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

0 0 5 minutes read

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++

// 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

// 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

# 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#

// 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

Javascript

<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] + "  ");
          }
          // Print the remaining elements
          // in the described order
          else {
            document.write(a[j] + "  ");
            document.write(a[i] + "  ");
          }
          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>

Output:

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

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!