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DescriptionQmcSearchGraph3.pdf	English: Search graph of the Quine-McCluskey algorithm for 3 variables.
Date	15 May 2020
Source	Own work
Author	Jochen Burghardt
Other versions	File:QmcSearchGraph3.pdf * File:QmcSearchGraph3_svg.svg * File:QmcSearchGraph3_Ab+c.pdf * File:QmcSearchGraph3_Ab+c_svg.svg

LaTeX source code

% To obtain the version without highlighting,
% change the color definitions of cLinF to agree with cLine, 
% that of cCirF and cCirG to agree with cCirc, 
% and remove the \thicklines commands.
\documentclass[12pt]{article}

\setlength{\unitlength}{1mm}

\usepackage[pdftex]{color}
\usepackage[paperwidth=130mm,paperheight=80mm]{geometry}

\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{130mm}
\setlength{\textheight}{80mm}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}

\pagestyle{empty}

% normal colors
\definecolor{cText}     {rgb}{0.00,0.00,0.00}
\definecolor{cLine}     {rgb}{0.50,0.50,0.99}
\definecolor{cCirc}     {rgb}{0.40,0.40,0.99}
\definecolor{cDigi}     {rgb}{0.70,0.00,0.00}

% highlighting colors
\definecolor{cCirG}     {rgb}{0.40,0.99,0.40}   % given
\definecolor{cCirF}     {rgb}{0.00,0.60,0.00}   % found by algorithm
\definecolor{cLinF}     {rgb}{0.50,0.99,0.50}

\begin{document}

\newcommand{\node}[5]{%
        \textcolor{#1}{\put(#2,#3){\circle*{2}}}%
        \textcolor{cText}{\put(#2,#3){\put(1,1.6){\makebox(0,0)[l]{$#4$}}}}%
        \textcolor{cDigi}{\put(#2,#3){\put(1,-1.6){\makebox(0,0)[l]{\scriptsize\texttt{#5}}}}}%
}

