Lexicographical smallest alternate Array

Given an array arr[] of distinct elements, the task is to rearrange the array such that it is lexicographically smallest and of the form arr[0] > arr[1] < arr[2] > arr[3] < …
Examples:

Input: arr[] = {3, 2, 1, 4, 5} 
Output: 2 1 4 3 5
Input: arr[] = {10, 22} 
Output: 22 10 

Approach: In order to get the lexicographically smallest array, we can choose the minimum element as the first element but that will not satisfy the condition where the first element has to be strictly greater than the second element. 
Now, the second-best choice is to choose the second minimum from the array and the only element which is smaller than it is the smallest element which will be the second element of the array. 
Apply the same process for the rest of the array elements, choose the second minimum of the remaining elements and then choose the minimum for every two consecutive positions which can be obtained by first sorting the given array then swapping every two consecutive elements.
Below is the implementation of the above approach: 

C++

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;

// Function to print the
// contents of an array
void printArr(int arr[], int n)
{
    for (int i = 0; i < n; i++) {
        cout << arr[i] << " ";
    }
}

// Function to find the lexicographically
// smallest alternating array
void smallestArr(int arr[], int n)
{

    // Sort the array
    sort(arr, arr + n);

    // Swap every two consecutive elements
    for (int i = 0; i + 1 < n; i = i + 2) {
        swap(arr[i], arr[i + 1]);
    }

    // Print the re-arranged array
    printArr(arr, n);
}

// Driver code
int main()
{
    int arr[] = { 3, 2, 1, 4, 5 };
    int n = sizeof(arr) / sizeof(arr[0]);

    smallestArr(arr, n);

    return 0;
}

Java

// Java implementation of the approach
import java.util.Arrays;

class GFG
{

    // Function to print the
    // contents of an array
    static void printArr(int[] arr, int n)
    {
        for (int i = 0; i < n; i++)
            System.out.print(arr[i] + " ");
    }

    // Function to find the lexicographically
    // smallest alternating array
    static void smallestArr(int[] arr, int n)
    {

        // Sort the array
        Arrays.sort(arr);

        // Swap every two consecutive elements
        for (int i = 0; i + 1 < n; i = i + 2)
        {
            int temp = arr[i];
            arr[i] = arr[i + 1];
            arr[i + 1] = temp;
        }

        // Print the re-arranged array
        printArr(arr, n);
    }

    // Driver code
    public static void main(String[] args)
    {
        int[] arr = { 3, 2, 1, 4, 5 };
        int n = arr.length;
        smallestArr(arr, n);
    }
}

// This code is contributed by
// sanjeev2552

Python3

# Python3 implementation of the approach

# Function to print the
# contents of an array
def printArr(arr, n):
    for i in range(n):
        print(arr[i], end = " ");

# Function to find the lexicographically
# smallest alternating array
def smallestArr(arr, n):

    # Sort the array
    arr.sort();

    # Swap every two consecutive elements
    for i in range(0, n - 1, 2):

        temp = arr[i];
        arr[i] = arr[i + 1];
        arr[i + 1] = temp;

    # Print the re-arranged array
    printArr(arr, n);

# Driver code
if __name__ == '__main__':

    arr = [ 3, 2, 1, 4, 5 ];
    n = len(arr);
    smallestArr(arr, n);

# This code contributed by Rajput-Ji

C#

// C# implementation of the approach
using System;

class GFG
{

    // Function to print the
    // contents of an array
    static void printArr(int[] arr, int n)
    {
        for (int i = 0; i < n; i++)
            Console.Write(arr[i] + " ");
    }

    // Function to find the lexicographically
    // smallest alternating array
    static void smallestArr(int[] arr, int n)
    {

        // Sort the array
        Array.Sort(arr);

        // Swap every two consecutive elements
        for (int i = 0; i + 1 < n; i = i + 2)
        {
            int temp = arr[i];
            arr[i] = arr[i + 1];
            arr[i + 1] = temp;
        }

        // Print the re-arranged array
        printArr(arr, n);
    }

    // Driver code
    public static void Main(String[] args)
    {
        int[] arr = { 3, 2, 1, 4, 5 };
        int n = arr.Length;
        smallestArr(arr, n);
    }
}

// This code is contributed by 29AjayKumar

PHP

<?php
// PHP implementation of the approach

// Function to print the
// contents of an array
function printArr($arr, $n)
{
    for ($i = 0; $i < $n; $i++)
    {
        echo $arr[$i];
        echo " ";
    }
}

// Function to find the lexicographically
// smallest alternating array
function smallestArr($arr, $n)
{

    // Sort the array
    sort($arr);

    // Swap every two consecutive elements
    for ($i = 0; $i + 1 < $n; $i = $i + 2)
    {
        $temp = $arr[$i];
        $arr[$i] = $arr[$i + 1];
        $arr[$i + 1] = $temp;
    }

    // Print the re-arranged array
    printArr($arr, $n);
}

// Driver code
$arr = array( 3, 2, 1, 4, 5 );
$n = count($arr);

smallestArr($arr, $n);

// This code is contributed by Naman_Garg.
?>

Javascript

// javascript implementation of the approach

    // Function to print the
    // contents of an array
    function printArr(arr, n)
    {
        for (var i = 0; i < n; i++)
            document.write(arr[i] + " ");
    }

    // Function to find the lexicographically
    // smallest alternating array

    function smallestArr( arr,  n)
    {

        // Sort the array
        arr.sort();

        // Swap every two consecutive elements
        for (var i = 0; i + 1 < n; i = i + 2)
        {
            var temp = arr[i];
            arr[i] = arr[i + 1];
            arr[i + 1] = temp;
        }

        // Print the re-arranged array
        printArr(arr, n);
    }

    // Driver code
        var arr = [ 3, 2, 1, 4, 5 ] ;
        var n = arr.length;
        smallestArr(arr, n);

// This code is contributed by bunnyram19.

Output:

2 1 4 3 5

Time Complexity: O(nlogn)

Auxiliary Space: O(1)