Create intro_sort.py (TheAlgorithms#3877)

* Create intro_sort.py

* modified intro_sort.py

* add doctest

* modified code

black intro_sort.py

* add more test

* Update intro_sort.py

added doctest, modified code

* black intro_sort.py

* add type hint

* modified code

Author: YeonJeongLee00

Diff for: sorts/intro_sort.py

@@ -0,0 +1,173 @@
+"""
+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)
+    12
+    """
+    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
+    """
+    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))