File:QmcSearchGraph3.pdf
Summary
Description |
English: Search graph of the Quine-McCluskey algorithm for 3 variables. |
Date | |
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 |
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% 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}
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