**π‘ Problem Formulation:** Given an array, the challenge is to determine whether it can be sorted into ascending order through a series of conditional swaps of adjacent elements. For example, if we have an input array `[3, 1, 2]`

, we want to check if itβs possible to reach the sorted output `[1, 2, 3]`

by only swapping adjacent elements under certain conditions.

## Method 1: Bubble Sort Variant Check

This method extends the concept of the traditional bubble sort. By limiting the number of swaps available or placing a condition on when a swap can occur, you can check if the array can be sorted. This method typically involves iterating over the array and attempting swaps while adhering to the given conditions.

Here’s an example:

def conditional_bubble_sort(arr, can_swap): for i in range(len(arr) - 1): if can_swap(arr[i], arr[i + 1]): arr[i], arr[i + 1] = arr[i + 1], arr[i] return arr def check_sortable(arr, can_swap): for _ in range(len(arr)): arr = conditional_bubble_sort(arr, can_swap) return arr == sorted(arr) # Define your swap condition here def can_swap(a, b): return a > b example_arr = [3, 1, 2] print(check_sortable(example_arr, can_swap))

The output would be `True`

.

This code snippet checks if the array can be sorted by repetitively applying our conditional swap, defined in `can_swap`

. It uses a helper function, `conditional_bubble_sort`

, which attempts to sort the array while respecting the conditional swap criterion. If the array matches the sorted version after enough iterations, it returns `True`

.

## Method 2: Greedy Swap Check

Greedy algorithms make the locally optimal choice at each stage. This greedy swap check investigates the possibility of sorting an array by comparing each adjacent element and deciding whether a swap should be made based on a given condition. The process continues until no more swaps can be made under the condition.

Here’s an example:

def greedy_swap_sortable(arr, can_swap): swapped = True while swapped: swapped = False for i in range(len(arr)-1): if can_swap(arr[i], arr[i+1]): arr[i], arr[i+1] = arr[i+1], arr[i] swapped = True return arr == sorted(arr) # You can use the previously defined `can_swap` here print(greedy_swap_sortable(example_arr, can_swap))

The output would be `True`

.

This snippet uses a greedy approach to determine if sorting the array is possible with the conditional swaps. Here, `greedy_swap_sortable`

performs swaps in a single pass and repeats the process until no swaps occur, indicating a sorted array or the impossibility of sorting under the conditions.

## Method 3: Optimized Check with Early Stopping

This method enhances previous algorithms by including an early stopping mechanism. If an iteration completes without any swaps, the algorithm terminates, concluding that the array is either sorted or cannot be further sorted given the swapping conditions.

Here’s an example:

def optimized_sortable_check(arr, can_swap): for _ in range(len(arr)): swapped = False for i in range(len(arr)-1): if can_swap(arr[i], arr[i+1]): arr[i], arr[i+1] = arr[i+1], arr[i] swapped = True if not swapped: break return arr == sorted(arr) print(optimized_sortable_check(example_arr, can_swap))

The output would be `True`

.

In this example, the `optimized_sortable_check`

function iterates over the array, swaps elements conditionally and checks if a full pass was made without swapping. If so, it concludes the check early, which is efficient for nearly-sorted arrays.

## Method 4: Detecting Patterns and Constraints

Analyzing the array for patterns and specific constraints that would prevent sorting can sometimes provide a quick check. This method assumes some prior knowledge of the conditions under which sorting is not possible.

Here’s an example:

def pattern_based_sortable_check(arr, can_swap): # Check for specific patterns here. This is a placeholder. return "Implement pattern checks" # This example will not produce valid output as it's placeholder logic print(pattern_based_sortable_check(example_arr, can_swap))

The output would depend on the specific pattern checks implemented.

This method anticipates the presence of certain array configurations that would inhibit sorting given the swap conditions. It usually requires domain-specific knowledge or insight into the problem constraints.

## Bonus One-Liner Method 5: List Comprehension and Conditional Check

This Pythonic approach uses list comprehension to create a one-liner that applies a check across the array. While less explicit, it leverages Python’s expressive syntax for a concise check.

Here’s an example:

sortable = all(can_swap(arr[i], arr[i+1]) for i in range(len(arr)-1)) and arr == sorted(arr) print(sortable)

The output would be `True`

.

The one-liner checks each adjacent pair in the array with the condition defined by `can_swap`

. It returns `True`

if every adjacent pair meets the condition and if the array is sorted, otherwise `False`

.

## Summary/Discussion

**Method 1:**Bubble Sort Variant Check. Good for learning purposes and easy to understand. Not efficient for large arrays since it does not incorporate any optimizations.**Method 2:**Greedy Swap Check. Performs well on small to medium-sized arrays. May be less efficient on large arrays that are far from sorted.**Method 3:**Optimized Check with Early Stopping. Includes an improvement that can lead to faster checks on nearly-sorted arrays. It still might be inefficient if the non-sortable pattern is at the end of a large array.**Method 4:**Detecting Patterns and Constraints. Quick and efficient if the pattern or constraint can be easily identified. However, it may not work for all arrays, as it relies on specific knowledge of the array’s characteristics.**Bonus One-Liner Method 5:**List Comprehension and Conditional Check. Very concise and Pythonic. However, it lacks clarity for those unfamiliar with list comprehensions and may still iterate over the entire array even if non-sortability could be detected early.

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.