# Counting Sortby Isai Damier, Android Engineer @ Google

```/***************************************************************************
* Author: Isai Damier
* Project: geekviewpoint
* Package: datastructure
*
* Description: A LinkedList is a data structure that allows access
*   to a collection of data using pointers/references. While an
*   array can also be defined as above, LinkedLists and arrays differ
*   in how they are stored in memory and in the operations they
*   allow. Unlike an array that must be stored in a block of memory,
*   the nodes of a LinkedList can be stored anywhere because each
*   node has a reference to the node that succeeds it. Because the
*   nodes are stored so loosely, inserting nodes into a LinkedList
*   is easy; whereas in an array, all the succeeding elements must
*   be shifted. Of course, insertion also means changing the size of
*   the array, which means creating the entire array anew.
*
*   Perhaps the greatest beauty of LinkedList is that it allows
*   accessing an entire sequence of nodes using only one variable:
*   a reference to the first node in the sequence.
*
*   Countless operations can be performed on LinkedLists. Following
*   are a few, ranging from the common to the very interesting.
**************************************************************************/

Node tail = null;

/************************************************************************
* Time Complexity of Solution:
*   O(n*log n).
*
*
* Technical Details: If the elements of this LinkedList fall within a
*   known short range, then it makes sense to use an integer algorithm
*   like counting sort (ref geekviewpoint/java/sorting/counting_sort),
*   since integer algorithms are very fast.
*
*   To keep the implementation simple, assume the elements range from 0
*   to max, inclusive. Counting sort then proceeds by creating a bucket
*   for each key; incrementing a counter each time a key recurs in the
*   list; then emptying the buckets back into the LinkedList.
************************************************************************/
public void countingSort(int max) {
//create a bucket for each key
int A[] = new int[max + 1];//Java initializes int arrays to 0.
//count recurrence of keys
for (Node t = head; null != t; t = t.next) {
A[t.data]++;
}
//swap sorted data back into LinkedList
for (int i = 0; i < A.length; i++) {
for (int x = 0; x < A[i]; x++) {
t.data = i;
t = t.next;
}
}

}
}```
```public class SinglyLinkedListTest {

/**
* Test of countingSort method, of class SinglyLinkedList.
*/
@Test
public void testCountingSort() {
System.out.println("countingSort");
int[] input = {9, 4, 5, 2, 1, 12, 6, 7, 4, 8, 3, 0, 16, 19, 11};