#=======================================================================
# 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).
#
# Description: If this LinkedList contains a loop/cycle, indicate
# the node where the cycle/loop begins. Understand that this
# LinkedList is not necessary circular: maybe it is; may be it
# is not. The LinkedList may be P-shaped. This algorithm will
# work either way.
#
# Technical Details: This algorithm was invented by R. W. Floyd.
# The basis for the algorithm is that if a path eventually
# loops, then two travelers walking at different speed will
# keep meeting each other.
#
# Particularly. Let x and y be travelers such that y is walking
# twice as fast as x (i.e. y = 2x). Further, let s be the place
# where x and y first started walking at the same time. Then
# when x and y meet again, the distance from s to the start of
# the loop is the exact same distance from the present meeting
# place of x and y to the start of the loop.
#
# BTY: reversing a P-shaped LinkedList still results in a
# P-shaped LinkedList with the same self.head and linear section;
# only the direction of the circular portion is reversed.
#=====================================================================
import collections
class SinglyLinkedList( object ):
def __init__( self ):
self.head , self.tail = None, None
def cycleStart( self ) :
if None == self.head or None == self.head.next:
return None
# slow and fast both started at head after one step,
# slow is at self.head.next and fast is at self.head.next.next
slow = self.head.next
fast = slow.next
# each keep walking until they meet again.
while slow != fast:
slow = slow.next
try:
fast = fast.next.next
except AttributeError:
return None # no cycle if NoneType reached
# from self.head to beginning of loop is same as from fast to
# beginning of loop
slow = self.head
while slow != fast:
slow = slow.next
fast = fast.next
return slow # beginning of loop
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 cycleStart method, of class SinglyLinkedList.
#=====================================================================
def testCycleStart( 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] )
cy = linkedList.find( 18 )
linkedList.tail.right = cy
self.assertEquals( cy, linkedList.cycleStart() )
