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 the elements in this linked list in ascending
  #   order.
  #
  # Technical Details: Sorting a LinkedList in place is very costly:
  #   in the order of O(n^2# log(n)) with a good algorithm.
  #   Therefore it makes sense to create an array from the list,
  #   sort the array, and then empty the array into the list by
  #   index. It's kind of like: unbutton a shirt; move the buttons
  #   around; then button the shirt anew. (I think it's a good analogy.)
  #=====================================================================
 
 import collections
class SinglyLinkedList( object ):

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

  def sort( self ) :
    if 2 > self.size():
      return

    A = [0] * self.size()
    # unfasten the buttons (i.e. unbutton the shirt)
    x = 0
    t = self.head
    while None != t:
      A[x] = t.data # list fills array
      x += 1
      t = t.next

    self._mergesort( A, 0, len( A ) - 1 )
    # refasten the buttons (i.e. button the shirt anew)
    x = 0
    t = self.head
    while None != t:
      t.data = A[x] # array fills list
      x += 1
      t = t.next

  def _mergesort( self, aList, first, last ):
    # break problem into smaller structurally identical pieces
    mid = ( first + last ) / 2
    if first < last:
      self._mergesort( aList, first, mid )
      self._mergesort( aList, mid + 1, last )

    # merge solved pieces to get solution to original problem
    a, f, l = 0, first, mid + 1
    tmp = [None] * ( last - first + 1 )

    while f <= mid and l <= last:
      if aList[f] < aList[l] :
        tmp[a] = aList[f]
        f += 1
      else:
        tmp[a] = aList[l]
        l += 1
      a += 1

    if f <= mid :
      tmp[a:] = aList[f:mid + 1]

    if l <= last:
      tmp[a:] = aList[l:last + 1]

    a = 0
    while first <= last:
      aList[first] = tmp[a]
      first += 1
      a += 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 sort method, of class SinglyLinkedList.
  #=====================================================================
  def testSort( 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.sort()
    self.assertEquals( tape, linkedList.toArray() )