sorts.flash_sort
================

.. py:module:: sorts.flash_sort

.. autoapi-nested-parse::

   Flash Sort Algorithm Implementation

   Flash sort is a distribution sorting algorithm showing linear computational
   complexity O(n) for uniformly distributed datasets and relatively little
   additional memory requirement. The basic idea is to use the distribution
   of the values to be sorted to determine their approximate final positions
   directly, without comparing and moving each element through many intermediate
   positions as done by other algorithms.

   The algorithm was developed by Karl-Dietrich Neubert in 1998 and builds upon
   the idea of bucket sort. It works by classifying elements into classes and
   then sorting each class.

   Time Complexity:
   - Best Case: O(n) when data is uniformly distributed
   - Average Case: O(n + k) where k is the number of classes
   - Worst Case: O(n²) when data is not uniformly distributed

   Space Complexity: O(k) where k is the number of classes

   Source: https://en.wikipedia.org/wiki/Flashsort



Attributes
----------

.. autoapisummary::

   sorts.flash_sort.test_cases


Functions
---------

.. autoapisummary::

   sorts.flash_sort.flash_sort


Module Contents
---------------

.. py:function:: flash_sort(arr: list[int | float]) -> list[int | float]

   Sorts a list using the Flash Sort algorithm.

   Flash sort is particularly efficient for uniformly distributed data.
   It uses the distribution of values to determine approximate positions.

   Args:
       arr: List of integers or floats to be sorted

   Returns:
       Sorted list in ascending order

   Examples:
   >>> flash_sort([4, 2, 7, 1, 9, 3])
   [1, 2, 3, 4, 7, 9]
   >>> flash_sort([])
   []
   >>> flash_sort([5])
   [5]
   >>> flash_sort([3, 3, 3, 3])
   [3, 3, 3, 3]
   >>> flash_sort([-1, -5, 0, 3, 2])
   [-5, -1, 0, 2, 3]
   >>> flash_sort([1.5, 2.3, 0.1, 3.7, 1.2])
   [0.1, 1.2, 1.5, 2.3, 3.7]
   >>> flash_sort([10, 9, 8, 7, 6, 5, 4, 3, 2, 1])
   [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
   >>> import random
   >>> data = random.sample(range(100), 20)
   >>> flash_sort(data) == sorted(data)
   True
   >>> flash_sort([42])
   [42]
   >>> flash_sort([2.5, 1.1, 3.3, 2.5, 1.1])
   [1.1, 1.1, 2.5, 2.5, 3.3]


.. py:data:: test_cases
   :type:  list[list[int | float]]