Shuffle array {a1, a2, .. an, b1, b2, .. bn} as {a1, b1, a2, b2, a3, b3, ……, an, bn} without using extra space

Last Updated : 13 Apr, 2023

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 ` `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, 2, 9, 15 };` `    ``int` `n = ``sizeof``(a) / ``sizeof``(a[0]);`   `    ``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

 `# 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.`

Javascript

 `// Shuffles an array of size 2n.` `// Indexes are considered starting` `// from 1.` `function` `shuffleArray(a, n) {` `  ``let temp;` `  ``n = Math.floor(n / 2);`   `  ``for` `(let 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` `// The first element is bogus. We have used` `  ``// one based indexing for simplicity.` `const a = [-1, 1, 3, 5, 7, 2, 4, 6, 8];` `const n = a.length;`   `shuffleArray(a, n);`   `for` `(let i = 1; i < n; i++) {` `  ``console.log(a[i] + ``" "``);` `}`

Output:

`1 2 3 4 5 6 7 8`

Another Efficient Approach:

The O(n) approach can be improved by sequentially placing the elements at their correct position.
The criteria of finding the target index remains same.
The main thing here to realize is that if we swap the current element with an element with greater index, then we can end up traversing on this element which has been placed at its correct position.
In order to avoid this we increment this element by the max value in the array so when we come to this index we can simply ignore it.
When we have traversed the array from 2 to n-1, we need to re-produce the original array by subtracting the max value from element which is greater than max value..
Note : Indexes are considered 1 based in array for simplicity.
Below is the implementation of the above approach:

C++

 `#include ` `using` `namespace` `std;`   `// Function to shuffle arrays` `void` `Shuffle(``int` `arr[], ``int` `n) {` `    ``// Find the maximum element between the last element of the array and the middle element of the array` `    ``int` `max = (arr[n] > arr[n / 2]) ? arr[n] : arr[n / 2];`   `    ``// 'i' is traversing index and 'j' index for right half series` `    ``for` `(``int` `i = 2, j = 0; i <= n - 1; i++) {` `        ``// Check if on left half of array` `        ``if` `(i <= n / 2) {` `            ``// Check if this index has been visited or not` `            ``if` `(arr[i] < max) {` `                ``int` `temp = arr[2 * i - 1];`   `                ``// Increase the element by max` `                ``arr[2 * i - 1] = arr[i] + max;`   `                ``// As it's on the left half` `                ``arr[i] = temp;` `            ``}` `        ``}` `        ``// Right half` `        ``else` `{` `            ``// Index of right half series(b1, b2, b3)` `            ``j++; `   `            ``// Check if this index has been visited or not` `            ``if` `(arr[i] < max) {` `                ``int` `temp = arr[2 * j];`   `                ``// No need to add max as element is` `                ``arr[2 * j] = arr[i];`   `                ``// On right half` `                ``arr[i] = temp; ` `            ``}` `        ``}` `    ``}`   `    ``// Re-produce the original array` `    ``for` `(``int` `i = 2; i <= n - 1; i++) {` `        ``if` `(arr[i] > max) {` `            ``arr[i] = arr[i] - max;` `        ``}` `    ``}` `}`   `// Driver Program` `int` `main() {` `    ``int` `arr[] = { -1, 1, 3, 5, 7, 2, 4, 6, 8 };` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]) - 1;`   `    ``// Function Call` `    ``Shuffle(arr, n);`   `    ``for` `(``int` `i = 1; i <= n; i++) {` `        ``cout << arr[i] << ``" "``;` `    ``}` `    ``cout << endl;`   `    ``return` `0;` `}`

