Shuffle 2n integers in format {a1, b1, a2, b2, a3, b3, ……, an, bn} without using extra space

Given an array of 2n elements in the following format { a1, a2, a3, a4, ….., an, b1, b2, b3, b4, …., bn }. The task is shuffle the array to {a1, b1, a2, b2, a3, b3, ……, an, bn } without using extra space. 

Examples:

Input : arr[] = { 1, 2, 9, 15 }
Output : 1 9 2 15

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

Method 1: Brute Force

A brute force solution involves two nested loops to rotate the elements in the second half of the array to the left. The first loop runs n times to cover all elements in the second half of the array. The second loop rotates the elements to the left. Note that the start index in the second loop depends on which element we are rotating and the end index depends on how many positions we need to move to the left.

Below is the implementation of this approach: 

C++

// C++ Naive program to shuffle an array of size 2n
#include <bits/stdc++.h>
using namespace std;

// function to shuffle an array of size 2n
void shuffleArray(int a[], int n)
{
    // Rotate the element to the left
    for (int i = 0, q = 1, k = n; i < n; i++, k++, q++)
        for (int j = k; j > i + q; j--)
            swap(a[j - 1], a[j]);
}

// Driven Program
int main()
{
    int a[] = { 1, 3, 5, 7, 2, 4, 6, 8 };
    int n = sizeof(a) / sizeof(a[0]);

    shuffleArray(a, n / 2);

    for (int i = 0; i < n; i++)
        cout << a[i] << " ";

    return 0;
}

Java

// Java Naive program to shuffle an array of size 2n

import java.util.Arrays;

public class GFG {
    // method to shuffle an array of size 2n
    static void shuffleArray(int a[], int n)
    {
        // Rotate the element to the left
        for (int i = 0, q = 1, k = n; i < n; i++, k++, q++)
            for (int j = k; j > i + q; j--) {
                // swap a[j-1], a[j]
                int temp = a[j - 1];
                a[j - 1] = a[j];
                a[j] = temp;
            }
    }

    // Driver Method
    public static void main(String[] args)
    {
        int a[] = { 1, 3, 5, 7, 2, 4, 6, 8 };

        shuffleArray(a, a.length / 2);

        System.out.println(Arrays.toString(a));
    }
}

Python3

# Python3 Naive program to
# shuffle an array of size 2n

# Function to shuffle an array of size 2n
def shuffleArray(a, n):

    # Rotate the element to the left
    i, q, k = 0, 1, n
    while(i < n):
        j = k
        while(j > i + q):
            a[j - 1], a[j] = a[j], a[j - 1]
            j -= 1
        i += 1
        k += 1
        q += 1

# Driver Code
a = [1, 3, 5, 7, 2, 4, 6, 8]
n = len(a)
shuffleArray(a, int(n / 2))
for i in range(0, n):
    print(a[i], end = " ")

# This code is contributed by Smitha Dinesh Semwal.

C#

// C# Naive program to shuffle an
// array of size 2n
using System;

class GFG {
    // method to shuffle an array of size 2n
    static void shuffleArray(int[] a, int n)
    {
        // Rotate the element to the left
        for (int i = 0, q = 1, k = n;
             i < n; i++, k++, q++)
            for (int j = k; j > i + q; j--) {
                // swap a[j-1], a[j]
                int temp = a[j - 1];
                a[j - 1] = a[j];
                a[j] = temp;
            }
    }

    // Driver Code
    public static void Main()
    {
        int[] a = { 1, 3, 5, 7, 2, 4, 6, 8 };

        shuffleArray(a, a.Length / 2);
        for (int i = 0; i < a.Length; i++)
            Console.Write(a[i] + " ");
    }
}

// This code is contributed
// by ChitraNayal

Javascript

<script>
// Javascript Naive program to shuffle an array of size 2n

    // method to shuffle an array of size 2n
    function shuffleArray(a,n)
    {
        // Rotate the element to the left
        for (let i = 0, q = 1, k = n; i < n; i++, k++, q++)
            for (let j = k; j > i + q; j--) {
                // swap a[j-1], a[j]
                let temp = a[j - 1];
                a[j - 1] = a[j];
                a[j] = temp;
            }
    }

    // Driver Method
    let a=[ 1, 3, 5, 7, 2, 4, 6, 8];
    shuffleArray(a, a.length / 2);

    document.write(a.join(" "));

    //This code is contributed by avanitrachhadiya2155

</script>

Output

1 2 3 4 5 6 7 8 

Time Complexity: O(n²)
Auxiliary Space: O(1)

Method 2: (Divide and Conquer):

The idea is to use Divide and Conquer Technique. Divide the given array into half (say arr1[] and arr2[]) and swap second half element of arr1[] with first half element of arr2[]. Recursively do this for arr1 and arr2.

Let us explain with the help of an example. 

1. Let the array be a1, a2, a3, a4, b1, b2, b3, b4
2. Split the array into two halves: a1, a2, a3, a4 : b1, b2, b3, b4
3. Exchange element around the center: exchange a3, a4 with b1, b2 correspondingly. 
   you get: a1, a2, b1, b2, a3, a4, b3, b4
4. Recursively split a1, a2, b1, b2 into a1, a2 : b1, b2 
   then split a3, a4, b3, b4 into a3, a4 : b3, b4.
5. Exchange elements around the center for each subarray we get: 
   a1, b1, a2, b2 and a3, b3, a4, b4.

Note: This solution only handles the case when n = 2ⁱ where i = 0, 1, 2, …etc.

