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 6We 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++
#include <bits/stdc++.h>
using namespace std;
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]);
}
}
int main()
{
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
import java.io.*;
public class GFG {
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;
}
}
static public void main(String[] args)
{
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] + " ");
}
}
|
Python
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]
if __name__ == "__main__":
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=" ")
|
C#
using System;
public class GFG {
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;
}
}
static public void Main(String[] args)
{
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] + " ");
}
}
|
Javascript
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;
}
}
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] + " ");
}
|
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 <iostream>
using namespace std;
void Shuffle(int arr[], int n) {
int max = (arr[n] > arr[n / 2]) ? arr[n] : arr[n / 2];
for (int i = 2, j = 0; i <= n - 1; i++) {
if (i <= n / 2) {
if (arr[i] < max) {
int temp = arr[2 * i - 1];
arr[2 * i - 1] = arr[i] + max;
arr[i] = temp;
}
}
else {
j++;
if (arr[i] < max) {
int temp = arr[2 * j];
arr[2 * j] = arr[i];
arr[i] = temp;
}
}
}
for (int i = 2; i <= n - 1; i++) {
if (arr[i] > max) {
arr[i] = arr[i] - max;
}
}
}
int main() {
int arr[] = { -1, 1, 3, 5, 7, 2, 4, 6, 8 };
int n = sizeof(arr) / sizeof(arr[0]) - 1;
Shuffle(arr, n);
for (int i = 1; i <= n; i++) {
cout << arr[i] << " ";
}
cout << endl;
return 0;
}
|
C#
using System;
class GFG
{
static void Shuffle(int[] arr, int n)
{
int max = (arr[n] > arr[n / 2]) ?
arr[n] : arr[n / 2];
for (int i = 2, j = 0; i <= n - 1; i++)
{
if (i <= n / 2)
{
if (arr[i] < max)
{
int temp = arr[2 * i - 1];
arr[2 * i - 1] = arr[i] + max;
arr[i] = temp;
}
}
else
{
j++;
if (arr[i] < max)
{
int temp = arr[2 * j];
arr[2 * j] = arr[i];
arr[i] = temp;
}
}
}
for (int i = 2; i <= n - 1; i++)
{
if (arr[i] > max)
{
arr[i] = arr[i] - max;
}
}
}
public static void Main()
{
int[] arr = { -1, 1, 3, 5, 7, 2, 4, 6, 8 };
int n = arr.Length - 1;
Shuffle(arr, n);
for (int i = 1; i <= n; i++)
{
Console.Write(arr[i] + " ");
}
Console.WriteLine();
}
}
|
Java
import java.util.*;
class Main {
static void Shuffle(int[] arr, int n) {
int max = (arr[n] > arr[n / 2]) ? arr[n] : arr[n / 2];
for (int i = 2, j = 0; i <= n - 1; i++) {
if (i <= n / 2) {
if (arr[i] < max) {
int temp = arr[2 * i - 1];
arr[2 * i - 1] = arr[i] + max;
arr[i] = temp;
}
}
else {
j++;
if (arr[i] < max) {
int temp = arr[2 * j];
arr[2 * j] = arr[i];
arr[i] = temp;
}
}
}
for (int i = 2; i <= n - 1; i++) {
if (arr[i] > max) {
arr[i] = arr[i] - max;
}
}
}
public static void main(String[] args) {
int[] arr = { -1, 1, 3, 5, 7, 2, 4, 6, 8 };
int n = arr.length - 1;
Shuffle(arr, n);
for (int i = 1; i <= n; i++) {
System.out.print(arr[i] + " ");
}
System.out.println();
}
}
|
Python3
def Shuffle(arr, n):
max = arr[n] if arr[n] > arr[n // 2] else arr[n // 2]
j = 0
for i in range(2, n):
if i <= n // 2:
if arr[i] < max:
temp = arr[2 * i - 1]
arr[2 * i - 1] = arr[i] + max
arr[i] = temp
else:
j += 1
if arr[i] < max:
temp = arr[2 * j]
arr[2 * j] = arr[i]
arr[i] = temp
for i in range(2, n):
if arr[i] > max:
arr[i] -= max
if __name__ == '__main__':
arr = [-1, 1, 3, 5, 7, 2, 4, 6, 8]
n = len(arr) - 1
Shuffle(arr, n)
for i in range(1, n + 1):
print(arr[i], end=' ')
print()
|
Javascript
function Shuffle(arr, n) {
let max = (arr[n] > arr[Math.floor(n / 2)]) ? arr[n] : arr[Math.floor(n / 2)];
for (let i = 2, j = 0; i <= n - 1; i++) {
if (i <= Math.floor(n / 2)) {
if (arr[i] < max) {
let temp = arr[2 * i - 1];
arr[2 * i - 1] = arr[i] + max;
arr[i] = temp;
}
}
else {
j++;
if (arr[i] < max) {
let temp = arr[2 * j];
arr[2 * j] = arr[i];
arr[i] = temp;
}
}
}
for (let i = 2; i <= n - 1; i++) {
if (arr[i] > max) {
arr[i] = arr[i] - max;
}
}
}
let arr = [-1, 1, 3, 5, 7, 2, 4, 6, 8];
let n = arr.length - 1;
Shuffle(arr, n);
for (let i = 1; i <= n; i++) {
console.log(arr[i] + " ");
}
console.log();
|
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