**π‘ Problem Formulation:** You have a dataset represented as a list of lists (rows) in Python. The challenge is to extract rows where the elements form an arithmetic sequence, i.e., the difference between consecutive elements is constant. For example, given the input `[[1, 3, 5], [2, 4, 7], [9, 12, 15]]`

, the desired output would be `[[1, 3, 5], [9, 12, 15]]`

, as these rows contain elements with a common difference.

## Method 1: Using Loops and Conditions

This method involves iterating through each row and checking the difference between consecutive elements. If all differences are equal, the row is extracted. The process is straightforward and easy to understand for those familiar with basic Python programming.

Here’s an example:

def extract_rows_with_common_difference(data): result = [] for row in data: if all(row[i] - row[i - 1] == row[1] - row[0] for i in range(2, len(row))): result.append(row) return result input_data = [[1, 3, 5], [2, 4, 7], [9, 12, 15]] print(extract_rows_with_common_difference(input_data))

Output:

[[1, 3, 5], [9, 12, 15]]

This code defines a function `extract_rows_with_common_difference()`

which takes a dataset (list of lists) as input. Inside the function, it iterates through each row, checking if the differences between consecutive elements are the same. If they are, the row is appended to the result list, which is then returned.

## Method 2: Using List Comprehensions

List comprehensions offer a more concise way to write loops in Python. This method uses a single expression to filter the rows that have a common difference between consecutive elements.

Here’s an example:

def extract_rows_with_common_diff_comp(data): return [ row for row in data if all(row[i] - row[i - 1] == row[1] - row[0] for i in range(2, len(row))) ] input_data = [[1, 3, 5], [2, 4, 7], [9, 12, 15]] print(extract_rows_with_common_diff_comp(input_data))

Output:

[[1, 3, 5], [9, 12, 15]]

In this snippet, the function `extract_rows_with_common_diff_comp()`

employs a list comprehension to iterate through the dataset and includes only those rows that pass the conditional check for consistent differences between elements.

## Method 3: Using NumPy Library

NumPy is a powerful numerical processing library in Python. This method leverages NumPy’s vectorized operations to quickly determine whether the differences between the elements are constant across the row.

Here’s an example:

import numpy as np def extract_rows_with_common_diff_numpy(data): array = np.array(data) diffs = np.diff(array, axis=1) return array[np.all(diffs[:, 1:] == diffs[:, [0]], axis=1)].tolist() input_data = [[1, 3, 5], [2, 4, 7], [9, 12, 15]] print(extract_rows_with_common_diff_numpy(input_data))

Output:

[[1, 3, 5], [9, 12, 15]]

Here, the `extract_rows_with_common_diff_numpy()`

function converts the input list of lists into a NumPy array and computes the first-order differences along the rows. Rows are included in the result if all differences match the first one, using NumPy’s efficient array operations.

## Method 4: Using itertools Combinations

The itertools library in Python provides a method called combinations that can be used to iterate through pairs of elements. We can use this to check if the common difference condition is met.

Here’s an example:

from itertools import combinations def extract_rows_with_common_diff_itertools(data): result = [] for row in data: if len(set(row[i] - row[j] for i, j in combinations(range(len(row)), 2))) == 1: result.append(row) return result input_data = [[1, 3, 5], [2, 4, 7], [9, 12, 15]] print(extract_rows_with_common_diff_itertools(input_data))

Output:

[[1, 3, 5], [9, 12, 15]]

The function `extract_rows_with_common_diff_itertools()`

uses the combinations method from the itertools library to create all possible pairs of indices for the elements in the row and checks if all differences are the same.

## Bonus One-Liner Method 5: Using a One-Liner with filter and lambda

For those who love Python one-liners, this method applies the filter function in combination with a lambda to achieve the same result in a single line of code.

Here’s an example:

input_data = [[1, 3, 5], [2, 4, 7], [9, 12, 15]] result = list(filter(lambda row: all(row[i] - row[i-1] == row[1] - row[0] for i in range(2, len(row))), input_data)) print(result)

Output:

[[1, 3, 5], [9, 12, 15]]

The code here utilizes the `filter()`

function along with a lambda expression to filter out the rows that do not maintain a common difference.

## Summary/Discussion

**Method 1: Using Loops and Conditions.**Easy to understand. May be slower for large datasets.**Method 2: Using List Comprehensions.**More Pythonic and compact. Similar performance to Method 1.**Method 3: Using NumPy Library.**Very fast with large datasets. Requires NumPy installation.**Method 4: Using itertools Combinations.**Offers a different approach. Can be less efficient due to the number of combinations generated.**Bonus One-Liner Method 5: Using a One-Liner with filter and lambda.**Compact and elegant. May sacrifice readability for beginners.