Counting Sorter Algorithm
Bucket sort may be used for many of the same tasks as counting sort, with a like time analysis; however, compared to counting sort, bucket sort necessitates associated lists, dynamic arrays or a large amount of preallocated memory to keep the sets of items within each bucket, whereas counting sort instead stores a individual number (the count of items) per bucket. Because counting sort uses key values as indexes into an array, it is not a comparison sort, and the Ω(n log N) Although radix sorting itself dates back far longer,
counting sort, and its application to radix sorting, were both invented by Harold H. Seward in 1954.
using System;
using System.Linq;
namespace Algorithms.Sorters.Integer
{
/// <summary>
/// Counting sort is an algorithm for sorting a collection of objects according to keys that are small integers; that
/// is, it is an integer sorting algorithm. It operates by counting the number of objects that have each distinct key
/// value, and using arithmetic on those counts to determine the positions of each key value in the output sequence.
/// Its running time is linear in the number of items and the difference between the maximum and minimum key values, so
/// it is only suitable for direct use in situations where the variation in keys is not significantly greater than the
/// number of items. However, it is often used as a subroutine in another sorting algorithm, radix sort, that can
/// handle larger keys more efficiently.
/// </summary>
public class CountingSorter : IIntegerSorter
{
/// <summary>
/// <para>
/// Sorts input array using counting sort algorithm.
/// </para>
/// <para>
/// Time complexity: O(n+k), where k is the range of the non-negative key values.
/// </para>
/// <para>
/// Space complexity: O(n+k), where k is the range of the non-negative key values.
/// </para>
/// </summary>
/// <param name="array">Input array.</param>
public void Sort(int[] array)
{
if (array.Length == 0)
{
return;
}
var max = array.Max();
var min = array.Min();
var count = new int[max - min + 1];
var output = new int[array.Length];
for (var i = 0; i < array.Length; i++)
{
count[array[i] - min]++;
}
for (var i = 1; i < count.Length; i++)
{
count[i] += count[i - 1];
}
for (var i = array.Length - 1; i >= 0; i--)
{
output[count[array[i] - min] - 1] = array[i];
count[array[i] - min]--;
}
Array.Copy(output, array, array.Length);
}
}
}
