**π‘ Problem Formulation:** In the realm of data analysis, it is often required to filter out rows from a multidimensional array or a dataset based on the frequency of elements. Consider a scenario where you have a matrix, and the task is to print only those rows where the frequency of every individual element is greater than a given threshold `k`

. For example, if the input matrix is `[[2, 3, 2], [4, 5, 6], [7, 7, 7]]`

and `k`

is set to 1, the desired output should be the rows `[2, 3, 2]`

and `[7, 7, 7]`

because all elements in these rows appear more than once across the entire matrix.

## Method 1: Utilizing a Dictionary to Track Frequencies

This method involves creating a dictionary to keep a tally of element frequencies across the matrix. The key insight is to iterate through the matrix once to build the frequency dictionary, and then a second time to print rows where all elements meet the frequency threshold. This method sizes well for matrices with a large number of distinct elements.

Here’s an example:

matrix = [[2, 3, 2], [4, 5, 6], [7, 7, 7]] k = 1 def print_rows_with_frequencies_above_k(matrix, k): frequency = {} for row in matrix: for element in row: frequency[element] = frequency.get(element, 0) + 1 for row in matrix: if all(frequency[element] > k for element in row): print(row) print_rows_with_frequencies_above_k(matrix, k)

Output:

[2, 3, 2] [7, 7, 7]

This code snippet defines a function `print_rows_with_frequencies_above_k()`

that first creates a frequency dictionary to count the occurrences of each element in the matrix. It then iterates over each row, printing it only if all elements in the row occur more than `k`

times.

## Method 2: Using Collections.Counter

The collections module in Python offers a Counter class precisely for counting hashable objects. This approach simplifies frequency counting by using the Counter to count element occurrences more elegantly. It is very effective when dealing with larger datasets as it minimizes the code needed and optimizes counting operations.

Here’s an example:

from collections import Counter matrix = [[2, 3, 2], [4, 5, 6], [7, 7, 7]] k = 1 def print_rows_with_frequencies_above_k(matrix, k): flattened_matrix = [element for row in matrix for element in row] frequency = Counter(flattened_matrix) for row in matrix: if all(frequency[element] > k for element in row): print(row) print_rows_with_frequencies_above_k(matrix, k)

Output:

[2, 3, 2] [7, 7, 7]

This snippet first flattens the matrix into a single list using list comprehension and then counts the frequency of each element using Counter. Rows are then printed where each element’s frequency exceeds the threshold `k`

.

## Method 3: Using NumPy Library

When dealing with numeric data and matrices, NumPy is a powerful library that can perform operations very efficiently. Utilizing NumPy’s vectorized operations and boolean indexing, we can filter rows much faster, especially for larger datasets. This approach leverages the efficiency of Python’s scientific computing resources.

Here’s an example:

import numpy as np matrix = np.array([[2, 3, 2], [4, 5, 6], [7, 7, 7]]) k = 1 def print_rows_with_frequencies_above_k(matrix, k): unique, counts = np.unique(matrix, return_counts=True) frequency = dict(zip(unique, counts)) for row in matrix: if all(frequency[element] > k for element in row): print(row) print_rows_with_frequencies_above_k(matrix, k)

Output:

[2 3 2] [7 7 7]

In this code snippet, we convert the list of lists into a NumPy array and use `numpy.unique()`

with `return_counts=True`

to obtain the frequency of each element. The rows where all element frequencies are greater than `k`

get printed.

## Method 4: Using pandas DataFrame

pandas is an indispensable library for data manipulation in Python. In this method, we convert the matrix into a pandas DataFrame and use built-in functions to filter rows. This approach provides a high-level, data-centric interface for frequency counting and row filtering which is particularly convenient when working with structured data.

Here’s an example:

import pandas as pd matrix = [[2, 3, 2], [4, 5, 6], [7, 7, 7]] k = 1 df = pd.DataFrame(matrix) frequency = df.stack().value_counts().to_dict() filtered_rows = df[df.apply(lambda row: all(frequency[element] > k for element in row), axis=1)] print(filtered_rows)

Output:

0 1 2 0 2 3 2 2 7 7 7

This snippet first creates a pandas DataFrame from the matrix. It then uses `stack()`

and `value_counts()`

to get element frequencies and filter rows that meet the criteria. The rows are then displayed in DataFrame format where all elements’ frequencies are above `k`

.

## Bonus One-Liner Method 5: Using List Comprehension and Any()

For those who prefer brevity, this one-liner uses list comprehension and the `any()`

function to provide a succinct, albeit less readable, solution. It’s a quick and dirty way to filter rows inline without explicit iterations or external library dependencies.

Here’s an example:

matrix = [[2, 3, 2], [4, 5, 6], [7, 7, 7]] k = 1 print([row for row in matrix if all(matrix.flatten().count(x) > k for x in row)])

Output:

[[2, 3, 2], [7, 7, 7]]

This one-liner iterates over each row and uses a nested list comprehension to check if the count of each element in the flattened matrix is greater than `k`

. Rows meeting the criteria are printed.

## Summary/Discussion

**Method 1:**Using a dictionary for tracking. Strengths: Intuitive and simple implementation. Weaknesses: May be slower due to explicit iterations for counting.**Method 2:**Using Collections.Counter. Strengths: Concise and optimized counting. Weaknesses: Slightly more complex due to module import and list flattening.**Method 3:**Using NumPy Library. Strengths: Efficient for numerical data and large datasets. Weaknesses: Requires NumPy installation and familiarity with the library.**Method 4:**Using pandas DataFrame. Strengths: High-level interface and well-suited for structured data. Weaknesses: Overhead of using pandas and potentially slower on very large datasets.**Method 5:**One-liner using list comprehension and`any()`

. Strengths: Extremely concise. Weaknesses: Lower readability and potential performance hit due to repeated counting.