C++ Count Sort Implementation

Introduction

Counting sort is an algorithm generally used for sorting smaller integers. It is able to sort integer input in linear time and is ideal for situations where a large number of integer keys need to be sorted. For smaller sets, a comparison sort is probably more appropriate. It is best used when the integer keys are not larger than the number of items in the set and is thus, frequently combined with radix sort, which allows for larger input keys.

Background

Based on Introduction to Algorithms Third Edition p. 195.

Counting sort assumes that each of the n input elements is an integer in the range 0 to k, for some integer k. When k=O(n), the sort runs in theta(n) time. Counting sort determines, for each input element x, the number of elements less than x. It uses this information to place element x directly into its position in the output array. For example, if 17 elements are less than x, then x belongs in output position 18.

CONFUSING NOTE: This algorithm assumes that the C array starts at index 0 and
the A array starts at index 1. This had to be accounted for in the actual code.
I did this by making the bounds of some of the loops go from 0 to k inclusive
and by subtracting 1 in from the array index of B in line 11 of the algorithm.

COUNTING-SORT(A, B, k)

1)     let C[0..k] b. a new array<<br mode="hold" />2)     for i=0 to k do
3)          C[i] = 0
4)     for j to length[A] do
5)          C [ A[ j ]] C [ A[ j ]] + 1
6)     //C[i] now contains the number of elements equal to i.
7)     for i = 1 to k do
8)          C[i] = C[i] + C[i − 1]
9)     // C[i] now contains the number of elements less than or equal to i.
10)    for j length[A] down to 1 do
11)         B[C[A[j]]] = A[j]
12)         C[A[j]] = C[A[j]] − 1

Using the Code

To use the code in your own program, copy and paste the count sort function below into your code. The code is designed to be modular. It takes as input the array to be sorted and a value k, which represents the largest value in the array.

/* Count Sort
	Input: int arrayA - An array that contains the data to be sorted.
	       int k - An integer representing the largest input value.
	Output: int* - The function returns a pointer to the original array
		       with the sorted output.
        Compiled With: g++ for i686-apple-darwin10
                       gcc version 4.2.1 (Apple Inc. build 5666)
*/
int *countSort(int arrayA[], int k) {

	//Calculate the length of arrayA.
	int arrayA_length = sizeof(arrayA);

	//Declare a new array B. B holds the sorted output.
	int * arrayB = (int *)malloc(arrayA_length * sizeof(int));

	//Declare a new array C. C provides a temporary workspace.
	int * arrayC = (int *)malloc((k+1) * sizeof(int));
		
	//Initialize the elments of that array to 0.
	for(int i = 0; i <= k; i++)
		arrayC[i] = 0;

	//Count the number of each number (confusing I know) and place that
	//value into the array C.
	for(int j = 0; j < arrayA_length; j++)
		arrayC[arrayA[j]] = arrayC[arrayA[j]] + 1;
	
	//Place the number of elements less than each value at i into array C.	
	for(int i = 1; i <= k; i++)
		arrayC[i] = arrayC[i] + arrayC[i-1];

	//Place each element of arrayA into its correct sorted position in the
	//output array B.
	for(int j = arrayA_length - 1; j >= 0; j--) {
		arrayB[arrayC[arrayA[j]] - 1] = arrayA[j];
		arrayC[arrayA[j]] = arrayC[arrayA[j]] - 1;
	}

	//Overwrite the original arrayA with the output arrayB.
	for(int i = 0; i < sizeof(arrayA); i++)
		arrayA[i] = arrayB[i];

	//Release any used memory. You want to do this because you don't want
	//multiple calls to the sort to use an increasingly large amount of
	//memory.
	free(arrayB);
	free(arrayC);

	//Return a pointer to the output arrayB.
	return arrayA;
}
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