``````#!/usr/bin/env python3
"""
Illustrate how to implement bucket sort algorithm.

Author: OMKAR PATHAK
This program will illustrate how to implement bucket sort algorithm

Wikipedia says: Bucket sort, or bin sort, is a sorting algorithm that works
by distributing the elements of an array into a number of buckets.
Each bucket is then sorted individually, either using a different sorting
algorithm, or by recursively applying the bucket sorting algorithm. It is a
distribution sort, and is a cousin of radix sort in the most to least
significant digit flavour.
Bucket sort is a generalization of pigeonhole sort. Bucket sort can be
implemented with comparisons and therefore can also be considered a
comparison sort algorithm. The computational complexity estimates involve the
number of buckets.

Time Complexity of Solution:
Worst case scenario occurs when all the elements are placed in a single bucket.
The overall performance would then be dominated by the algorithm used to sort each
bucket. In this case, O(n log n), because of TimSort

Average Case O(n + (n^2)/k + k), where k is the number of buckets

If k = O(n), time complexity is O(n)

Source: https://en.wikipedia.org/wiki/Bucket_sort
"""
from __future__ import annotations

def bucket_sort(my_list: list) -> list:
"""
>>> data = [-1, 2, -5, 0]
>>> bucket_sort(data) == sorted(data)
True
>>> data = [9, 8, 7, 6, -12]
>>> bucket_sort(data) == sorted(data)
True
>>> data = [.4, 1.2, .1, .2, -.9]
>>> bucket_sort(data) == sorted(data)
True
>>> bucket_sort([]) == sorted([])
True
>>> import random
>>> collection = random.sample(range(-50, 50), 50)
>>> bucket_sort(collection) == sorted(collection)
True
"""
if len(my_list) == 0:
return []
min_value, max_value = min(my_list), max(my_list)
bucket_count = int(max_value - min_value) + 1
buckets: list[list] = [[] for _ in range(bucket_count)]

for i in range(len(my_list)):
buckets[(int(my_list[i] - min_value) // bucket_count)].append(my_list[i])

return [v for bucket in buckets for v in sorted(bucket)]

if __name__ == "__main__":
from doctest import testmod

testmod()
assert bucket_sort([4, 5, 3, 2, 1]) == [1, 2, 3, 4, 5]
assert bucket_sort([0, 1, -10, 15, 2, -2]) == [-10, -2, 0, 1, 2, 15]
``````

#### Bucket Sort  