C#

 `// C# program for above approach` `using` `System; `   `class` `GFG ` `{` `    `  `    ``// Function to shuffle arrays` `    ``static` `void` `Shuffle(``int``[] arr, ``int` `n)` `    ``{` `        ``int` `max = (arr[n] > arr[n / 2]) ? ` `                         ``arr[n] : arr[n / 2];`   `        ``// 'i' is traversing index and ` `        ``// j index for right half series` `        ``for` `(``int` `i = 2, j = 0; i <= n - 1; i++) ` `        ``{`   `            ``// Check if on left half of array` `            ``if` `(i <= n / 2) ` `            ``{` `                `  `                ``// Check if this index ` `                ``// has been visited or not` `                ``if` `(arr[i] < max) ` `                ``{` `                    ``int` `temp = arr[2 * i - 1];`   `                    ``// Increase the element by max` `                    ``arr[2 * i - 1] = arr[i] + max;`   `                    ``// As it i on left half` `                    ``arr[i] = temp;` `                ``}` `            ``}` `          `  `            ``// Right half` `            ``else` `            ``{` `                `  `                ``// Index of right half ` `                ``// series(b1, b2, b3)` `                ``j++; `   `                ``// Check if this index ` `                ``// has been visited or not` `                ``if` `(arr[i] < max) ` `                ``{` `                    ``int` `temp = arr[2 * j];`   `                    ``// No need to add max ` `                    ``// as element is` `                    ``arr[2 * j] = arr[i];` `                  `  `                    ``// On right half` `                    ``arr[i] = temp; ` `                ``}` `            ``}` `        ``}`   `        ``// Re-produce the original array` `        ``for` `(``int` `i = 2; i <= n - 1; i++) ` `        ``{` `            ``if` `(arr[i] > max) ` `            ``{` `                ``arr[i] = arr[i] - max;` `            ``}` `        ``}` `    ``}` `    ``// Driver Program` `    ``public` `static` `void` `Main()` `    ``{` `        ``int``[] arr = { -1, 1, 3, 5, 7, 2, 4, 6, 8 };` `        ``int` `n = arr.Length - 1;` `      `  `        ``// Function Call` `        ``Shuffle(arr, n);` `        ``for` `(``int` `i = 1; i <= n; i++) ` `        ``{` `            ``Console.Write(arr[i] + ``" "``);` `        ``}` `        ``Console.WriteLine();` `    ``}` `}` `// This code is contributed by Armaan23`

Java

 `import` `java.util.*;`   `class` `Main {` `    ``// Function to shuffle arrays` `    ``static` `void` `Shuffle(``int``[] arr, ``int` `n) {` `        ``// Find the maximum element between the last element of the array and the middle element of the array` `        ``int` `max = (arr[n] > arr[n / ``2``]) ? arr[n] : arr[n / ``2``];`   `        ``// 'i' is traversing index and 'j' index for right half series` `        ``for` `(``int` `i = ``2``, j = ``0``; i <= n - ``1``; i++) {` `            ``// Check if on left half of array` `            ``if` `(i <= n / ``2``) {` `                ``// Check if this index has been visited or not` `                ``if` `(arr[i] < max) {` `                    ``int` `temp = arr[``2` `* i - ``1``];`   `                    ``// Increase the element by max` `                    ``arr[``2` `* i - ``1``] = arr[i] + max;`   `                    ``// As it's on the left half` `                    ``arr[i] = temp;` `                ``}` `            ``}` `            ``// Right half` `            ``else` `{` `                ``// Index of right half series(b1, b2, b3)` `                ``j++; `   `                ``// Check if this index has been visited or not` `                ``if` `(arr[i] < max) {` `                    ``int` `temp = arr[``2` `* j];`   `                    ``// No need to add max as element is` `                    ``arr[``2` `* j] = arr[i];`   `                    ``// On right half` `                    ``arr[i] = temp; ` `                ``}` `            ``}` `        ``}`   `        ``// Re-produce the original array` `        ``for` `(``int` `i = ``2``; i <= n - ``1``; i++) {` `            ``if` `(arr[i] > max) {` `                ``arr[i] = arr[i] - max;` `            ``}` `        ``}` `    ``}`   `    ``// Driver Program` `    ``public` `static` `void` `main(String[] args) {` `        ``int``[] arr = { -``1``, ``1``, ``3``, ``5``, ``7``, ``2``, ``4``, ``6``, ``8` `};` `        ``int` `n = arr.length - ``1``;`   `        ``// Function Call` `        ``Shuffle(arr, n);`   `        ``for` `(``int` `i = ``1``; i <= n; i++) {` `            ``System.out.print(arr[i] + ``" "``);` `        ``}` `        ``System.out.println();` `    ``}` `}`

Javascript

Output

```1 2 3 4 5 6 7 8
```

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