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    <div class="moz-cite-prefix">And Im still confused. <br>
      <br>
      Roelof<br>
      <br>
      <br>
      <br>
      Dudley Brooks schreef op 16-2-2015 om 19:41:<br>
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      <div class="moz-cite-prefix">Plus I should say that the "first"
        (or whichever) step might also really be more than one step. 
        The crucial idea is that there are individual step(s) versus
        "lumped" step(s), where the individual step(s) are the base
        case(s) and the "lumped" step(s) are the recursive
        invocation(s).<br>
        <br>
        On 2/16/15 10:31 AM, Dudley Brooks wrote:<br>
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        <div class="moz-cite-prefix">You're right, of course.  I guess
          the more precise way to say what I meant is that you
          *separate* a single step from everything else, dealing with
          everything else as a lump ... or two lumps ... or three lumps
          ... or ...<br>
          <br>
          I did at least say that "a 'single step' might have more than
          one step."  ;^)  My mistake was the use of the word "first".<br>
          <br>
          On 2/16/15 5:07 AM, Joel Neely wrote:<br>
        </div>
        <blockquote
cite="mid:CAEEzXAioDrGUgkg8QvGaAP4sBWoi0FxbbOhJdmqTr2cd4BB-_A@mail.gmail.com"
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          <div dir="ltr">
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">I'm
              sorry, but I must disagree with the generalization.</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small"><br>
            </div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">You
              described "the very nature" of a typical recursion over a
              list:</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">(1) deal
              with the head, then</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">(2) deal
              with everything else.</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small"><br>
            </div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">But
              lists are not the only recursive structure. Infix-order
              processing of a tree, for example, is more naturally
              described as:</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">(1) deal
              with the left sub-tree (the first "everything else"),</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">(2) deal
              with the parent (analogous to the head of a list),</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">(3) deal
              with the right sub-tree (the second "everything else").</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small"><br>
            </div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">At the
              risk of a spoiler...</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small"><br>
            </div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">.</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small"><br>
            </div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">.</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small"><br>
            </div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">.</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small"><br>
            </div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">.</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small"><br>
            </div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">One
              approach to the Towers of Hanoi problem emerges nicely
              from thinking of the moves as a tree.</div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small"><br>
            </div>
            <div class="gmail_default"
              style="font-family:georgia,serif;font-size:small">-jn-</div>
          </div>
          <div class="gmail_extra"><br>
            <div class="gmail_quote">On Sun, Feb 15, 2015 at 2:54 PM,
              Dudley Brooks <span dir="ltr"><<a
                  moz-do-not-send="true"
                  href="mailto:dbrooks@runforyourlife.org"
                  target="_blank">dbrooks@runforyourlife.org</a>></span>
              wrote:<br>
              <blockquote class="gmail_quote" style="margin:0 0 0
                .8ex;border-left:1px #ccc solid;padding-left:1ex">In my
                opinion, advising Mr Wobben to watch the pattern of
                moves will *not* lead him to the recursive solution,
                since the pattern of moves is really iterative.<br>
                <br>
                My hint would be to remember the very nature of
                recursion itself (for *any* problem):  Do the first
                step.  Then (to put it very dramatically) do *everything
                else* in *a single step*!  (Realizing that "everything
                else" is really the same problem, just made slightly
                smaller.)<br>
                <br>
                Note:  "A single step" might itself have more than one
                step.  My point is that recursion consists of (to put it
                humorously):  To do ABCDEFGHIJKLMNOPQRSTUVWXYZ, first
                you do A, then you do BCDEFGHIJKLMNOPQRSTUVWXYZ.  And,
                of course, "first" might actually be "last"!  And
                remembering the story of the Gordian Knot might help
                too.  (I apologize that trying not to be too explicit in
                the hint possibly makes it even more obscure.)<br>
                <br>
                Here's another hint that's useful for all kinds of
                programming problems, not just recursion:  Most problems
                consist of not only what you're trying to solve, but
                also what the restrictions are on what you're allowed to
                do to solve it.  Often some good insights come from
                imagining how you could solve the problem if you could
                ignore one or more of the restrictions (that's what I
                meant by the Gordian Knot reference).  So for the Towers
                of Hanoi, think about what the restrictions are on what
                kind of moves you're allowed to make.  Remove one of
                those restrictions.<br>
                <br>
                (Speaking of the iterative solution, the fun thing about
                actually physically doing the Towers of Hanoi is that,
                even though you're doing it by remembering the steps of
                the iterative pattern, as you watch the towers grow and
                shrink you can kind of "see" the recursion.)
                <div class="HOEnZb">
                  <div class="h5"><br>
                    <br>
                    On 2/15/15 12:51 AM, Roelof Wobben wrote:<br>
                    <blockquote class="gmail_quote" style="margin:0 0 0
                      .8ex;border-left:1px #ccc solid;padding-left:1ex">
                      YCH schreef op 15-2-2015 om 9:45:<br>
                      <blockquote class="gmail_quote" style="margin:0 0
                        0 .8ex;border-left:1px #ccc
                        solid;padding-left:1ex"> How about if I say
                        "Actually target was c not b and here is one
                        more<br>
                        disc. I put it on a. Now you should move all to
                        c"<br>
                        <br>
                        <br>
                      </blockquote>
                      <br>
                      Hanoi 1 a b c<br>
                      <br>
                      A -> C<br>
                      <br>
                      Hanoi 2 a b c<br>
                      <br>
                      A -> B<br>
                      A -> C<br>
                      B -> C<br>
                      <br>
                      Hanoi 3 a b c<br>
                      <br>
                      A -> C<br>
                      A -> B<br>
                      C -> B<br>
                      A -> C<br>
                      B -> A<br>
                      B -> C<br>
                      A -> C<br>
                      <br>
                      <br>
                      Roelof<br>
                      <br>
                      <br>
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                    </blockquote>
                    <br>
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            <br>
            <br clear="all">
            <div><br>
            </div>
            -- <br>
            <div class="gmail_signature">Beauty of style and harmony and
              grace and good rhythm depend on simplicity. - Plato</div>
          </div>
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      <pre wrap="">_______________________________________________
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</pre>
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