#### Intro Sort

P
S
I
```"""
Introspective Sort is a 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]
>>> array = [21, 15, 11, 45, -2, -11, 46]
>>> insertion_sort(array, 0, len(array))
[-11, -2, 11, 15, 21, 45, 46]
>>> array = [-2, 0, 89, 11, 48, 79, 12]
>>> insertion_sort(array, 0, len(array))
[-2, 0, 11, 12, 48, 79, 89]
>>> array = ['a', 'z', 'd', 'p', 'v', 'l', 'o', 'o']
>>> insertion_sort(array, 0, len(array))
['a', 'd', 'l', 'o', 'o', 'p', 'v', 'z']
>>> array = [73.568, 73.56, -45.03, 1.7, 0, 89.45]
>>> insertion_sort(array, 0, len(array))
[-45.03, 0, 1.7, 73.56, 73.568, 89.45]
"""
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:
"""
>>> heap_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]
>>> heap_sort([-2, -11, 0, 0, 0, 87, 45, -69, 78, 12, 10, 103, 89, 52])
[-69, -11, -2, 0, 0, 0, 10, 12, 45, 52, 78, 87, 89, 103]
>>> heap_sort(['b', 'd', 'e', 'f', 'g', 'p', 'x', 'z', 'b', 's', 'e', 'u', 'v'])
['b', 'b', 'd', 'e', 'e', 'f', 'g', 'p', 's', 'u', 'v', 'x', 'z']
>>> heap_sort([6.2, -45.54, 8465.20, 758.56, -457.0, 0, 1, 2.879, 1.7, 11.7])
[-457.0, -45.54, 0, 1, 1.7, 2.879, 6.2, 11.7, 758.56, 8465.2]
"""
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, ((len(array) - 0) // 2) + 1, len(array) - 1)
12
>>> array = [13, 2, 6, 8, 1, 7, 8, 22, 14, 56, 27, 79, 23, 45, 14, 12]
>>> median_of_3(array, 0, ((len(array) - 0) // 2) + 1, len(array) - 1)
13
>>> array = [4, 2, 6, 8, 1, 7, 8, 22, 15, 14, 27, 79, 23, 45, 14, 16]
>>> median_of_3(array, 0, ((len(array) - 0) // 2) + 1, len(array) - 1)
14
"""
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)
8
>>> array = [21, 15, 11, 45, -2, -11, 46]
>>> partition(array, 0, len(array), 15)
3
>>> array = ['a', 'z', 'd', 'p', 'v', 'l', 'o', 'o']
>>> partition(array, 0, len(array), 'p')
5
>>> array = [6.2, -45.54, 8465.20, 758.56, -457.0, 0, 1, 2.879, 1.7, 11.7]
>>> partition(array, 0, len(array), 2.879)
6
"""
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(f"{sort(unsorted) = }")
```