# Shuffle array {a1, a2, .. an, b1, b2, .. bn} as {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
```

We have discussed O(n2) and O(n Log n) solutions of this problem in below post.
Shuffle 2n integers in format {a1, b1, a2, b2, a3, b3, ……, an, bn} without using extra space
Here a new solution is discussed that works in linear time. We know that the first and last numbers don’t move from their places. And, we keep track of the index from which any number is picked and where the target index is. We know that, if we’re picking ai, it has to go to the index 2 * i – 1 and if bi, it has to go 2 * i. We can check from where we have picked a certain number based on the picking index if it greater or less than n.
We will have to do this for 2 * n – 2 times, assuming that n = half of length of array.
We, get two cases, when n is even and odd, hence we initialize appropriately the start variable.
Note: Indexes are considered 1 based in array for simplicity.

C++

``````
// C++ program to shuffle an array in O(n) time
// and O(1) extra space
#include <bits/stdc++.h>
using namespace std;

// Shuffles an array of size 2n. Indexes
// are considered starting from 1.
void shufleArray(int a[], int n)
{
n = n / 2;

for (int start = n + 1, j = n + 1, done = 0, i;
done < 2 * n - 2; done++) {
if (start == j) {
start--;
j--;
}

i = j > n ? j - n : j;
j = j > n ? 2 * i : 2 * i - 1;

swap(a[start], a[j]);
}
}

// Driven Program
int main()
{
// The first element is bogus. We have used
// one based indexing for simplicity.
int a[] = { -1, 1, 3, 5, 7, 2, 4, 6, 8 };
int n = sizeof(a) / sizeof(a);

shufleArray(a, n);

for (int i = 1; i < n; i++)
cout << a[i] << " ";

return 0;
}
``````

Java

``````
// Java program to shuffle an
// array in O(n) time and O(1)
// extra space
import java.io.*;

public class GFG {

// Shuffles an array of size 2n.
// Indexes are considered starting
// from 1.
static void shufleArray(int[] a, int n)
{
int temp;
n = n / 2;

for (int start = n + 1, j = n + 1, done = 0, i;
done < 2 * n - 2; done++) {
if (start == j) {
start--;
j--;
}

i = j > n ? j - n : j;
j = j > n ? 2 * i : 2 * i - 1;
temp = a[start];
a[start] = a[j];
a[j] = temp;
}
}

// Driver code
static public void main(String[] args)
{
// The first element is bogus. We have used
// one based indexing for simplicity.
int[] a = { -1, 1, 3, 5, 7, 2, 4, 6, 8 };
int n = a.length;

shufleArray(a, n);

for (int i = 1; i < n; i++)
System.out.print(a[i] + " ");
}
}

// This Code is contributed by vt_m.
``````

Python 3

``````
# Python 3 program to shuffle an array
# in O(n) time and O(1) extra space

# Shuffles an array of size 2n. Indexes
# are considered starting from 1.
def shufleArray(a, n):

n = n // 2

start = n + 1
j = n + 1
for done in range( 2 * n - 2) :
if (start == j) :
start -= 1
j -= 1

i = j - n if j > n else j
j = 2 * i if j > n else 2 * i - 1

a[start], a[j] = a[j], a[start]

# Driver Code
if __name__ == "__main__":

# The first element is bogus. We have used
# one based indexing for simplicity.
a = [ -1, 1, 3, 5, 7, 2, 4, 6, 8 ]
n = len(a)

shufleArray(a, n)

for i in range(1, n):
print(a[i], end = " ")

# This code is contributed
# by ChitraNayal
``````

C#

``````
// C# program to shuffle an
// array in O(n) time and O(1)
// extra space
using System;

public class GFG {

// Shuffles an array of size 2n.
// Indexes are considered starting
// from 1.
static void shufleArray(int[] a, int n)
{
int temp;
n = n / 2;

for (int start = n + 1, j = n + 1, done = 0, i;
done < 2 * n - 2; done++) {
if (start == j) {
start--;
j--;
}

i = j > n ? j - n : j;
j = j > n ? 2 * i : 2 * i - 1;
temp = a[start];
a[start] = a[j];
a[j] = temp;
}
}

// Driven code
static public void Main(String[] args)
{
// The first element is bogus. We have used
// one based indexing for simplicity.
int[] a = { -1, 1, 3, 5, 7, 2, 4, 6, 8 };
int n = a.Length;

shufleArray(a, n);

for (int i = 1; i < n; i++)
Console.Write(a[i] + " ");
}
}

// This Code is contributed by vt_m.
``````

PHP

``````
<?php
// PHP program to shuffle an
// array in O(n) time and O(1)
// extra space

// Shuffles an array of size 2n.
// Indexes are considered starting
// from 1.
function shufleArray(\$a, \$n)
{

\$k = intval(\$n / 2);

for (\$start = \$k + 1,
\$j = \$k + 1, \$done = 0;
\$done < 2 * \$k - 2; \$done++)
{
if (\$start == \$j)
{
\$start--;
\$j--;
}

\$i = \$j > \$k ? \$j - \$k : \$j;
\$j = \$j > \$k ? 2 * \$i : 2 * \$i - 1;
\$temp = \$a[\$start];
\$a[\$start] = \$a[\$j];
\$a[\$j] = \$temp;

}
for (\$i = 1; \$i < \$n; \$i++)
echo \$a[\$i] . " ";
}

// Driver code

// The first element is bogus.
// We have used one based
// indexing for simplicity.
\$a = array(-1, 1, 3, 5, 7, 2, 4, 6, 8);
\$n = count(\$a);
shufleArray(\$a, \$n);

// This code is contributed by Sam007
?>

``````