Although sorting a one-dimensional array is a well-known problem tackled in most programming courses and tutorials, organizing more complex data structures, such as a two-dimensional array, might pose a greater challenge. In this article, we will explore the implementation of the bubble sort algorithm that effectively sorts a 2D array in Python, analyze how it operates, and dive into some related concepts that will help with understanding the method and adapting it when needed.

**Bubble Sort for 2D Array**

To start, let’s first consider what it entails to sort a 2D array, and distinguish it from sorting a 1D array. Here is an example:

1D_Array = [5, 2, 8, 1, 4] 2D_Array = [[8, 2, 6], [1, 5, 4], [9, 3, 7]]

While sorting the 1D array only requires putting a series of numbers in the right order, sorting a 2D array refers to organizing numbers not only within rows and columns but also across them. Sorting a 2D array can be achieved in numerous ways, but our focus will be on applying the bubble sort algorithm.

**Step-by-Step Guide to Sorting a 2D Array with Bubble Sort**

Let’s now delve into the step-by-step explanation of applying bubble sort to a 2D array:

1. Create a Python function that takes in a 2D array.

2. Flatten the 2D array into a 1D array.

3. Apply the bubble sort algorithm to the 1D array.

4. Reshape the sorted 1D array back into a 2D array with the original dimensions.

And here’s how the function will look in Python:

def bubble_sort_2D(arr): n = len(arr) k = len(arr[0]) # Flatten the 2D array into a 1D array flat_arr = [elem for row in arr for elem in row] # Perform bubble sort on the 1D array for i in range(len(flat_arr)): for j in range(0, len(flat_arr)-i-1): if flat_arr[j] > flat_arr[j+1]: flat_arr[j], flat_arr[j+1] = flat_arr[j+1], flat_arr[j] # Reshape the 1D array back into a 2D array sorted_arr = [flat_arr[i:i+k] for i in range(0, len(flat_arr), k)] return sorted_arr

We now have a clear and efficient function for sorting a 2D array in Python using the bubble sort algorithm.

**Main Keywords for This Section:** Bubble sort, 1D array, 2D array, Python function, flatten, reshape.

## Overview of Bubble Sort Algorithm

Bubble sort is a foundational sorting algorithm that works by sequentially iterating through the list and comparing two adjacent elements. If the elements are in the wrong order, they are swapped. This process is repeated until the whole list is fully sorted.

**Main advantage** of the bubble sort algorithm is its **simplicity**. However, its **main drawback** lies in its **performance**, as it is not the most efficient sorting method for large datasets, with a worst-case time complexity of O(n^2). Although it may not be the best choice for highly efficient solutions, it still proves sufficient in smaller applications and for teaching purposes.

**Main Keywords for This Section:** Bubble sort algorithm, simplicity, performance, time complexity.

## Pandas for Easy Data Manipulation and Sorting

While the bubble sort is an important sorting algorithm to learn, there are more efficient ways to deal with 2D data structures, particularly when using the **Pandas library**. With Pandas, you can easily load, manipulate, and sort data using its powerful and intuitive dataframe structure.

Here’s a brief example of how to sort a 2D list using Pandas:

import pandas as pd data = [[8, 2, 6], [1, 5, 4], [9, 3, 7]] # Load the data into a Pandas DataFrame df = pd.DataFrame(data) # Sort the DataFrame sorted_df = df.stack().sort_values().unstack() # Convert the sorted DataFrame into a 2D list sorted_data = sorted_df.to_numpy().tolist()

Pandas offers a wide range of extra functionalities that can greatly enhance your data manipulation and analysis workflow, making it a powerful alternative to using classical sorting algorithms like bubble sort in some cases.

**Main Keywords for This Section:** Pandas library, efficient, 2D data structures, sorting, DataFrame.