## Python, sort, counting_sort.py

``````"""
This is pure Python implementation of counting sort algorithm
For doctests run following command:
python -m doctest -v counting_sort.py
or
python3 -m doctest -v counting_sort.py
For manual testing run:
python counting_sort.py
"""

def counting_sort(collection):
"""Pure implementation of counting sort algorithm in Python
:param collection: some mutable ordered collection with heterogeneous
comparable items inside
:return: the same collection ordered by ascending
Examples:
>>> counting_sort([0, 5, 3, 2, 2])
[0, 2, 2, 3, 5]
>>> counting_sort([])
[]
>>> counting_sort([-2, -5, -45])
[-45, -5, -2]
"""
# if the collection is empty, returns empty
if collection == []:
return []

# get some information about the collection
coll_len = len(collection)
coll_max = max(collection)
coll_min = min(collection)

# create the counting array
counting_arr_length = coll_max + 1 - coll_min
counting_arr = [0] * counting_arr_length

# count how much a number appears in the collection
for number in collection:
counting_arr[number - coll_min] += 1

# sum each position with it's predecessors. now, counting_arr[i] tells
# us how many elements <= i has in the collection
for i in range(1, counting_arr_length):
counting_arr[i] = counting_arr[i] + counting_arr[i - 1]

# create the output collection
ordered = [0] * coll_len

# place the elements in the output, respecting the original order (stable
# sort) from end to begin, updating counting_arr
for i in reversed(range(0, coll_len)):
ordered[counting_arr[collection[i] - coll_min] - 1] = collection[i]
counting_arr[collection[i] - coll_min] -= 1

return ordered

def counting_sort_string(string):
"""
>>> counting_sort_string("thisisthestring")