Last Updated : 24 Feb, 2025
Counting Sort is a non-comparison-based sorting algorithm. It is particularly efficient when the range of input values is small compared to the number of elements to be sorted. The basic idea behind Counting Sort is to count the frequency of each distinct element in the input array and use that information to place the elements in their correct sorted positions. For example, for input [1, 4, 3, 2, 2, 1], the output should be [1, 1, 2, 2, 3, 4]. The important thing to notice is that the range of input elements is small and comparable to the size of the array.
Working of Counting SortCode Implementation
- Declare an auxiliary array countArray[] of size max(inputArray[])+1 and initialize it with 0.
- Traverse array inputArray[] and map each element of inputArray[] as an index of countArray[] array, i.e., execute countArray[inputArray[i]]++ for 0 <= i < N.
- Calculate the prefix sum at every index of array inputArray[].
- Create an array outputArray[] of size N.
- Traverse array inputArray[] from end and update outputArray[ countArray[ inputArray[i] ] – 1] = inputArray[i]. Also, update countArray[inputArray[i] ] = countArray[ inputArray[i] ]- – .
The provided Python code demonstrates Counting Sort, a non-comparison-based sorting algorithm. Counting Sort works by determining each element's count in the input sequence, then reconstructing the sorted array. The code comprises a single function countSort that sorts a given string arr in alphabetical order. It uses auxiliary arrays count and output to keep track of character frequencies and sorted positions. The algorithm counts characters' occurrences, modifies the count array to hold their positions, and constructs the sorted output array. The driver code initializes a string, applies the countSort function, and prints the sorted character array. This algorithm's efficiency relies on its linear time complexity, making it ideal for a range of values with a limited span.
Python
def countSort(arr):
# The output character array that will have sorted arr
output = [0 for i in range(256)]
# Create a count array to store count of individual
# characters and initialize count array as 0
count = [0 for i in range(256)]
# For storing the resulting answer since the
# string is immutable
ans = ["" for _ in arr]
# Store count of each character
for i in arr:
count[ord(i)] += 1
# Change count[i] so that count[i] now contains actual
# position of this character in output array
for i in range(256):
count[i] += count[i-1]
# Build the output character array
for i in range(len(arr)):
output[count[ord(arr[i])]-1] = arr[i]
count[ord(arr[i])] -= 1
# Copy the output array to arr, so that arr now
# contains sorted characters
for i in range(len(arr)):
ans[i] = output[i]
return ans
# Driver program to test above function
arr = "geeksforgeeks"
ans = countSort(arr)
print ("Sorted character array is %s" %("".join(ans)))
Sorted character array is eeeefggkkorss
Time Complexity: O(n)
Space Complexity: O(n)
Using counter methodThis program implements the Counting Sort algorithm using the collections.Counter() method in Python. Counting Sort is a sorting algorithm that works by counting the occurrence of each distinct element in the input list and using that information to determine the position of each element in the output list. The algorithm has a time complexity of O(n+k), where n is the number of elements in the input list and k is the range of the input data, and a space complexity of O(k).
Algorithm:
Python
- Convert the input string into a list of characters.
- Count the occurrence of each character in the list using the collections. Counter() method.
- Sort the keys of the resulting Counter object to get the unique characters in the list in sorted order.
- For each character in the sorted list of keys, create a list of repeated characters using the corresponding count from the Counter object.
- Concatenate the lists of repeated characters to form the sorted output list.
from collections import Counter
def counting_sort(arr):
count = Counter(arr)
output = []
for c in sorted(count.keys()):
output += [c] * count[c]
return output
arr = "geeksforgeeks"
arr = list(arr)
arr = counting_sort(arr)
output = ''.join(arr)
print("Sorted character array is", output)
Sorted character array is eeeefggkkorss
from functools import reduce
# Input string
string = "geeksforgeeks"
# Sort the characters using reduce and lambda function
sorted_str = reduce(lambda x, y: x+y, sorted(string))
# Print the sorted string
print("Sorted string:", sorted_str)
Sorted string: eeeefggkkorss
Time Complexity:
Space Complexity:
Please refer complete article on Counting Sort for more details!
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