Counting Sort
by Isai Damier

#=======================================================================
# 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 )
    t = self.head
    while None != t:
      counter[t.data] += 1
      t = t.next

    t = self.head
    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
from algorithms.SinglyLinkedList import SinglyLinkedList
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]
    linkedList = SinglyLinkedList()
    for i in range( len( tape ) ):
      linkedList.addToTail( tape[i] )

    self.assertEquals( tape, linkedList.toArray() )
    tape.sort()
    self.assertNotEquals( tape, linkedList.toArray() )
    linkedList.countingsort( 19 )
    self.assertEquals( tape, linkedList.toArray() )