# Cycle Startby Isai Damier, Android Engineer @ Google

```#=======================================================================
# Author: Isai Damier
# 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
#     only the direction of the circular portion is reversed.
#=====================================================================

import collections

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

def cycleStart( self ) :
return None

# slow and fast both started at head after one step,
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
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
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]