#### Counting Sort

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```"""
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(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")
"""
return "".join([chr(i) for i in counting_sort([ord(c) for c in string])])

if __name__ == "__main__":
# Test string sort

user_input = input("Enter numbers separated by a comma:\n").strip()
unsorted = [int(item) for item in user_input.split(",")]
print(counting_sort(unsorted))
```

#### Problem Statement

Given an unsorted array of `n` elements, write a function to sort the array.

#### Approach

• Find out the maximum element (let's call it `max`) from the given array.
• Initialize an array of length `max+1` with all elements set to 0 to store the array's count.
• Store the count of each element at their respective index in the array's count.
• Store cumulative sum of the elements of the count array. It helps in placing the elements into the correct index of the sorted array.
• Find the index of each element of the original array in the array's count. This gives the cumulative count.
• Place the element at the index calculated and decrease its count by one.

#### Time Complexity

`O(n+k)`: where `k` is the range of the non-negative key values.

#### Space Complexity

`O(n+k)`: where `k` is the range of the non-negative key values.

#### Founder's Name

• Harold H. Seward.

#### Example

``````countingSort(array, size)
max <- find largest element in array
initialize count array with all zeros
for j <- 0 to size
find the total count of each unique element and
store the count at jth index in count array
for i <- 1 to max
find the cumulative sum and store it in count array itself
for j <- size down to 1
restore the elements to array
decrease count of each element restored by 1
``````

#### Video Explanation

A video explaining the Counting Sort Algorithm

#### Animation Explanation

Counting Sort visualization