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"""

Introspective Sort is hybrid sort (Quick Sort + Heap Sort + Insertion Sort)

if the size of the list is under 16, use insertion sort

https://en.wikipedia.org/wiki/Introsort

"""

import math

def insertion_sort(array: list, start: int = 0, end: int = 0) -> list:

"""

>>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12]

>>> insertion_sort(array, 0, len(array))

[1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79]

"""

end = end or len(array)

for i in range(start, end):

temp_index = i

temp_index_value = array[i]

while temp_index != start and temp_index_value < array[temp_index - 1]:

array[temp_index] = array[temp_index - 1]

temp_index -= 1

array[temp_index] = temp_index_value

return array

def heapify(array: list, index: int, heap_size: int) -> None: # Max Heap

"""

>>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12]

>>> heapify(array, len(array) // 2 ,len(array))

"""

largest = index

left_index = 2 * index + 1 # Left Node

right_index = 2 * index + 2 # Right Node

if left_index < heap_size and array[largest] < array[left_index]:

largest = left_index

if right_index < heap_size and array[largest] < array[right_index]:

largest = right_index

if largest != index:

array[index], array[largest] = array[largest], array[index]

heapify(array, largest, heap_size)

def heap_sort(array: list) -> list:

"""

>>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12]

>>> heap_sort(array)

[1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79]

"""

n = len(array)

for i in range(n // 2, -1, -1):

heapify(array, i, n)

for i in range(n - 1, 0, -1):

array[i], array[0] = array[0], array[i]

heapify(array, 0, i)

return array

def median_of_3(

array: list, first_index: int, middle_index: int, last_index: int

) -> int:

"""

>>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12]

>>> median_of_3(array, 0, 0 + ((len(array) - 0) // 2) + 1, len(array) - 1)

"""

if (array[first_index] > array[middle_index]) != (

array[first_index] > array[last_index]

return array[first_index]

elif (array[middle_index] > array[first_index]) != (

array[middle_index] > array[last_index]

return array[middle_index]

else:

return array[last_index]

def partition(array: list, low: int, high: int, pivot: int) -> int:

"""

>>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12]

>>> partition(array, 0, len(array), 12)

"""

i = low

j = high

while True:

while array[i] < pivot:

i += 1

j -= 1

while pivot < array[j]:

j -= 1

if i >= j:

return i

array[i], array[j] = array[j], array[i]

i += 1

def sort(array: list) -> list:

"""

:param collection: some mutable ordered collection with heterogeneous

comparable items inside

:return: the same collection ordered by ascending

Examples:

>>> sort([4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12])

[1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79]

>>> sort([-1, -5, -3, -13, -44])

[-44, -13, -5, -3, -1]

>>> sort([])

[]

>>> sort([5])

[5]

>>> sort([-3, 0, -7, 6, 23, -34])

[-34, -7, -3, 0, 6, 23]

>>> sort([1.7, 1.0, 3.3, 2.1, 0.3 ])

[0.3, 1.0, 1.7, 2.1, 3.3]

>>> sort(['d', 'a', 'b', 'e', 'c'])

['a', 'b', 'c', 'd', 'e']

"""

if len(array) == 0:

return array

max_depth = 2 * math.ceil(math.log2(len(array)))

size_threshold = 16

return intro_sort(array, 0, len(array), size_threshold, max_depth)

def intro_sort(

array: list, start: int, end: int, size_threshold: int, max_depth: int

) -> list:

"""

>>> array = [4, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12]

>>> max_depth = 2 * math.ceil(math.log2(len(array)))

>>> intro_sort(array, 0, len(array), 16, max_depth)

[1, 2, 4, 6, 7, 8, 8, 12, 14, 14, 22, 23, 27, 45, 56, 79]

"""

while end - start > size_threshold:

if max_depth == 0:

return heap_sort(array)

max_depth -= 1

pivot = median_of_3(array, start, start + ((end - start) // 2) + 1, end - 1)

p = partition(array, start, end, pivot)

intro_sort(array, p, end, size_threshold, max_depth)

end = p

return insertion_sort(array, start, end)

if __name__ == "__main__":

import doctest

doctest.testmod()

user_input = input("Enter numbers separated by a comma : ").strip()

unsorted = [float(item) for item in user_input.split(",")]

print(sort(unsorted))

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