**π‘ Problem Formulation:** Given a list of tuples, the challenge is to count how many unique bidirectional pairs exist. A bidirectional pair is defined as two tuples where the second is a reverse of the first (i.e., (a, b) and (b, a) are considered the same pair). For example, input: [(1, 2), (2, 1), (3, 4), (4, 3)] should output: 2 unique bidirectional pairs.

## Method 1: Using a Set for Unique Pairs

This method involves iterating over the list of tuples, storing each as a frozenset in another set allowing for the storage of unique bidirectional pairs since frozensets are unordered collections.

Here’s an example:

pairs = [(1, 2), (2, 1), (3, 4), (4, 3)] unique_pairs = set() for pair in pairs: unique_pairs.add(frozenset(pair)) print(len(unique_pairs))

Output: 2

In this snippet, we loop through each tuple in the list and create a `frozenset`

because it is an unordered collection where (1, 2) and (2, 1) become indistinguishable. Adding these to a set ensures only unique pairs are counted, and finally, the length of the set gives the desired result.

## Method 2: Sorting Tuples Before Adding to Set

By first sorting each tuple in a standardized order before adding them to a set, we create a uniform representation of each bidirectional pair, thus enabling us to count unique pairs accurately.

Here’s an example:

pairs = [(1, 2), (2, 1), (3, 4), (4, 3)] unique_pairs = set() for pair in pairs: unique_pairs.add(tuple(sorted(pair))) print(len(unique_pairs))

Output: 2

Each tuple is sorted so that it always appears in the same order (smallest element first), and then it’s turned back into a tuple and added to the set. This ensures that all bidirectional pairs are stored in only one way, hence making it easy to count unique pairs.

## Method 3: Using a Counter with Frozensets

Utilize the `Counter`

class from the `collections`

module with frozensets to elegantly count and manage bidirectional tuple pairs.

Here’s an example:

from collections import Counter pairs = [(1, 2), (2, 1), (3, 4), (4, 3)] counted_pairs = Counter(frozenset(pair) for pair in pairs) print(sum(counted_pairs.values()) // 2)

Output: 2

The code uses a generator to transform each tuple in the list into a `frozenset`

and passes it to the `Counter`

constructor. Since each bidirectional tuple is counted twice, we divide the total by 2 to get the count of unique bidirectional pairs.

## Method 4: Dictionary-based Method

This method involves creating a dictionary where each sorted tuple is a key, and its value is a count of occurrences. It’s effective for counting unique tuples while maintaining their original order of appearance.

Here’s an example:

pairs = [(1, 2), (2, 1), (3, 4), (4, 3)] counted_pairs = {} for pair in pairs: ordered_pair = tuple(sorted(pair)) counted_pairs[ordered_pair] = counted_pairs.get(ordered_pair, 0) + 1 print(len(counted_pairs))

Output: 2

The `sorted`

function ensures each pair is in a consistent order, which lets us use the tuple as a key in a dictionary, effectively counting unique pairs by the existence of keys in the dictionary.

## Bonus One-Liner Method 5: Using Set Comprehension

A concise and elegant Python one-liner utilizing set comprehension to achieve the same goal, it showcases Python’s ability to condense logic into a single line of code.

Here’s an example:

pairs = [(1, 2), (2, 1), (3, 4), (4, 3)] unique_pairs_count = len({frozenset(pair) for pair in pairs}) print(unique_pairs_count)

Output: 2

This one-liner transforms each tuple to a `frozenset`

(removing the notion of direction) and adds it to a set, automatically ensuring uniqueness. The length of the resulting set is the count of unique bidirectional pairs.

## Summary/Discussion

**Method 1:**Using a Set with Frozensets. Strengths: Simple and straightforward. Weaknesses: May have slight overhead due to the creation of frozensets.**Method 2:**Sorting Tuples Before Adding to Set. Strengths: Easy to understand and follows a logical process. Weaknesses: Additional sorting step may introduce inefficiency for large lists.**Method 3:**Counter with Frozensets. Strengths: Provides additional information, like the occurrence of each pair. Weaknesses: Slightly more complex, requires understanding of the Counter class.**Method 4:**Dictionary-based Method. Strengths: Efficient in terms of maintaining the order while counting. Weaknesses: More verbose than the set-based methods.**Method 5:**Using Set Comprehension. Strengths: Very concise and Pythonic. Weaknesses: May sacrifice readability for those not familiar with comprehensions.

Emily Rosemary Collins is a tech enthusiast with a strong background in computer science, always staying up-to-date with the latest trends and innovations. Apart from her love for technology, Emily enjoys exploring the great outdoors, participating in local community events, and dedicating her free time to painting and photography. Her interests and passion for personal growth make her an engaging conversationalist and a reliable source of knowledge in the ever-evolving world of technology.