Alternative Sorting

Given an array of integers, print the array in such a way that the first element is first maximum and second element is first minimum and so on.

Examples :

Input : arr[] = {7, 1, 2, 3, 4, 5, 6}
Output : 7 1 6 2 5 3 4

Input : arr[] = {1, 6, 9, 4, 3, 7, 8, 2}
Output : 9 1 8 2 7 3 6 4

A simple solution is to first print maximum element, then minimum, then second maximum, and so on. Time complexity of this approach is O(n²).

An efficient solution involves following steps. 

1. Sort input array using a O(n Log n) algorithm. 
2. We maintain two pointers, one from beginning and one from end in sorted array. We alternatively print elements pointed by two pointers and move them toward each other.

Implementation:

C++

// C++ program to print an array in alternate
// sorted manner.
#include <bits/stdc++.h>
using namespace std;

// Function to print alternate sorted values
void alternateSort(int arr[], int n)
{
    // Sorting the array
    sort(arr, arr+n);

    // Printing the last element of array
    // first and then first element and then
    // second last element and then second
    // element and so on.
    int i = 0, j = n-1;
    while (i < j) {
        cout << arr[j--] << " ";
        cout << arr[i++] << " ";
    }

    // If the total element in array is odd
    // then print the last middle element.
    if (n % 2 != 0)
        cout << arr[i];
}

// Driver code
int main()
{
    int arr[] = {1, 12, 4, 6, 7, 10};
    int n = sizeof(arr)/sizeof(arr[0]);
    alternateSort(arr, n);
    return 0;
}

Java

// Java program to print an array in alternate
// sorted manner
import java.io.*;
import java.util.Arrays;

class AlternativeString
{
    // Function to print alternate sorted values
    static void alternateSort(int arr[], int n)
    {
        Arrays.sort(arr);

        // Printing the last element of array
        // first and then first element and then
        // second last element and then second
        // element and so on.
        int i = 0, j = n-1;
        while (i < j) {
            System.out.print(arr[j--] + " ");
            System.out.print(arr[i++] + " ");
        }

        // If the total element in array is odd
        // then print the last middle element.
        if (n % 2 != 0)
            System.out.print(arr[i]);
    }

    /* Driver program to test above functions */
    public static void main (String[] args)
    {
        int arr[] = {1, 12, 4, 6, 7, 10};
        int n = arr.length;
        alternateSort(arr, n);
    }
}
/*This code is contributed by Prakriti Gupta*/

Python3

# Python 3 program to print an array
# in alternate sorted manner.

# Function to print alternate sorted
# values
def alternateSort(arr, n):

    # Sorting the array
    arr.sort()

    # Printing the last element of array
    # first and then first element and then
    # second last element and then second
    # element and so on.
    i = 0
    j = n-1

    while (i < j):

        print(arr[j], end =" ")
        j-= 1
        print(arr[i], end =" ")
        i+= 1

    # If the total element in array is odd
    # then print the last middle element.
    if (n % 2 != 0):
        print(arr[i])


# Driver code
arr = [1, 12, 4, 6, 7, 10]
n = len(arr)

alternateSort(arr, n)

# This code is contributed by
# Smitha Dinesh Semwal

C#

// C# program to print an array in alternate
// sorted manner
using System;

class AlternativeString {

    // Function to print alternate sorted values
    static void alternateSort(int[] arr, int n)
    {
        Array.Sort(arr);

        // Printing the last element of array
        // first and then first element and then
        // second last element and then second
        // element and so on.
        int i = 0, j = n - 1;
        while (i < j) {
            Console.Write(arr[j--] + " ");
            Console.Write(arr[i++] + " ");
        }

        // If the total element in array is odd
        // then print the last middle element.
        if (n % 2 != 0)
            Console.WriteLine(arr[i]);
    }

    /* Driver program to test above functions */
    public static void Main()
    {
        int[] arr = { 1, 12, 4, 6, 7, 10 };
        int n = arr.Length;
        alternateSort(arr, n);
    }
}

//

PHP

<?php
// PHP program to print an array in
// alternate sorted manner.

// Function to print alternate
// sorted values
function alternateSort($arr, $n)
{
    // Sorting the array
    sort($arr);

    // Printing the last element
    // of array  first and then
    // first element and then second
    // last element and then second
    // element and so on.
    $i = 0;
    $j = $n - 1;
    while ($i < $j)
    {
        echo $arr[$j--]." ";
        echo $arr[$i++]." ";
    }

    // If the total element in array
    // is odd then print the last
    // middle element.
    if ($n % 2 != 0)
        echo $arr[$i];
}

// Driver code
$arr= array(1, 12, 4, 6, 7, 10);
$n = sizeof($arr) / sizeof($arr[0]);

alternateSort($arr, $n);

// This code is contributed by Mithun Kumar
?>

Javascript

<script>
      // JavaScript program to print an array in alternate
      // sorted manner.

      // Function to print alternate sorted values
      function alternateSort(arr, n)
      {

        // Sorting the array
        console.log(arr);
        arr.sort(function (a, b)
        {
          return a - b;
        });
        console.log(arr);

        // Printing the last element of array
        // first and then first element and then
        // second last element and then second
        // element and so on.
        var i = 0,
          j = n - 1;
        while (i < j)
        {
          document.write(arr[j--] + " ");
          document.write(arr[i++] + " ");
        }

        // If the total element in array is odd
        // then print the last middle element.
        if (n % 2 != 0) document.write(arr[i]);
      }

      // Driver code
      var arr = [1, 12, 4, 6, 7, 10];
      var n = arr.length;
      alternateSort(arr, n);

      // This code is contributed by rdtank.
    </script>

Output

12 1 10 4 7 6 

Time Complexity: O(n Log n) 
Auxiliary Space : O(1), since no extra space has been taken.

This article is contributed by Sachin Bisht. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.