\color{cLine}
\begin{picture}(125,70)%
% 0-variable conjuncts
\put(60,65){\line(-3,-1){30}}%...
 \put(30,55){\line(-5,-2){25}}% true - a
\put(60,65){\line(-5,-3){33}}%  true - A
\put(60,65){\line(-3,-5){6}}%...
 \put(54,55){\line(-1,-2){5}}%  true - b
\put(60,65){\line(1,-2){5}}%...
 \put(65,55){\line(3,-5){6}}%   true - B
\put(60,65){\line(5,-3){33}}%   true - c
\put(60,65){\line(5,-2){25}}%...
 \put(85,55){\line(3,-1){30}}%  true - C
\node{cCirc}{ 60}{65}{\it true}{---}%                           true
% 1-variable conjuncts
\put(5,45){\line(0,-1){20}}%    a - ab
\put(5,45){\line(1,-2){10}}%    a - aB
\put(5,45){\line(1,-1){20}}%    a - ac
\put(5,45){\line(3,-2){30}}%    a - aC
\put(27,45){\line(5,-6){10}}%...
 \put(37,33){\line(1,-1){8}}%   A - Ab
\put(27,45){\line(4,-3){16}}%...
 \put(43,33){\line(3,-2){12}}%  A - AB
\put(27,45){\line(5,-3){10}}%...
 \put(37,39){\line(2,-1){28}}%  A - Ac
\put(27,45){\line(2,-1){8}}%...
 \put(35,41){\line(5,-2){40}}%  A - AC
\put(49,45){\line(-5,-2){20}}%...
 \put(29,37){\line(-2,-1){24}}% b - ab
\put(49,45){\line(-1,-5){4}}%   b - Ab
\put(49,45){\line(5,-3){20}}%...
 \put(69,33){\line(2,-1){16}}%  b - bc
\put(49,45){\line(2,-1){16}}%...
 \put(65,37){\line(5,-2){30}}%  b - bC
\put(71,45){\line(-3,-1){36}}%...
 \put(35,33){\line(-5,-2){20}}% B - aB
\put(71,45){\line(-4,-5){16}}%  B - AB
\put(71,45){\line(5,-3){30}}%...
 \put(101,27){\line(2,-1){4}}%  B - Bc
\put(71,45){\line(2,-1){24}}%...
 \put(95,33){\line(5,-2){20}}%  B - BC
\thicklines
\textcolor{cLinF}{\put(93,45){\line(-4,-1){32}}}%...
 \textcolor{cLinF}{\put(61,37){\line(-3,-1){36}}}%      c - ac
\textcolor{cLinF}{\put(93,45){\line(-3,-2){12}}}%...
 \textcolor{cLinF}{\put(81,37){\line(-4,-3){16}}}%      c - Ac
\textcolor{cLinF}{\put(93,45){\line(-2,-5){8}}}%        c - bc
\textcolor{cLinF}{\put(93,45){\line(3,-5){12}}}%        c - Bc
\thinlines
\put(115,45){\line(-4,-1){80}}% C - aC
\put(115,45){\line(-2,-1){40}}% C - AC
\put(115,45){\line(-1,-1){20}}% C - bC
\put(115,45){\line(0,-1){20}}%  C - BC
\node{cCirc}{  5}{45}{a}{1--}%                                  a
\node{cCirc}{ 27}{45}{\overline{a}}{0--}%                       A
\node{cCirc}{ 49}{45}{b}{-1-}%                                  b
\node{cCirc}{ 71}{45}{\overline{b}}{-0-}%                       B
\node{cCirF}{ 93}{45}{c}{--1}%                                  c
\node{cCirc}{115}{45}{\overline{c}}{--0}%                       C
% 2-variable conjuncts
\put(5,25){\line(0,-1){20}}%    ab - abc
\put(5,25){\line(3,-4){15}}%    ab - abC
\put(15,25){\line(1,-1){20}}%   aB - aBc
\put(15,25){\line(5,-3){25}}%...
 \put(40,10){\line(2,-1){10}}%  aB - aBC
\put(35,25){\line(-3,-4){15}}%  aC - abC
\put(35,25){\line(3,-4){15}}%   aC - aBC
\put(55,25){\line(2,-1){40}}%   AB - ABc
\put(55,25){\line(5,-2){25}}%...
 \put(80,15){\line(3,-1){30}}%  AB - ABC
\put(75,25){\line(1,-4){5}}%    AC - AbC
\put(75,25){\line(5,-3){25}}%...
 \put(100,10){\line(2,-1){10}}% AC - ABC
\put(95,25){\line(-4,-1){60}}%...
 \put(35,10){\line(-3,-1){15}}% bC - abC
\put(95,25){\line(-3,-4){15}}%  bC - AbC
\put(115,25){\line(-4,-1){20}}%...
 \put(95,20){\line(-3,-1){45}}% BC - aBC
\put(115,25){\line(-1,-4){5}}%  BC - ABC
\thicklines
\textcolor{cLinF}{\put(25,25){\line(-1,-1){20}}}%       ac - abc
\textcolor{cLinF}{\put(25,25){\line(1,-2){10}}}%        ac - aBc
\textcolor{cLinF}{\put(45,25){\line(1,-1){20}}}%        Ab - Abc
\textcolor{cLinF}{\put(45,25){\line(5,-3){25}}}%...
 \textcolor{cLinF}{\put(70,10){\line(2,-1){10}}}%       Ab - AbC
\textcolor{cLinF}{\put(65,25){\line(0,-1){20}}}%        Ac - Abc
\textcolor{cLinF}{\put(65,25){\line(3,-2){30}}}%        Ac - ABc
\textcolor{cLinF}{\put(85,25){\line(-4,-1){80}}}%       bc - abc
\textcolor{cLinF}{\put(85,25){\line(-1,-1){20}}}%       bc - Abc
\textcolor{cLinF}{\put(105,25){\line(-4,-1){40}}}%...
 \textcolor{cLinF}{\put(65,15){\line(-3,-1){30}}}%      Bc - aBc
\textcolor{cLinF}{\put(105,25){\line(-1,-2){10}}}%      Bc - ABc
\thinlines
\node{cCirc}{  5}{25}{ab}{11-}%                                 ab
\node{cCirc}{ 15}{25}{a\overline{b}}{10-}%                      aB
\node{cCirc}{ 25}{25}{ac}{1-1}%                                 ac
\node{cCirc}{ 35}{25}{a\overline{c}}{1-0}%                      aC
\node{cCirF}{ 45}{25}{\overline{a}b}{01-}%                      Ab
\node{cCirc}{ 55}{25}{\overline{a}\overline{b}}{00-}%           AB
\node{cCirc}{ 65}{25}{\overline{a}c}{0-1}%                      Ac
\node{cCirc}{ 75}{25}{\overline{a}\overline{c}}{0-0}%           AC
\node{cCirc}{ 85}{25}{bc}{-11}%                                 bc
\node{cCirc}{ 95}{25}{b\overline{c}}{-10}%                      bC
\node{cCirc}{105}{25}{\overline{b}c}{-01}%                      Bc
\node{cCirc}{115}{25}{\overline{b}\overline{c}}{-00}%           BC
% 3-variable conjuncts
\node{cCirG}{  5}{ 5}{abc}{111}%                                abc
\node{cCirc}{ 20}{ 5}{ab\overline{c}}{110}%                     abC
\node{cCirG}{ 35}{ 5}{a\overline{b}c}{101}%                     aBc
\node{cCirc}{ 50}{ 5}{a\overline{b}\overline{c}}{100}%          aBC
\node{cCirG}{ 65}{ 5}{\overline{a}bc}{011}%                     Abc
\node{cCirG}{ 80}{ 5}{\overline{a}b\overline{c}}{010}%          AbC
\node{cCirG}{ 95}{ 5}{\overline{a}\overline{b}c}{001}%          ABc
\node{cCirc}{110}{ 5}{\overline{a}\overline{b}\overline{c}}{000}%       ABC
\end{picture}
\end{document}

Licensing edit

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

to share – to copy, distribute and transmit the work
to remix – to adapt the work

Under the following conditions:

attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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	Date/Time	Thumbnail	Dimensions	User	Comment
current	07:40, 15 May 2020		766 × 470 (28 KB)	Jochen Burghardt (talk \| contribs)	Uploaded own work with UploadWizard

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The following page uses this file:

User:Chumwa/OgreBot/Charente-Maritime/2020 May 11-20

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Software used	TeX
Conversion program	pdfTeX-1.40.18
Encrypted	no
Page size	368.504 x 226.772 pts
Version of PDF format	1.5

File:QmcSearchGraph3.pdf

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