Algorithm: Counting Sort

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Hey folks, whats up..?

I've reading about algorithms a lot lately. I have this awesome site GeeksforGeeks, they teach all things about computer, such as algorithms, data structures, c, c++ and some of the interview experiences from the people who got selected in the IT Giants like Google, Facebook, Amazon etc..

I was reading about radix sort when encounter a problem with some fraction of the program. So moderator of the site suggested me another algorithm to understand the radixsort. That is counting algorithm. Here are the details.

Counting sort  is a sorting technique based on keys between a specific range. It works by counting the number of objects having distinct key values (kind of hashing). Then doing some arithmetic to calculate the position of each object in the output sequence.

Let us understand it with the help of an example.
For simplicity, consider the data in the range 0 to 9. 
Input data: 1, 4, 1, 2, 7, 5, 2
  1) Take a count array to store the count of each unique object.
  Index:     0  1  2  3  4  5  6  7  8  9
  Count:     0  2  2  0   1  1  0  1  0  0

  2) Modify the count array such that each element at each index 
  stores the sum of previous counts. 
  Index:     0  1  2  3  4  5  6  7  8  9
  Count:     0  2  4  4  5  6  6  7  7  7

The modified count array indicates the position of each object in 
the output sequence.
 
  3) Output each object from the input sequence followed by 
  decreasing its count by 1.
  Process the input data: 1, 4, 1, 2, 7, 5, 2. Position of 1 is 2.
  Put data 1 at index 2 in output. Decrease count by 1 to place 
  next data 1 at an index 1 smaller than this index.
Following is C implementation of counting sort.
// C Program for counting sort
#include <stdio.h>
#include <string.h>
#define RANGE 255
 
// The main function that sort the given string str in alphabatical order
void countSort(char *str)
{
    // The output character array that will have sorted str
    char output[strlen(str)];
 
    // Create a count array to store count of inidividul characters and
    // initialize count array as 0
    int count[RANGE + 1], i;
    memset(count, 0, sizeof(count));
 
    // Store count of each character
    for(i = 0; str[i]; ++i)
        ++count[str[i]];
 
    // Change count[i] so that count[i] now contains actual position of
    // this character in output array
    for (i = 1; i <= RANGE; ++i)
        count[i] += count[i-1];
 
    // Build the output character array
    for (i = 0; str[i]; ++i)
    {
        output[count[str[i]]-1] = str[i];
        --count[str[i]];
    }
 
    // Copy the output array to str, so that str now
    // contains sorted characters
    for (i = 0; str[i]; ++i)
        str[i] = output[i];
}
 
// Driver program to test above function
int main()
{
    char str[] = "geeksforgeeks";//"applepp";
 
    countSort(str);
 
    printf("Sorted string is %s\n", str);
    return 0;
}
Output:
Sorted character array is eeeefggkkorss

Time Complexity: O(n+k) where n is the number of elements in input array and k is the range of input.
(You might be thinking what is time complexity. Here is the WikiPedia Article on that.)

Auxiliary Space: O(n+k)

Points to be noted:
1. Counting sort is efficient if the range of input data is not significantly greater than the number of objects to be sorted. Consider the situation where the input sequence is between range 1 to 10K and the data is 10, 5, 10K, 5K.
2. It is not a comparison based sorting. It running time complexity is O(n) with space proportional to the range of data.
3. It is often used as a sub-routine to another sorting algorithm like radix sort.
4. Counting sort uses a partial hashing to count the occurrence of the data object in O(1).
5. Counting sort can be extended to work for negative inputs also.

Exercise:
1. Modify above code to sort the input data in the range from M to N.
2. Modify above code to sort negative input data.
3. Is counting sort stable and online?
4. Thoughts on parallelizing the counting sort algorithm.

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