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Find Intersection

#======================================================================= # 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: Find the node (intersection) where the two given # LinkedList coalesce. # # Technical Details: The idea is that two linked lists form a Y-shaped # structure. The structure may be degenerated. As shown below, the use # of a hashmap greatly reduces the complexity of the problem. # # # To keep things simple, we consider t2 and t2 equal iff they both # point to the same memory location. A broader definition of # equality: Two nodes t2 and t1 are equal if they and their respective # sublists are equal. #===================================================================== import collections class SinglyLinkedList( object ): def __init__( self ): self.head , self.tail = None, None @classmethod def findIntersection( self, head1, head2 ): intersect = {} t = head1 while None != t: intersect[t] = True t = t.next # first duplicate is intersection t = head2 while None != t: if None != intersect.get( t ): return t t = t.next return None 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 findIntersection method, of class SinglyLinkedList. #===================================================================== def testFindIntersection( self ): in_1 = [29, 14, 35, 2, 1, 12, 6, 7, 4, 8, 3, 0, 16, 19, 11] in_2 = [99, 78, 8, 3, 23] list_1 = SinglyLinkedList() list_2 = SinglyLinkedList() for i in range( len( in_1 ) ): list_1.addToTail( in_1[i] ) self.assertEquals( len( in_1 ), list_1.size() ) for i in range( len( in_2 ) ): list_2.addToTail( in_2[i] ) self.assertEquals( len( in_2 ), list_2.size() ) # set intersection: list_1 and list_2 form a Y at element 6 exp = 6 found = list_1.find( exp ) self.assertIsNotNone( found ) list_2.addAllToTail( found ) self.assertEquals( 14, list_2.size() ) n = SinglyLinkedList.findIntersection( list_1.head, list_2.head ) self.assertEquals( exp, n.data )