**π‘ Problem Formulation:** In the realm of matrix operations, a common task is to determine if a matrix would stay the same if each row were reversed. Imagine taking a 2D array representing our matrix and flipping each row horizontally. Would the flipped matrix still equate to the original? Consider an input matrix `[[1,2],[2,1]]`

; reversing each row gives us `[[2,1],[1,2]]`

, which is different from the original. This article explores various Python methods to check for this intriguing invariance.

## Method 1: Brute Force Comparison

This method entails individually reversing each row of the matrix and then comparing the reversed row to the original. The function specification would involve iterating through the matrix, using slice notation to reverse each row, and ensuring that the modified row matches the original.

Here’s an example:

def check_unchanged(matrix): for row in matrix: if row != row[::-1]: return False return True matrix = [[1, 2, 3], [4, 5, 4], [3, 2, 1]] print(check_unchanged(matrix))

Output: `True`

The above code snippet works by checking for each row whether the reverse of the row is the same as the original. It uses Python’s slice notation `row[::-1]`

to reverse the row, and if all rows are symmetric, then the function returns `True`

, else `False`

.

## Method 2: Numpy Array Equivalence

For a matrix represented as a NumPy array, we can reverse each row and check for equivalence with the original matrix using the `numpy.array_equal()`

function. A NumPy array can be reversed along rows easily using slicing as well.

Here’s an example:

import numpy as np def unchanged_with_numpy(matrix): reversed_matrix = np.fliplr(matrix) return np.array_equal(matrix, reversed_matrix) matrix = np.array([[1, 2, 1], [4, 5, 4], [1, 2, 1]]) print(unchanged_with_numpy(matrix))

Output: `True`

This method leverages NumPy’s `fliplr()`

function, which flips the entries in each row of the matrix left/right. The `array_equal()`

function then determines whether the flipped matrix is the same as the original, returning a boolean result.

## Method 3: Using Python’s All with List Comprehension

Combining Python’s `all()`

function with list comprehension can provide a succinct way to check if all rows in a matrix are symmetrical. By using this approach, each comparison operation can be expressed inline within a single expression, providing an elegant solution.

Here’s an example:

matrix = [[1, 2, 3], [4, 5, 4], [3, 2, 1]] print(all(row == row[::-1] for row in matrix))

Output: `True`

This code utilizes a list comprehension that reverses each row inline and returns `True`

if all row comparisons hold symmetry. The `all()`

function provides a clean way to enforce that the condition must be met for every row in the matrix.

## Method 4: Lambda Function with Map

Using a lambda function combined with the map function, we can achieve the same check. This method can be terse and might be more readable to those familiar with functional programming idioms in Python.

Here’s an example:

matrix = [[1, 2, 3], [4, 5, 4], [3, 2, 1]] print(all(map(lambda row: row == row[::-1], matrix)))

Output: `True`

The lambda function within the `map()`

reverses each row and checks it against the original row. The `all()`

then determines if each element in the iterator (each result of the lambda function application) is `True`

, meaning the matrix remains unchanged after row reversals.

## Bonus One-Liner Method 5: Using Generator Expression

The use of a generator expression is alike the list comprehension approach but with potentially more efficient memory usage, particularly for large matrices.

Here’s an example:

matrix = [[1, 2, 3], [4, 5, 4], [3, 2, 1]] print(all(row == row[::-1] for row in matrix))

Output: `True`

While this code visually resembles the list comprehension approach, here, the expressions inside the parentheses generate values on the fly. It means that no additional list is constructed, making it a resource-efficient solution for large datasets.

## Summary/Discussion

**Method 1: Brute Force Comparison.**Straightforward and easy to understand. May be inefficient for large matrices due to explicit looping and comparison.**Method 2: Numpy Array Equivalence.**Utilizes the power and speed of NumPy for array operations. Ideally suited for numerical matrices and requires NumPy to be installed.**Method 3: Python’s All with List Comprehension.**Concise and Pythonic. Efficient for short matrices, and becomes even more readable for those familiar with list comprehensions.**Method 4: Lambda Function with Map.**More functional programming style. It can be less intuitive for beginners but is concise and efficient.**Method 5: Using Generator Expression.**Memory efficient. Recommended for large matrices where memory usage is a concern.