Counting Sortby Isai Damier, Android Engineer @ Google

```#=======================================================================
# Author: Isai Damier
# Title: Singly Linked List
# 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.
#=======================================================================
#=====================================================================
# Time Complexity of Solution:
#   O(n*log n).
#
# Description: sort this LinkedList
#
# 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/python/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.
#******#==============================================================

import collections
class SinglyLinkedList( object ):

def __init__( self ):
self.head , self.tail = None, None

def countingsort( self, k ):
counter = [0] * ( k + 1 )
while None != t:
counter[t.data] += 1
t = t.next

for i in range( len( counter ) ):
while 0 < counter[i]:
t.data = i;
t = t.next
counter[i] -= 1

class Node( object ):

def __init__( self, data, next = None ):
self.data = data
self.next = next
```
```import unittest
import random

class Test( unittest.TestCase ):
#=====================================================================
# Test of countingSort method, of class SinglyLinkedList.
#=====================================================================
def testCountingSort( self ):
tape = [9, 4, 5, 2, 1, 12, 6, 7, 4, 8, 3, 0, 16, 19, 11]