**π‘ Problem Formulation:** Given a list or array of integers where each integer represents a ball labeled with a box number, the challenge is to write a program in Python that finds the maximum number of balls in any box. For instance, if the input is `[1, 2, 1, 2, 1]`

, the desired output is `3`

, since the box labeled ‘1’ contains the most balls.

## Method 1: Using a Dictionary

An effective and intuitive method to solve this problem is through the use of a dictionary. In this approach, you iterate over each ball and increment the corresponding box count in a dictionary. This method is easy to understand and handy for more complex operations on the distribution of balls.

Here’s an example:

def max_balls_in_box(balls): box_count = {} for ball in balls: box_count[ball] = box_count.get(ball, 0) + 1 return max(box_count.values()) print(max_balls_in_box([1, 2, 1, 2, 1])) # Output will be 3

The output of this code is `3`

.

This code snippet starts by defining a function `max_balls_in_box()`

which takes an array of integers as input. Inside the function, a dictionary named `box_count`

is used to maintain the count of balls in each box. For every ball in the list, the box count is incremented using the `get`

method, which provides a default value of 0 if the box does not exist yet in the dictionary. Finally, the function returns the maximum value from the `box_count`

dictionary.

## Method 2: Using the Counter Class from collections

Python’s standard library offers a `Counter`

class from the `collections`

module designed to count objects. It simplifies the counting process and enhances code readability significantly.

Here’s an example:

from collections import Counter def max_balls_in_box(balls): box_count = Counter(balls) return max(box_count.values()) print(max_balls_in_box([1, 2, 1, 2, 1])) # Output will be 3

The output of this code is `3`

.

This snippet begins by importing the `Counter`

class from the `collections`

module. The `max_balls_in_box()`

function assigns the `Counter`

instance of the `balls`

list to `box_count`

, which automatically counts the occurrence of each box label. As in the previous method, `max()`

is used to find the highest count of balls in a box.

## Method 3: Sorting and Iterative Traversal

Another approach to solve this problem is by sorting the list of balls and then iteratively counting the consecutive similar numbers to find the box with the maximum balls. While being less efficient for large datasets due to sorting, this method is a straightforward solution.

Here’s an example:

def max_balls_in_box(balls): balls.sort() max_count, current_count = 0, 1 for i in range(1, len(balls)): if balls[i] == balls[i - 1]: current_count += 1 else: max_count = max(max_count, current_count) current_count = 1 return max(max_count, current_count) print(max_balls_in_box([1, 2, 1, 2, 1])) # Output will be 3

The output of this code is `3`

.

The function `max_balls_in_box()`

first sorts the list, which groups the same box labels together. Iterating through the sorted list, it compares each element to its predecessor to count the number of same consecutive box labels. If the current label differs from the previous one, it updates the `max_count`

if necessary and resets the `current_count`

for the next label.

## Method 4: Using Lambda and max functions

Combining the `lambda`

function with `max`

allows us to find the maximum number of balls in a box with a concise expression. This method is very Pythonic but could be slightly slower for larger datasets as it computes the maximum in every iteration.

Here’s an example:

def max_balls_in_box(balls): return max(balls, key=lambda x: balls.count(x), default=0) print(max_balls_in_box([1, 2, 1, 2, 1])) # Output will be 3

The output of this code is `3`

.

Here, the `max_balls_in_box()`

function utilizes a lambda function passed as the key parameter to Python’s built-in `max()`

function. The lambda calculates the count of each unique ball label in the list. Instead of returning the label with the maximum count, it correctly returns the highest count itself. The `default=0`

parameter ensures that if the list is empty, it returns 0.

## Bonus One-Liner Method 5: Using max and list comprehension

A one-liner seasoned with Python list comprehension can also achieve the result. This approach evaluates a compact expression but can be less optimal for performance due to its lack of short-circuiting.

Here’s an example:

def max_balls_in_box(balls): return max([balls.count(ball) for ball in set(balls)]) if balls else 0 print(max_balls_in_box([1, 2, 1, 2, 1])) # Output will be 3

The output of this code is `3`

.

The function `max_balls_in_box()`

in this one-liner uses a list comprehension to create a list of ball counts for each unique ball label by first converting the list to a set. The `max()`

function then finds the highest count in this list. The conditional expression ensures that if the list is empty, the value returned is 0.

## Summary/Discussion

**Method 1:**Using a Dictionary. Beneficial for its simplicity and potential for further data manipulation. However, it can be inefficient for large numbers of boxes due to the dictionary’s maintenance overhead.**Method 2:**Using the Counter Class from collections. Streamlined and readable, this method is excellent for easy implementation. While more efficient than a dictionary, it may still be slower than other methods for exceptionally large data sets.**Method 3:**Sorting and Iterative Traversal. Straightforward and efficient for small datasets. Major disadvantage is its lack of scalability for larger datasets due to the time complexity of sorting.**Method 4:**Using Lambda and max functions. Elegant and compact, this method is perfect for small-scale problems. However, it is potentially inefficient because`count`

is calculated for every element.**Bonus One-Liner Method 5:**Using max and list comprehension. This one-liner is clever and concise but can be resource-heavy for large input sizes, as it does not take advantage of any short-circuiting.