(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 60169, 1871]*) (*NotebookOutlinePosition[ 60836, 1895]*) (* CellTagsIndexPosition[ 60792, 1891]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["1997 Mathematica Developer Conference Challenge Problem", "Subtitle"], Cell["Problem Statement", "Subsubtitle"], Cell[TextData[{ "Create the function TreeGraphic[d_Integer] that produces a Graphics object \ for a tree with ", Cell[BoxData[ \(3\[CenterDot]2\^d\)]], " leaves, arranged and connected as shown below." }], "Text"], Cell[TextData[{ "In particular, the ", Cell[BoxData[ \(3\[CenterDot]2\^d\)]], " leaves should be arranged on a circle, their ", Cell[BoxData[ \(3\[CenterDot]2\^\(d - 1\)\)]], " neighbors should be arranged between them on a smaller concentric circle, \ and so on, until one vertex is placed at the center of all the circles. 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(2) A semicolon was added to the line beginning \"Lines[0] =\" to suppress \ output.\ \>", "Text"], Cell["\<\ We had 90 minutes to work on this problem and submit a solution. I \ thought that would be plenty of time, as I had often done harder things in \ 90 minutes, as had many others in the room. Boy was I wrong! I felt like I \ was not thinking clearly, and the time went by quickly. One solution was \ submitted in a little over an hour, and one began to hear numerous muttered \ curses (including a few of my own) as the deadline approached. I was \ fortunate to find something that worked, and submitted my solution with a few \ minutes to spare. The deadline was extended to 10:20, and apparently two \ other solutions were submitted by that time. Reportedly solutions continued \ to come until after midnight; I left the room after the 10:20 deadline.\ \>", "Text"], Cell["\<\ We had been told the solutions would be based on elegance. Elegance \ is subjective, of course. I spent a lot of time trying to decide whether to \ write a constructive program like Matthew Cook's sample solution (below), or \ to write a recursive solution like the one I submitted. I would have \ preferred to use a constructive solution as they tend to be shorter and \ faster, but they are also more subtle to construct. As time grew shorter, I \ decided the first condition of elegance is that the program should work, and \ that was the only thing I could accomplish within the time limit! That turned \ out to be the right strategy. My solution won not because it was elegant (I \ don't claim that it is) but because it was the only one of the four submitted \ \"on time\" that actually did what it was supposed to do.\ \>", "Text"], Cell["\<\ Incidentally, I just have to mention that my solution actually \ produces the picture given to us during the contest, without rotation. \ Matthew's solution produces an image rotated 90 degrees. But then he said it \ was OK to do so!\ \>", "Text"] }, Closed]], Cell[CellGroupData[{ Cell["Matthew Cook's Example Solution", "Section"], Cell[BoxData[ \(TreeGraphic[d_Integer] := \ \n Graphics[Table[ \(Line[{k + 1, k, k + 1} #]&\)\ /@\n Partition[ Table[\({Cos[#], Sin[#]}&\)[2 Pi\ t/\((6*2^k)\)], \n{t, 1 + 6*2^k}], 3, 4], {k, 0, d}], AspectRatio -> Automatic]\)], "Input"] }, Closed]], Cell[CellGroupData[{ Cell["Thanks", "Section"], Cell["\<\ I want to express my thanks to: -- Wolfram Research for the generous prize of my choice of application \ package. (I chose Wavelet Explorer.) -- Matthew Cook, who came up with a problem of appropriate difficulty, not \ too easy but not impossible , and the other employees of Wolfram Research who \ helped administer the contest that evening. -- All the contestants in the competition, probably 25-30 altogether, who \ joined in the spirit of competition for the fun of it. \ \>", "Text"] }, Closed]] }, Open ]] }, Open ]] }, FrontEndVersion->"Microsoft Windows 3.0", ScreenRectangle->{{0, 1024}, {0, 740}}, WindowSize->{504, 349}, WindowMargins->{{34, Automatic}, {Automatic, 21}}, TabSpacings->2 ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. 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