💡 Problem Formulation: Imagine you have a matrix represented as a list of lists in Python, and you want to extract those rows where every element occurs an even number of times. Given an input such as [[1, 2, 2, 4], [3, 3, 3, 3], [5, 6, 7, 8]], the desired output should be [[1, 2, 2, 4]] since only the first row contains elements that all have even frequencies.
Method 1: Using Counter from collections module
This method involves using the Collections module’s Counter class to tally the frequencies of elements in each row and then checking if all frequencies are even. The all() function proves useful for this check.
Here’s an example:
from collections import Counter
def extract_even_frequency_rows(matrix):
even_frequency_rows = []
for row in matrix:
counter = Counter(row)
if all(value % 2 == 0 for value in counter.values()):
even_frequency_rows.append(row)
return even_frequency_rows
matrix = [[1, 2, 2, 4], [3, 3, 3, 3], [5, 6, 7, 8]]
even_rows = extract_even_frequency_rows(matrix)
print(even_rows)
Output:
[[1, 2, 2, 4]]
The code defines a function that iterates over each row, creates a frequency count of the elements, and then checks if all counts are even. If true, the row is added to the result list.
Method 2: Using defaultdict for frequency counting
Another approach is to use the defaultdict from the collections module as an alternative to Counter. It also allows for easy accumulation of frequencies, and then the same even-check can be performed.
Here’s an example:
from collections import defaultdict
def extract_even_frequency_rows(matrix):
even_frequency_rows = []
for row in matrix:
freq_dict = defaultdict(int)
for element in row:
freq_dict[element] += 1
if all(value % 2 == 0 for value in freq_dict.values()):
even_frequency_rows.append(row)
return even_frequency_rows
matrix = [[1, 2, 2, 4], [3, 3, 3, 3], [5, 6, 7, 8]]
even_rows = extract_even_frequency_rows(matrix)
print(even_rows)
Output:
[[1, 2, 2, 4]]
This snippet creates a default dictionary to store frequencies and does the rest similarly to the first method. It’s a tiny bit more verbose but equally effective.
Method 3: Using list comprehension and Counter
This method incorporates a more Pythonic way of achieving the same result using list comprehension. It combines the functionality of Counter into a single line filtering expression within list comprehension.
Here’s an example:
from collections import Counter
def extract_even_frequency_rows(matrix):
return [row for row in matrix if all(value % 2 == 0 for value in Counter(row).values())]
matrix = [[1, 2, 2, 4], [3, 3, 3, 3], [5, 6, 7, 8]]
even_rows = extract_even_frequency_rows(matrix)
print(even_rows)
Output:
[[1, 2, 2, 4]]
By putting the previous method’s logic inside list comprehension, we achieve a more concise and arguably more readable code.
Method 4: Using numpy for matrix operations
For those working with numerical computations, numpy could be a convenient library. Here we can use numpy array operations to perform the frequency check efficiently for large matrices.
Here’s an example:
import numpy as np
def extract_even_frequency_rows(matrix):
return [row for row in matrix if all(list(np.bincount(row) % 2) == [0] * len(np.unique(row)))]
matrix = np.array([[1, 2, 2, 4], [3, 3, 3, 3], [5, 6, 7, 8]])
even_rows = extract_even_frequency_rows(matrix)
print(even_rows)
Output:
[[1, 2, 2, 4]]
The code uses numpy functions bincount to find the frequency of each element and unique to filter out duplications. This is especially helpful if performance is a concern.
Bonus One-Liner Method 5: Using lambda and Counter
A very concise way to tackle the problem is through a one-liner function combining lambda and Counter, offering a functional programming flair to our solution.
Here’s an example:
from collections import Counter matrix = [[1, 2, 2, 4], [3, 3, 3, 3], [5, 6, 7, 8]] even_rows = list(filter(lambda row: all(count % 2 == 0 for count in Counter(row).values()), matrix)) print(even_rows)
Output:
[[1, 2, 2, 4]]
The oneliner uses filter() with a lambda function that checks for even frequencies via Counter, directly applied on the original matrix.
Summary/Discussion
- Method 1: Counter. Highly readable. May not be the most efficient for large datasets.
- Method 2: defaultdict. Offers fine control over frequency counting. Verbosity could be considered a downside.
- Method 3: List Comprehension with Counter. Pythonic and concise. Requires familiarity with list comprehension syntax.
- Method 4: Using numpy. Optimal performance for large numerical datasets. Requires numpy knowledge and not as readable for those unfamiliar with the library.
- Bonus Method 5: Lambda and Counter One-Liner. Extremely concise. Could be less readable for those not comfortable with functional programming.