Counting Pairs: Efficient Solution with Python and Counter

Have you ever felt like Ana, buried under an avalanche of data, looking for patterns in the chaos? Today, we will unravel the mystery of lost socks and learn a valuable lesson about how programming helps us find order in disorder. 🧶

🔮 Problem Statement

Ana faces a seemingly simple task, but surprisingly common in the world of software development: she needs to organize a pile of mismatched socks. Each sock has a unique identifier, and her goal is to determine how many complete pairs she can form.

The function we will develop will receive an array arr[n] where each element represents the ID of a sock in the basket. Our mission is to return an integer representing the total number of complete pairs that can be formed from those socks.

Parameters:

int arr[n]: An array of integers, where each integer represents the ID of a sock.

Return Value:

int: The number of complete pairs that can be formed from the socks in the array.

Example:

>>> count_by_pair([10, 10, 20, 20, 30, 50])
2

In this example, we have two pairs: a pair of socks with ID 10 and another pair with ID 20. The socks with ID 30 and 50 do not have a match.

Additional Note: The order of the socks in the array does not matter. What matters is the frequency with which each sock ID appears.

🧩 Step-by-Step Solution

To solve this problem, we will leverage the power of Python’s Counter class. This class allows us to count the frequency with which each element appears in a list efficiently.

from collections import Counter

We import the Counter class from the collections module. Counter is like a customizable counter that allows us to track the frequency of each element in our collection.

def count_by_pair(arr):

We define our count_by_pair function, which takes an array arr as input. This function will be responsible for analyzing the sock basket and calculating the number of complete pairs.

    return sum([val // 2 for val in Counter(arr).values() if not val % 2])

This line is the heart of our solution. First, we create a Counter object from the array arr, which will store the frequency of each sock ID. Then, we iterate over the values (frequencies) of the Counter, and only consider those values that are even (if not val % 2). For each even value, we calculate the integer division by 2 (val // 2), which represents the number of complete pairs we can form with that amount of socks. Finally, we sum all these numbers to obtain the total number of complete pairs.

from collections import Counter

def count_by_pair(arr):
	"level: easy; points: 3"
	return sum([val // 2 for val in Counter(arr).values() if not val % 2])

🧠 Key Concepts

The key to understanding this solution lies in several fundamental concepts. First, the Counter class from the collections module is crucial. A Counter is a specialized dictionary that stores the frequency of each element in a sequence as a dictionary where the keys are the elements and the values are their counts. This object is hashable, which allows performing counting operations efficiently. Second, list comprehension is a powerful tool for creating new lists concisely. List comprehension allows us to apply a transformation and a filter to the elements of an existing sequence, generating a new list with the results. Finally, the modulo (%) and integer division (//) operators are essential for determining if a number is even and for calculating the number of complete pairs that can be formed, respectively.

Did you know that the efficiency of the Counter class lies in its internal implementation, based on hash tables, which allows it to perform counting operations in average constant time O(1)? 🤯

💫 Final Thoughts

This solution, although concise, demonstrates the power of abstraction and code reuse. We could improve it to handle different types of socks (for example, socks with different colors or sizes) by extending the logic of comparison and grouping. We could also consider the case where there is an odd number of socks and determine how many “orphan” socks remain after forming all possible pairs. This basic function can be expanded over time, making it more and more robust as new use cases are discovered, as would be in a real inventory management system.

I hope this analysis has been helpful and inspiring. Feel free to experiment with the code, modify it, and adapt it to your own needs! If you want to continue learning about data structures and algorithms, do not hesitate to explore more articles on our blog! The world of software development is full of exciting challenges and opportunities to grow! 🔥