Below is implementation of this approach: 

C++

// C++ Effective  program to shuffle an array of size 2n

#include <bits/stdc++.h>
using namespace std;

// function to shuffle an array of size 2n
void shufleArray(int a[], int f, int l)
{
    if (f > l) {
        return;
    }

    // If only 2 element, return
    if (l - f == 1)
        return;

    // finding mid to divide the array
    int mid = (f + l) / 2;

    // using temp for swapping first half of second array
    int temp = mid + 1;

    // mmid is use for swapping second half for first array
    int mmid = (f + mid) / 2;

    // Swapping the element
    for (int i = mmid + 1; i <= mid; i++)
        swap(a[i], a[temp++]);

    // Recursively doing for first half and second half
    shufleArray(a, f, mid);
    shufleArray(a, mid + 1, l);
}

// Driven Program
int main()
{
    int a[] = { 1, 3, 5, 7, 2, 4, 6, 8 };
    int n = sizeof(a) / sizeof(a[0]);

    shufleArray(a, 0, n - 1);

    for (int i = 0; i < n; i++)
        cout << a[i] << " ";

    return 0;
}

Java

// Java Effective  program to shuffle an array of size 2n

import java.util.Arrays;

public class GFG {
    // method to shuffle an array of size 2n
    static void shufleArray(int a[], int f, int l)
    {
        if (f > l)
            return;

        // If only 2 element, return
        if (l - f == 1)
            return;

        // finding mid to divide the array
        int mid = (f + l) / 2;

        // using temp for swapping first half of second array
        int temp = mid + 1;

        // mmid is use for swapping second half for first array
        int mmid = (f + mid) / 2;

        // Swapping the element
        for (int i = mmid + 1; i <= mid; i++) {
            // swap a[i], a[temp++]
            int temp1 = a[i];
            a[i] = a[temp];
            a[temp++] = temp1;
        }

        // Recursively doing for first half and second half
        shufleArray(a, f, mid);
        shufleArray(a, mid + 1, l);
    }

    // Driver Method
    public static void main(String[] args)
    {
        int a[] = { 1, 3, 5, 7, 2, 4, 6, 8 };

        shufleArray(a, 0, a.length - 1);

        System.out.println(Arrays.toString(a));
    }
}

Python3

# Python3 effective program to
# shuffle an array of size 2n

# Function to shuffle an array of size 2n
def shufleArray(a, f, l):

    if (f > l):
        return

    # If only 2 element, return
    if (l - f == 1):
        return

    # Finding mid to divide the array
    mid = int((f + l) / 2)

    # Using temp for swapping first
    # half of the second array
    temp = mid + 1

    # Mid is use for swapping second
    # half for first array
    mmid = int((f + mid) / 2)

    # Swapping the element
    for i in range(mmid + 1, mid + 1):
        (a[i], a[temp]) = (a[temp], a[i])
        temp += 1

    # Recursively doing for first
    # half and second half
    shufleArray(a, f, mid)
    shufleArray(a, mid + 1, l)


# Driver Code
a = [1, 3, 5, 7, 2, 4, 6, 8]
n = len(a)
shufleArray(a, 0, n - 1)

for i in range(0, n):
    print(a[i], end = " ")

# This code is contributed by Smitha Dinesh Semwal

C#

// C# program to merge two
// sorted arrays with O(1) extra space.
using System;

// method to shuffle an array of size 2n

public class GFG {
    // method to shuffle an array of size 2n
    static void shufleArray(int[] a, int f, int l)
    {
        if (f > l)
            return;

        // If only 2 element, return
        if (l - f == 1)
            return;

        // finding mid to divide the array
        int mid = (f + l) / 2;

        // using temp for swapping first half of second array
        int temp = mid + 1;

        // mmid is use for swapping second half for first array
        int mmid = (f + mid) / 2;

        // Swapping the element
        for (int i = mmid + 1; i <= mid; i++) {
            // swap a[i], a[temp++]
            int temp1 = a[i];
            a[i] = a[temp];
            a[temp++] = temp1;
        }

        // Recursively doing for first half and second half
        shufleArray(a, f, mid);
        shufleArray(a, mid + 1, l);
    }

    // Driver Method
    public static void Main()
    {
        int[] a = { 1, 3, 5, 7, 2, 4, 6, 8 };

        shufleArray(a, 0, a.Length - 1);
        for (int i = 0; i < a.Length; i++)
            Console.Write(a[i] + " ");
    }
}

/*This code is contributed by 29AjayKumar*/

Javascript

<script>

// Javascript Effective program to
// shuffle an array of size 2n

// method to shuffle an array of size 2n
function shufleArray(a, f, l)
{
    if (f > l)
        return;

    // If only 2 element, return
    if (l - f == 1)
        return;

    // Finding mid to divide the array
    let mid = Math.floor((f + l) / 2);

    // Using temp for swapping first
    // half of second array
    let temp = mid + 1;

    // mmid is use for swapping second
    // half for first array
    let mmid = Math.floor((f + mid) / 2);

    // Swapping the element
    for(let i = mmid + 1; i <= mid; i++)
    {

        // Swap a[i], a[temp++]
        let temp1 = a[i];
        a[i] = a[temp];
        a[temp++] = temp1;
    }

    // Recursively doing for first
    // half and second half
    shufleArray(a, f, mid);
    shufleArray(a, mid + 1, l);
}

// Driver Code
let a = [ 1, 3, 5, 7, 2, 4, 6, 8 ];
shufleArray(a, 0, a.length - 1);

document.write(a.join(" "));

// This code is contributed by rag2127

</script>

Output

1 2 3 4 5 6 7 8 

Time Complexity: O(n log n)
Auxiliary Space: O(1)

Linear time solution

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