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Towers of Hanoi

Towers of Hanoi

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AfterBurner66	12 Sep, 2008 - 02:25 PM Post #1
New D.I.C Head Joined: 2 Aug, 2008 Posts: 16 My Contributions	Hi all! As a person who has not a Computer Science degree(I am a poor web developer!),but having much desire to learn as much as I can about CS topics,I have a (maybe easy ) question about the recursive algorithm that solves the "Towers of Hanoi" puzzle. I can understand that generally,having n discs and A,B,C pegs,the strategy is: 1.move (n-1) discs from A to B. 2.move nth disc from A to C. 3.move the (n-1) discs from B to C.Done! but this is implemented in whatever procedural language with a function,and the one thing that changes,is the order of arguments.OK so far but how do we assure that algorithm does recursively the moves that must be done and not something else?In other words how to be sure that changing of passed arguments leads to the correct solution?Because of two recursive functions used(I have studied implementations in Pascal,C,Java so far),it was difficult for me to construct a tracetable,because at the point of second recursive function call,things get much complicated I think,due to the fact that on return of function call,first recursive function is encountered first and after that we go to second etc. So is there any idea about how to construct a tracetable "safely",or at least how to trace the whole procedure? I tried also to solve the problem with the physical moves of discs required,but I didn't manage to map this to the recursive function calls.And something maybe more elementary:in what sense do we have recursion in this problem/ Any help or resource would be appreciated.Thanks in advance!
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AdamSpeight2008

12 Sep, 2008 - 05:42 PM

Post #2

LINQ D.I.C.

Joined: 29 May, 2008
Posts: 756

Windows

Thanked 48 times

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My Contributions

I hope this helps. It is a vb.net console app version.
When run it will visually show you the current depth of recursion and the variables values.


Module Module1
    Const ShowTrace As Boolean = True
    Dim level As Integer = 0
    Dim i As Integer = 0
    Dim c As Char = " "

    Sub Main()
        Hanoi(6)
        Console.ReadKey()
    End Sub

    Private Sub Hanoi(ByVal n As Integer)
        i = 0
        Call DoHanoi(1, 2, 3, n)
    End Sub


    Private Sub DoHanoi(ByVal f As Integer, ByVal u As Integer, ByVal t As Integer, ByVal n As Integer)
        If ShowTrace Then level += 1
        If ShowTrace Then Console.WriteLine(Strings.StrDup(level, c) & "Entering DoHanoi({0},{1},{2},{3})", f, u, t, n)
        If n = 1 Then
            i += 1
            Console.WriteLine(IIf(ShowTrace, Strings.StrDup(level, c), "") & "{0}. Move {1} to {2} ", i, f, t)
        Else
            DoHanoi(f, t, u, n - 1)
            DoHanoi(f, u, t, 1)
            DoHanoi(u, f, t, n - 1)
        End If
        If ShowTrace Then Console.WriteLine(Strings.StrDup(level, c) & "Exiting DoHanoi")
        If ShowTrace Then level -= 1

    End Sub
End Module

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AfterBurner66	13 Sep, 2008 - 06:41 PM Post #3
New D.I.C Head Joined: 2 Aug, 2008 Posts: 16 My Contributions	Thanks a lot AdamSpeight2008!This really helps.Though I don't know much VB,this is the better "towers of hanoi" program I've ever seen, by far.I can trace the procedure very well.Thanks again!
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