Python Program for Odd-Even Sort / Brick Sort

Given an array of integers, the task is to sort the elements in ascending order using Odd-Even Sort, also known as Brick Sort. This algorithm repeatedly performs two passes over the list one comparing adjacent odd-indexed pairs and the other comparing even-indexed pairs until the entire list becomes sorted.

For Example:

Input: [34, 2, 10, -9]
Output: [-9, 2, 10, 34]
Explanation: The algorithm alternates between odd and even phases, comparing and swapping elements in each phase until the array is sorted.

Algorithm Steps

1. Start with an unsorted array.
2. Perform an odd phase, where each odd-indexed element is compared with the next one and swapped if needed.
3. Perform an even phase, where even-indexed elements are compared with the next one and swapped if needed.
4. Repeat the odd and even phases alternately until no swaps are needed.
5. The array becomes fully sorted when both passes make no swaps.

Working of Odd-Even Sort

Let’s understand how the algorithm works step by step using the example [34, 2, 10, -9]:

Initial Array: [34, 2, 10, -9]

• Odd Phase (Compare indices 1 and 2): 2 and 10 are already in order -> [34, 2, 10, -9]
• Even Phase (Compare indices 0 and 1, 2 and 3): Swap 34 and 2 -> [2, 34, 10, -9] and Swap 10 and -9 -> [2, 34, -9, 10]
• Next Odd Phase: Compare 34 and -9 -> swap -> [2, -9, 34, 10]
• Next Even Phase: Compare 2 and -9 -> swap -> [-9, 2, 34, 10] and Compare 34 and 10 -> swap -> [-9, 2, 10, 34]

No further swaps needed the array is now sorted.

Using Odd-Even Logic

In this approach, sorting is performed manually through alternating odd and even phases using loops and swaps. It gives a clear understanding of how the algorithm operates internally.

Sorted array: [-9, 2, 10, 34]

Explanation:

• The variable isSorted ensures the loop runs until no swaps occur.
• In each odd phase, elements at indices 1, 3, 5, … are compared with their next element.
• In the even phase, elements at indices 0, 2, 4, … are compared similarly.
• The swapping process continues until all elements are in the correct order.

Using NumPy for Vectorized Odd-Even Sorting

For larger datasets, NumPy can be used to optimize comparison and swapping using vectorized operations, which reduces execution time significantly compared to standard loops.

Sorted array: [-9, 2, 10, 34]

Explanation:

• The list is converted to a NumPy array for vectorized processing.
• arr[1:n-1:2] and arr[2:n:2] select odd and even-indexed pairs.
• Boolean masks like odd_pairs help identify where swaps are needed.

Using Built-in sorted() Function

This approach leverages Python’s built-in sorted() function to simplify the sorting process. It sorts odd-indexed and even-indexed elements separately in each iteration, reducing manual comparisons and improving readability.

Sorted array: [-9, 10, 2, 34]

Explanation:

• The slicing arr[1::2] and arr[2::2] extract the odd and even indexed elements.
• sorted() sorts these slices internally, simplifying comparison logic.
• The second loop ensures the final adjustments are made to complete sorting.

Please refer complete article on Odd-Even Sort / Brick Sort for more details!