is contributed by AnkitRai01

<script>

      // JavaScript implementation to Rearrange array
      // such that difference of adjacent
      // elements is in descending order

      // Function to print array in given order
      function printArray(a, n) 
      {
        // Sort the array
        a.sort(function (a, b) {
          return a - b;
        });
        var i = 0;
        var j = n - 1;

        // Check elements till the middle index
        while (i <= j) {
          // check if length is odd
          // print the middle index at last
          if (i == j) {
            document.write(a[i] + "&nbsp;&nbsp;");
          }
          // Print the remaining elements
          // in the described order
          else {
            document.write(a[j] + "&nbsp;&nbsp;");
            document.write(a[i] + "&nbsp;&nbsp;");
          }
          i = i + 1;
          j = j - 1;
        }
        document.write("<br>");
      }

      // Driver code
      // array declaration
      var arr1 = [1, 2, 3, 4, 5, 6];

      // size of array
      var n1 = arr1.length;
      printArray(arr1, n1);
      
      
</script>

6 1 5 2 4 3

Time Complexity: O(N * logN) the inbuilt sort function takes N log N time to complete all operations, hence the overall time taken by the algorithm is N log N
Auxiliary Space: O(1) since no extra array is used so the space taken by the algorithm is constant