Stable Binary Sort

Given an array arr[] of integers, the task is to partition the array based on even and odd elements. The partition has to be stable, meaning the relative ordering of all even elements must remain the same before and after partitioning, and the same should hold true for all odd elements.

Note: For a binary array (containing only 0s and 1s), this partition process is equivalent to sorting the array.

Examples:

Input: arr[] = [1, 0, 1, 1, 0, 0]
Output: [0 ,0 ,0, 1, 1, 1]
Explanation: All even numbers came before the odd numbers.

Input: arr[] = [1, 2, 3, 4, 5]
Output: [2, 4, 1, 3, 5]
Explanation: All even numbers [2, 4] came before the odd numbers [1, 3, 5], and the relative ordering was also same.

Input: arr[] = [-5, -2, 0, 4, 7, 9]
Output: [-2, 0, 4, -5, 7, 9]
Explanation: All even numbers [-2, 0, 4] came before the odd numbers [-5, 7, 9], and the relative ordering was also same.

The idea is to to use Naive Partitioning Algorithm, We use a temporary array to store the rearranged elements. We first iterate over the original array and add all the even elements to the temporary array, maintaining their original order. Next, we add all the odd elements to the temporary array in the same manner.

This guarantees that even elements appear before odd elements while preserving the relative order of similar elements. Finally, we copy the elements from the temporary array back into the original array.

// C++ program to partition the array into even  // and odd elements using naive partition approach #include <iostream> #include <vector> using namespace std; // Function for stable partitioning of even-odd(binary) array  void partition(vector<int> &arr) {  int n = arr.size();    // create a temporary array to store the elements  vector<int> temp(n);  int idx = 0;    // First fill even elements into the temporary array  for (int i = 0; i < n; i++) {  if (arr[i] % 2 == 0)   temp[idx++] = arr[i];  }    // Now fill odd elements into the temporary array  for (int i = 0; i < n; i++) {  if (arr[i] & 1)   temp[idx++] = arr[i];  }    // copy the elements from temp to arr  arr = temp; } int main() {  vector<int> arr = {-5, -2, 0, 4, 7, 9};  partition(arr);    for (int i = 0; i < arr.size(); i++)   cout << arr[i] << " ";   return 0; } 

// C program to partition the array into even  // and odd elements using naive partition approach #include <stdio.h> #include <stdlib.h> // Function for stable partitioning of even-odd(binary) array  void partition(int arr[], int n) {    // create a temporary array to store the elements  int *temp = (int *)malloc(n * sizeof(int));  int idx = 0;    // First fill even elements into the temporary array  for (int i = 0; i < n; i++) {  if (arr[i] % 2 == 0)   temp[idx++] = arr[i];  }    // Now fill odd elements into the temporary array  for (int i = 0; i < n; i++) {  if (arr[i] & 1)   temp[idx++] = arr[i];  }    // copy the elements from temp to arr  for (int i = 0; i < n; i++) {  arr[i] = temp[i];  }  free(temp); } int main() {  int arr[] = {-5, -2, 0, 4, 7, 9};  int n = sizeof(arr) / sizeof(arr[0]);  partition(arr, n);    for (int i = 0; i < n; i++)   printf("%d ", arr[i]);   return 0; } 

// Java program to partition the array into even  // and odd elements using naive partition approach import java.util.Arrays; class GfG {    // Function for stable partitioning of even-odd(binary) array   static void partition(int[] arr) {    int n = arr.length;    // create a temporary array to store the elements  int[] temp = new int[n];  int idx = 0;    // First fill even elements into the temporary array  for (int i = 0; i < n; i++) {  if (arr[i] % 2 == 0)   temp[idx++] = arr[i];  }    // Now fill odd elements into the temporary array  for (int i = 0; i < n; i++) {  if (arr[i] % 2 != 0)   temp[idx++] = arr[i];  }    // copy the elements from temp to arr  System.arraycopy(temp, 0, arr, 0, n);  }  public static void main(String[] args) {  int[] arr = {-5, -2, 0, 4, 7, 9};  partition(arr);    for (int i = 0; i < arr.length; i++)   System.out.print(arr[i] + " ");  } } 

# Python program to partition the array into even  # and odd elements using naive partition approach # Function for stable partitioning of even-odd(binary) array  def partition(arr): # create a temporary list to store the elements temp = [] # First fill even elements into the temporary list for num in arr: if num % 2 == 0: temp.append(num) # Now fill odd elements into the temporary list for num in arr: if num % 2 != 0: temp.append(num) # copy the elements from temp to arr for i in range(len(arr)): arr[i] = temp[i] if __name__ == "__main__": arr = [-5, -2, 0, 4, 7, 9] partition(arr) print(' '.join(map(str, arr))) 

// C# program to partition the array into even  // and odd elements using naive partition approach using System; class GfG {    // Function for stable partitioning of even-odd(binary) array   static void Partition(int[] arr) {  int n = arr.Length;    // create a temporary array to store the elements  int[] temp = new int[n];  int idx = 0;    // First fill even elements into the temporary array  for (int i = 0; i < n; i++) {  if (arr[i] % 2 == 0)   temp[idx++] = arr[i];  }    // Now fill odd elements into the temporary array  for (int i = 0; i < n; i++) {  if (arr[i] % 2 != 0)   temp[idx++] = arr[i];  }    // copy the elements from temp to arr  Array.Copy(temp, arr, n);  }  static void Main() {  int[] arr = {-5, -2, 0, 4, 7, 9};  Partition(arr);    Console.WriteLine(string.Join(" ", arr));  } } 

// JavaScript program to partition the array into even  // and odd elements using naive partition approach // Function for stable partitioning of even-odd(binary) array  function partition(arr) {  // create a temporary array to store the elements  let temp = [];    // First fill even elements into the temporary array  for (let i = 0; i < arr.length; i++) {  if (arr[i] % 2 === 0)   temp.push(arr[i]);  }    // Now fill odd elements into the temporary array  for (let i = 0; i < arr.length; i++) {  if (arr[i] % 2 !== 0)   temp.push(arr[i]);  }    // copy the elements from temp to arr  for (let i = 0; i < arr.length; i++) {  arr[i] = temp[i];  } } // Driver Code let arr = [-5, -2, 0, 4, 7, 9]; partition(arr); console.log(arr.join(' ')); 

-2 0 4 -5 7 9 

Time Complexity: O(n), for traversing the array.
Auxiliary Space: O(n), for temporary array.