Python Program to Sort the 2D Array Across Columns

When a two-dimensional array or a 2D array is declared, it is treated like a matrix with rows and columns. Sorting a 2D array across columns means sorting the elements within each column independently, either in ascending or descending order.

Understanding Column-wise Sorting

Consider this 2D array ?

import numpy as np

# Original 2D array
arr = [[7, 9, 5, 7], 
       [9, 5, 9, 4], 
       [2, 7, 8, 6], 
       [8, 6, 6, 5]]

print("Original array:")
for row in arr:
    print(row)

Original array:
[7, 9, 5, 7]
[9, 5, 9, 4]
[2, 7, 8, 6]
[8, 6, 6, 5]

Matrix representation ?

7   9   5   7
9   5   9   4
2   7   8   6
8   6   6   5

Column-wise Sorting Process

When sorting columns in descending order ?

• Column 1: [7, 9, 2, 8] ? [9, 8, 7, 2]

• Column 2: [9, 5, 7, 6] ? [9, 7, 6, 5]

• Column 3: [5, 9, 8, 6] ? [9, 8, 6, 5]

• Column 4: [7, 4, 6, 5] ? [7, 6, 5, 4]

Using Bubble Sort Algorithm

Here's a complete implementation using bubble sort for column-wise sorting ?

def sort_columns_descending(matrix):
    """Sort each column in descending order using bubble sort"""
    rows = len(matrix)
    cols = len(matrix[0])
    
    # Sort each column independently
    for col in range(cols):
        # Bubble sort for current column
        for i in range(rows - 1):
            for j in range(rows - 1 - i):
                if matrix[j][col] < matrix[j + 1][col]:
                    # Swap elements in the column
                    matrix[j][col], matrix[j + 1][col] = matrix[j + 1][col], matrix[j][col]

def print_matrix(matrix, title):
    """Helper function to print matrix"""
    print(f"{title}:")
    for row in matrix:
        print(' '.join(f'{num:2d}' for num in row))
    print()

# Original array
arr = [[7, 9, 5, 7], 
       [9, 5, 9, 4], 
       [2, 7, 8, 6], 
       [8, 6, 6, 5]]

print_matrix(arr, "Original Matrix")

# Sort columns in descending order
sort_columns_descending(arr)

print_matrix(arr, "After Column-wise Sorting (Descending)")

Original Matrix:
 7  9  5  7
 9  5  9  4
 2  7  8  6
 8  6  6  5

After Column-wise Sorting (Descending):
 9  9  9  7
 8  7  8  6
 7  6  6  5
 2  5  5  4

Using NumPy for Efficient Sorting

NumPy provides a more efficient approach for column-wise sorting ?

import numpy as np

# Create array
arr = np.array([[7, 9, 5, 7], 
                [9, 5, 9, 4], 
                [2, 7, 8, 6], 
                [8, 6, 6, 5]])

print("Original array:")
print(arr)

# Sort each column in descending order
sorted_arr = -np.sort(-arr, axis=0)

print("\nColumn-wise sorted (descending):")
print(sorted_arr)

# Sort in ascending order
ascending_sorted = np.sort(arr, axis=0)
print("\nColumn-wise sorted (ascending):")
print(ascending_sorted)

Original array:
[[7 9 5 7]
 [9 5 9 4]
 [2 7 8 6]
 [8 6 6 5]]

Column-wise sorted (descending):
[[9 9 9 7]
 [8 7 8 6]
 [7 6 6 5]
 [2 5 5 4]]

Column-wise sorted (ascending):
[[2 5 5 4]
 [7 6 6 5]
 [8 7 8 6]
 [9 9 9 7]]

Comparison of Methods

Conclusion

Column-wise sorting rearranges elements within each column independently while maintaining the column structure. Use NumPy's sort(axis=0) for efficient sorting or implement custom algorithms for educational purposes.