# 5 Best Ways to Check if Rectangles Can Be Rearranged in a Non-Ascending Order of Breadths in Python

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5 Best Ways to check if it is possible to rearrange rectangles in a non-ascending order of breadths in Python

π‘ Problem Formulation: In Python, you might face the task of determining whether a collection of rectangles can be reordered so their breadths do not ascend. For instance, given a list of rectangle breadths like `[3, 4, 5, 1]`, we want to determine if it’s possible to arrange them in a sequence like `[5, 4, 3, 1]`, thereby satisfying the non-ascending order constraint.

## Method 1: Sorting and Direct Comparison

This method involves sorting the list of rectangle breadths in descending order and then comparing to ensure no breadth is less than the subsequent one. The Python function `sorted()` is used with the `reverse=True` parameter to sort the list.

Here’s an example:

```rectangles = [3, 4, 5, 1]
sorted_rectangles = sorted(rectangles, reverse=True)
can_rearrange = sorted_rectangles == rectangles
print(can_rearrange)```

Output: `False`

The code snippet sorts the rectangle breadths in non-ascending order and checks if the sorted list is the same as the original list. In this example, the output is `False`, indicating that the original list was not in non-ascending order, and rearrangement is needed.

## Method 2: Checking the Order Without Sorting

Instead of sorting, you can iterate through the list to ensure that each element is not smaller than its predecessor. This method uses a simple loop and the all() function for succinctness to check the property without altering the list.

Here’s an example:

```rectangles = [5, 4, 3, 1]
can_rearrange = all(rectangles[i] >= rectangles[i+1] for i in range(len(rectangles)-1))
print(can_rearrange)```

Output: `True`

The code checks the order by comparing each breadth with its successor. If all breadth comparisons comply with the non-ascending order, `True` is returned. This is more efficient than sorting if you only need to check the current order without modifying the list.

## Method 3: Using a Custom Comparator

This method introduces a custom compare function that sorts the rectangles by breadth, primarily useful when dealing with objects or more complex data structures than a simple list. The key parameter of sorted() is used to define the comparison basis.

Here’s an example:

```class Rectangle:
self.width = width

rectangles = [Rectangle(5, 3), Rectangle(2, 4), Rectangle(7, 5), Rectangle(6, 1)]
sorted_rectangles = sorted(rectangles, key=lambda r: r.breadth, reverse=True)
print(can_rearrange)```

Output: `True`

The snippet defines a `Rectangle` class and sorts the list of instances based on their breadth using a lambda function as the key argument to `sorted()`. The order is then checked to be non-ascending, giving a result of `True`.

## Method 4: Utilizing The Collections Module

This method involves using `Counter` from the collections module to count occurrences and determine if rearrangement is possible based on count comparison. This is an indirect but useful approach when dealing with duplicate breadths.

Here’s an example:

```from collections import Counter

rectangles = [3, 4, 4, 1]
print(can_rearrange)```

Output: `True`

Counts of each breadth are compared to ensure that the breadth is either less frequent or equally frequent as the succeeding breadth count, guaranteeing the possibility of non-ascending ordering.

## Bonus One-Liner Method 5: Pythonic One-Liner with List Comprehension

A pythonic one-liner using list comprehension checks the condition of non-ascending order succinctly by leveraging Python’s all() function and the fact that a list is indexable.

Here’s an example:

```rectangles = [5, 3, 4, 1]
can_rearrange = all(rectangles[i] >= rectangles[i+1] for i in range(len(rectangles)-1))
print(can_rearrange)```

Output: `False`

The one-liner elegantly performs the operation of checking the property of non-ascending order directly on the list without creating extra variables or using traditional loop constructs.

## Summary/Discussion

• Method 1: Sorting and Direct Comparison. Simple and straight-forward. Inefficient for large lists as it requires a full sort.
• Method 2: Checking the Order Without Sorting. Efficient for simply checking the order. Does not offer a rearranged list.
• Method 3: Using a Custom Comparator. Offers flexibility for complex data structures. Slightly more complex but very powerful.
• Method 4: Utilizing The Collections Module. Useful for handling duplicates. Unconventional, may not be straightforward for less experienced coders.
• Bonus Method 5: Pythonic One-Liner with List Comprehension. Elegant and concise. Most pythonic and great for smaller lists, but offers less readability for beginners.