Rearrange a given list such that it consists of alternating minimum maximum elements

Given a list of integers, rearrange the list such that it consists of alternating minimum maximum elements using only list operations. The first element of the list should be minimum and second element should be maximum of all elements present in the list. Similarly, third element will be next minimum element and fourth element is next maximum element and so on. Use of extra space is not permitted. Examples:

Input:  [1 3 8 2 7 5 6 4]
Output: [1 8 2 7 3 6 4 5]

Input:  [1 2 3 4 5 6 7]
Output: [1 7 2 6 3 5 4]

Input:  [1 6 2 5 3 4]
Output: [1 6 2 5 3 4]

The idea is to sort the list in ascending order first. Then we start popping elements from the end of the list and insert them into their correct position in the list. Below is the implementation of above idea – 

C++

// C++ program to rearrange a given list such that it
// consists of alternating minimum maximum elements
#include <bits/stdc++.h>
using namespace std;

// Function to rearrange a given list such that it
// consists of alternating minimum maximum elements
void alternateSort(list<int>& inp)
{
    // sort the list in ascending order
    inp.sort();

    // get iterator to first element of the list
    list<int>::iterator it = inp.begin();
    it++;

    for (int i=1; i<(inp.size() + 1)/2; i++)
    {
        // pop last element (next greatest)
        int val = inp.back();
        inp.pop_back();

        // insert it after next minimum element
        inp.insert(it, val);

        // increment the pointer for next pair
        ++it;
    }
}

// Driver code
int main()
{
    // input list
    list<int> inp({ 1, 3, 8, 2, 7, 5, 6, 4 });

    // rearrange the given list
    alternateSort(inp);

    // print the modified list
    for (int i : inp)
        cout << i << " ";

    return 0;
}

Java

// Java program to rearrange a given list such that it
// consists of alternating minimum maximum elements
import java.util.*;

class AlternateSort
{
    // Function to rearrange a given list such that it
    // consists of alternating minimum maximum elements
    // using LinkedList
    public static void alternateSort(LinkedList<Integer> ll)
    {
        Collections.sort(ll);

        for (int i = 1; i < (ll.size() + 1)/2; i++)
        {
            Integer x = ll.getLast();
            ll.removeLast();
            ll.add(2*i - 1, x);
        }

        System.out.println(ll);
    }

    public static void main (String[] args) throws java.lang.Exception
    {
        // input list
        Integer arr[] = {1, 3, 8, 2, 7, 5, 6, 4};

        // convert array to LinkedList
        LinkedList<Integer> ll = new LinkedList<Integer>(Arrays.asList(arr));

        // rearrange the given list
        alternateSort(ll);
    }
}

Python

# Python program to rearrange a given list such that it
# consists of alternating minimum maximum elements
inp = []

# Function to rearrange a given list such that it
# consists of alternating minimum maximum elements
def alternateSort():

    global inp

    # sort the list in ascending order
    inp.sort()

    # get index to first element of the list
    it = 0
    it = it + 1

    i = 1

    while ( i < (len(inp) + 1)/2 ):

        i = i + 1

        # pop last element (next greatest)
        val = inp[-1]
        inp.pop()

        # insert it after next minimum element
        inp.insert(it, val)

        # increment the pointer for next pair
        it = it + 2

# Driver code

# input list
inp=[ 1, 3, 8, 2, 7, 5, 6, 4 ]

# rearrange the given list
alternateSort()

# print the modified list
print (inp)

# This code is contributed by Arnab Kundu

C#

// C# program to rearrange a given list such that it
// consists of alternating minimum maximum elements
using System;
using System.Collections.Generic;

class GFG
{
    // Function to rearrange a given list such that it
    // consists of alternating minimum maximum elements
    // using List
    public static void alternateSort(List<int> ll)
    {
        ll.Sort();

        for (int i = 1; i < (ll.Count + 1)/2; i++)
        {
            int x = ll[ll.Count-1];
            ll.RemoveAt(ll.Count-1);
            ll.Insert(2*i - 1, x);
        }
        foreach(int a in ll)
        {
            Console.Write(a+" ");
        }

    }

    // Driver code
    public static void Main (String[] args)
    {
        // input list
        int []arr = {1, 3, 8, 2, 7, 5, 6, 4};

        // convert array to List
        List<int> ll = new List<int>(arr);

        // rearrange the given list
        alternateSort(ll);
    }
}

/* This code contributed by PrinciRaj1992 */

Javascript

<script>

// JavaScript program to rearrange a given list such that it
// consists of alternating minimum maximum elements
let inp = []

// Function to rearrange a given list such that it
// consists of alternating minimum maximum elements
function alternateSort(){

    // sort the list in ascending order
    inp.sort()

    // get index to first element of the list
    let it = 0
    it = it + 1

    let i = 1

    while ( i < (inp.length + 1)/2 ){

        i = i + 1

        // pop last element (next greatest)
        let val = inp[inp.length-1]
        inp.pop()

        // insert it after next minimum element
        inp.splice(it,0, val)

        // increment the pointer for next pair
        it = it + 2
    }
}

// Driver code

// input list
inp=[ 1, 3, 8, 2, 7, 5, 6, 4 ]

// rearrange the given list
alternateSort()

// print the modified list
for(let x of inp){
    document.write(x," ")
}

// This code is contributed by shinjanpatra

</script>

Output:

1 8 2 7 3 6 4 5

Time Complexity: O(N*logN), as we are using a sort function.

Auxiliary Space: O(1), as we are not using extra space.

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