Odd-Even Sort / Brick Sort

This is basically a variation of bubble-sort. This algorithm is divided into two phases- Odd and Even Phase. The algorithm runs until the array elements are sorted and in each iteration two phases occurs- Odd and Even Phases.
In the odd phase, we perform a bubble sort on odd indexed elements and in the even phase, we perform a bubble sort on even indexed elements.

C++

// A C++ Program to implement Odd-Even / Brick Sort
#include<bits/stdc++.h>
using namespace std;

// A function to sort the algorithm using Odd Even sort
void oddEvenSort(int arr[], int n)
{
    bool isSorted = false; // Initially array is unsorted

    while (!isSorted)
    {
        isSorted = true;

        // Perform Bubble sort on odd indexed element
        for (int i=1; i<=n-2; i=i+2)
        {
            if (arr[i] > arr[i+1])
             {
                swap(arr[i], arr[i+1]);
                isSorted = false;
              }
        }

        // Perform Bubble sort on even indexed element
        for (int i=0; i<=n-2; i=i+2)
        {
            if (arr[i] > arr[i+1])
            {
                swap(arr[i], arr[i+1]);
                isSorted = false;
            }
        }
    }

    return;
}

// A utility function to print an array of size n
void printArray(int arr[], int n)
{
   for (int i=0; i < n; i++)
       cout << arr[i] << " ";
   cout << "\n";
}

// Driver program to test above functions.
int main()
{
    int arr[] = {34, 2, 10, -9};
    int n = sizeof(arr)/sizeof(arr[0]);

    oddEvenSort(arr, n);
    printArray(arr, n);

    return (0);
}

Java

// Java Program to implement
// Odd-Even / Brick Sort
import java.io.*;

class GFG
{
    public static void oddEvenSort(int arr[], int n)
    {
        boolean isSorted = false; // Initially array is unsorted

        while (!isSorted)
        {
            isSorted = true;
            int temp =0;

            // Perform Bubble sort on odd indexed element
            for (int i=1; i<=n-2; i=i+2)
            {
                if (arr[i] > arr[i+1])
                {
                    temp = arr[i];
                    arr[i] = arr[i+1];
                    arr[i+1] = temp;
                    isSorted = false;
                }
            }

            // Perform Bubble sort on even indexed element
            for (int i=0; i<=n-2; i=i+2)
            {
                if (arr[i] > arr[i+1])
                {
                    temp = arr[i];
                    arr[i] = arr[i+1];
                    arr[i+1] = temp;
                    isSorted = false;
                }
            }
        }

        return;
    }
    public static void main (String[] args)
    {
        int arr[] = {34, 2, 10, -9};
        int n = arr.length;

        oddEvenSort(arr, n);
        for (int i=0; i < n; i++)
            System.out.print(arr[i] + " ");

        System.out.println(" ");
    }
}
// Code Contributed by Mohit Gupta_OMG <(0_o)>

Python3

# Python Program to implement
# Odd-Even / Brick Sort

def oddEvenSort(arr, n):
    # Initially array is unsorted
    isSorted = 0
    while isSorted == 0:
        isSorted = 1
        temp = 0
        for i in range(1, n-1, 2):
            if arr[i] > arr[i+1]:
                arr[i], arr[i+1] = arr[i+1], arr[i]
                isSorted = 0

        for i in range(0, n-1, 2):
            if arr[i] > arr[i+1]:
                arr[i], arr[i+1] = arr[i+1], arr[i]
                isSorted = 0

    return


arr = [34, 2, 10, -9]
n = len(arr)

oddEvenSort(arr, n);
for i in range(0, n):
    print(arr[i], end = ' ')

# Code Contributed by Mohit Gupta_OMG <(0_o)>

C#

// C# Program to implement
// Odd-Even / Brick Sort
using System;

class GFG
{
    public static void oddEvenSort(int []arr, int n)
    {
        // Initially array is unsorted
        bool isSorted = false;

        while (!isSorted)
        {
            isSorted = true;
            int temp =0;

            // Perform Bubble sort on
            // odd indexed element
            for (int i = 1; i <= n - 2; i = i + 2)
            {
                if (arr[i] > arr[i+1])
                {
                    temp = arr[i];
                    arr[i] = arr[i+1];
                    arr[i+1] = temp;
                    isSorted = false;
                }
            }

            // Perform Bubble sort on
            // even indexed element
            for (int i = 0; i <= n - 2; i = i + 2)
            {
                if (arr[i] > arr[i+1])
                {
                    temp = arr[i];
                    arr[i] = arr[i+1];
                    arr[i+1] = temp;
                    isSorted = false;
                }
            }
        }
        return;
    }

    // Driver code
    public static void Main ()
    {
        int []arr = {34, 2, 10, -9};
        int n = arr.Length;

        // Function calling
        oddEvenSort(arr, n);
        for (int i = 0; i < n; i++)
            Console.Write(arr[i] + " ");

        Console.WriteLine(" ");
    }
}

// This code is contributed by Sam007

Javascript

<script>

// Javascript Program to implement
// Odd-Even / Brick Sort

   function oddEvenSort(arr, n)
    {
        // Initially array is unsorted

        let isSorted = false;

        while (!isSorted)
        {
            isSorted = true;
            let temp =0;

            // Perform Bubble sort on odd indexed element
            for (let i=1; i<=n-2; i=i+2)
            {
                if (arr[i] > arr[i+1])
                {
                    temp = arr[i];
                    arr[i] = arr[i+1];
                    arr[i+1] = temp;
                    isSorted = false;
                }
            }

            // Perform Bubble sort on even indexed element
            for (let i=0; i<=n-2; i=i+2)
            {
                if (arr[i] > arr[i+1])
                {
                    temp = arr[i];
                    arr[i] = arr[i+1];
                    arr[i+1] = temp;
                    isSorted = false;
                }
            }
        }

        return;
    }

// Driver Code

        let arr = [34, 2, 10, -9];
        let n = arr.length;

        oddEvenSort(arr, n);
        for (let i=0; i < n; i++)
            document.write(arr[i] + " ");

        document.write(" ");

</script>

Output :

-9 2 10 34 

We demonstrate the above algorithm using the below illustration on the array = {3, 2, 3, 8, 5, 6, 4, 1}

Please refer wiki for proof of correctness.
Time Complexity : O(N²) where, N = Number of elements in the input array.
Auxiliary Space : O(1). Just like bubble sort this is also an in-place algorithm.
Exercise
In our program in each iteration we first do bubble sort on odd indexed elements and then a bubble sort on the even indexed elements.
Will we get a sorted result if we first perform a bubble sort on even indexed element first and then on the odd indexed element ?
References
https://en.wikipedia.org/wiki/Odd%E2%80%93even_sort 

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