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 ordervoid 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 codeint 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 orderimport java.util.*;class GFG { // Function to print array in given orderstatic 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 codepublic 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 orderusing System;class GFG { // Function to print array in given orderstatic 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 codepublic 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
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