an entry point （the method call） and an exit point （the end of a method’s execution）。 The Keyhole Problem In the example； the entry and exit point into the algorithm is FindRoute（）。 In turn； the entry of FindRoute（） is two parameters： start； indicating the beginning city； and finish； indicating the destination city。 The exit of FindRoute（） is an array of Node objects。 The array of Node objects needs to be preallocated with space so that all of the found cities can be added。 We can make an assumption at this point that we preallocate the number of nodes to the length of the data member DepthFirstSearch。root plus one。 The assumption is that the longest trip cannot exceed the number of cities available。 We know that the root node is an array of all starting point cities； thus the allocation can never be exceeded。 Focusing on the FindRoute（） method； the updated code looks like this： Public Function FindRoute（ByVal start As String； ByVal finish As String） As Node（） Dim returnArray（Me。root。Length ＋ 1） As Node Return returnArray End Function The code with the array allocation is a classic keyhole problem （an idea first introduced by Scott Meyers； see http：//aristeia。/TKP/）。 The problem of a keyhole is that you imple ment an algorithm based on assumptions that cause you to write code that works for that specific context； but would fail when executed in another context。 …………………………………………………………Page 126…………………………………………………………… 104 CH AP T E R 4 ■ L E A R N IN G AB OU T D AT A S TR U CT U R E S； DE CI SI ON S； A N D L O OP S The code allocates an array to the length of the root tree structure； and that is making a grand assumption。 Imagine if the Node developers decided to introduce connections that could be reached only via another city that is not included in the root nodes。 At that point； you could potentially exceed the available space in the array。 Another solution would be to allocate an array of arbitrary length X 。 But then； if there were X＋1 unique cities； another array could be violated。 The simplest solution would be to not allocate an array； but instead figure out how many elements you needed after having found a path。 However； this would not work； because then you would have no idea which city you had already visited。 Another solution （which will be discussed in Chapter 9） would be to use a collection class。 In this case； we are going to wash our hands of the problem and force the Node developers to modify their class。 The Node developers are going to add a shared method that tells the search algorithm how big the array needs to be。 The following is the modified FindRoute（） code。 Public Function FindRoute（ByVal start As String； ByVal finish As String） As Node（） Dim returnArray（Node。GetMaxPossibleDestinationsArraySize（）） As Node Return returnArray End Function Now the code doesn’t have a keyhole problem from the perspective of DepthFirstSearch； because Node will always indicate the appropriate size for the array。 If there is still not enough room； the problem will lie with Node。 This is not an ideal solution； but sometimes it’s the only option。 Using the For Loop The root node （root） references a list of cities that are available as a starting point。 To start off the search； the first step is to match the starting city with the start parameter by iterating over the list of cities。 For that； we need the For loop。 Here is the modified source code of FindRoute（）： Public Function FindRoute（ByVal start As String； ByVal finish As String） As Node（） Dim returnArray（Node。GetMaxPossibleDestinationsArraySize（）） As Node For c1 As Integer = 0 To root。Length 1 If Me。root（c1）。CityName。pareTo（start） = 0 Then returnArray（0） = Me。root（c1） FindNextLeg（returnArray； 1； finish； root（c1）） End If Next Return returnArray End Function The For loop starts counting at 0 and goes to the end of the root array using the Me。root。 Length property。 For each loop iteration； the root（c1）。CityName is tested to see if it is the starting city。 Then the starting city is assigned as the first city in the array that represents the found travel route （returnArray（0） = Me。root（c1））。 Finally； the method FindNextLeg（） is used to find a possible route to the destination。 …………………………………………………………Page 127…………………………………………………………… CH AP T E R 4 ■ L E A R N I N G A B OU T D AT A S TR U CT U R E S； DE CI SI ON S； A N D L O OP S 105 A For loop is used to go through a series based on some logic。 For the most part； that series involves incrementing or decrementing numbers； but it can use other kinds of logic。 The For loop has the following form： For ＇variable＇ ＇As type＇ = ＇starting condition＇ To ＇ending condition＇ ＇step size＇ ＇Operations of doing something＇ Next where： ＇variable＇： Defines the variable that will serve as the counter in the loop。 ＇As type＇： An optional definition used to define the type of the counter in the loop。 For the most part； the counter will be a numeric value。 However； you can have other types as long as the increment operators are supported。 ＇starting condition＇： Defines the initial state of the counter when the loop is started。 ＇ending condition＇： Defines the ending state that will terminate the looping。