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def quicksort(arr):
"""Recursively sorts an array using the Quicksort algorithm."""
if len(arr) <= 1:
return arr
pivot = arr[len(arr) // 2]
left = [x for x in arr if x < pivot]
middle = [x for x in arr if x == pivot]
right = [x for x in arr if x > pivot]
return quicksort(left) + middle + quicksort(right)
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def quicksort_inplace(arr, low=0, high=None):
"""In-place Quicksort implementation for efficiency."""
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if high is None:
high = len(arr) - 1
if low < high:
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pivot_index = partition(arr, low, high)
quicksort_inplace(arr, low, pivot_index - 1)
quicksort_inplace(arr, pivot_index + 1, high)
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def partition(arr, low, high):
pivot = arr[high]
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i = low
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for j in range(low, high):
if arr[j] <= pivot:
arr[i], arr[j] = arr[j], arr[i]
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i += 1
arr[i], arr[high] = arr[high], arr[i]
return i