#
Cycle Start

#======================================================================= # 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() )