💡 Problem Formulation: Given an array of integers, the task is to determine whether it can be sorted into ascending order with just one swap operation. A swap operation consists of choosing two indices and swapping the elements at these positions. For example, input [1, 5, 3, 4, 2], the desired output is True because swapping the elements at indices 1 and 4 results in a sorted array [1, 2, 3, 4, 5].
Method 1: Naive Approach
This method iterates over the array and checks each possible swap to see if it results in a sorted array. It has a function specification of def can_sort_with_one_swap(arr): which takes a list as input and returns a boolean.
Here’s an example:
def can_sort_with_one_swap(arr):
sorted_arr = sorted(arr)
for i in range(len(arr)):
for j in range(i + 1, len(arr)):
arr[i], arr[j] = arr[j], arr[i]
if arr == sorted_arr:
return True
arr[i], arr[j] = arr[j], arr[i]
return False
print(can_sort_with_one_swap([1, 5, 3, 4, 2]))Output: True
This code snippet defines a function that first creates a sorted copy of the input array. It then iterates through all unique pairs of indices, swapping them, and checks whether the modified array matches the sorted copy. It returns True at the first successful match, otherwise, it resets the swap and continues. If no swap results in a sorted array, it returns False.
Method 2: Optimized Search
This optimized method involves finding the two out-of-order pairs in one pass and then checking if swapping these would sort the array. It’s more efficient than the naive approach with a function signature of def can_sort_with_one_swap_optimized(arr):.
Here’s an example:
def can_sort_with_one_swap_optimized(arr):
i, j = -1, -1
for k in range(len(arr) - 1):
if arr[k] > arr[k + 1]:
if i == -1:
i = k
else:
j = k + 1
if j == -1 and i != -1:
j = i + 1
arr[i], arr[j] = arr[j], arr[i]
return arr == sorted(arr)
print(can_sort_with_one_swap_optimized([1, 5, 3, 4, 2]))Output: True
In this method, the indices i and j track the locations of the elements that might be swapped. The array is iterated once to detect these out-of-place elements. After potentially finding two candidates, one swap is tested, and the result is checked against the sorted array. This method minimizes unnecessary checks and swaps.
Method 3: Short Circuit Check
This method uses the fact that for an array to be sortable with one swap, there must be exactly two out-of-order elements. This function, def can_sort_with_short_circuit(arr):, performs an efficient check corresponding to this condition.
Here’s an example:
def can_sort_with_short_circuit(arr):
diff = [i for i in range(len(arr) - 1) if arr[i] > arr[i + 1]]
if not diff:
return True
if len(diff) > 2:
return False
i, j = diff[0], diff[-1] + 1
arr[i], arr[j] = arr[j], arr[i]
return arr == sorted(arr)
print(can_sort_with_short_circuit([1, 5, 3, 4, 2]))Output: True
This snippet finds the indices where the array is not in ascending order. If no such indices exist, the array is already sorted. If there are more than two, it’s not possible to sort with one swap. Otherwise, attempt the swap at the first and last indices found and compare with a sorted array.
Method 4: Greedy Approach
This greedy method checks for consecutive elements out of order and attempts to swap them. This might be more intuitive and can also handle cases with sorted sub-arrays and one disordered pair. Function signature: def can_sort_with_greedy(arr):
Here’s an example:
def can_sort_with_greedy(arr):
swapped = False
for i in range(len(arr) - 1):
if arr[i] > arr[i+1]:
if swapped:
return False
for j in range(i + 2, len(arr)):
if arr[i] > arr[j]:
arr[i], arr[j] = arr[j], arr[i]
swapped = True
break
if not swapped:
arr[i], arr[i+1] = arr[i+1], arr[i]
swapped = True
return arr == sorted(arr)
print(can_sort_with_greedy([1, 5, 3, 4, 2]))Output: True
The snippet iterates over the array and when an inverted order is detected, it searches for a potential candidate to swap. It ensures only one swap is made. If no second candidate is found, it swaps the current pair. The swapped flag is set to prevent multiple swaps, ensuring only one swap operation.
Bonus One-Liner Method 5: Pythonic Approach
This one-liner method takes advantage of Python’s expressive syntax and powerful built-in functions to achieve the same result with minimal code. Function signature: def can_sort_one_liner(arr):
Here’s an example:
can_sort_one_liner = lambda arr: any(arr[:i] + arr[i:i+2][::-1] + arr[i+2:] == sorted(arr) for i in range(len(arr) - 1)) print(can_sort_one_liner([1, 5, 3, 4, 2]))
Output: True
The one-liner uses a generator expression within the any function to check every possible one-element swap. It slices around the elements to be swapped, reverses their order with [::-1], and checks if the resulting array is sorted. The first True result short-circuits the process, confirming a one-swap sort is possible.
Summary/Discussion
- Method 1: Naive Approach. Exhaustive but clear. High time complexity makes it inefficient for large arrays.
- Method 2: Optimized Search. More efficient by minimizing comparisons. Still iterates through the entire array but performs fewer swaps.
- Method 3: Short Circuit Check. Quick elimination based on the number of out-of-place elements. Works well but relies on properly identifying the out-of-order pairs.
- Method 4: Greedy Approach. Intuitive and checks directly for the swap. Works well in practice but can be slower due to its inner loop.
- Method 5: Pythonic Approach. Compact and elegant, using Python’s list slicing and comprehension. However, not the most readable or efficient for large arrays.