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The Algorithms

Counting Sort

This is pure Python implementation of counting sort algorithm
For doctests run following command:
python -m doctest -v
python3 -m doctest -v
For manual testing run:

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
    >>> 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
    assert counting_sort_string("thisisthestring") == "eghhiiinrsssttt"

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

Problem Statement

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


  • 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.


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