File:LongestSubstring.pdf
Summary
| Description |
English: Example of the Longest common substring problem that has two different solutions: the strings "BADANAT" and "CANADAS" share the maximal-length substrings "ADA" and "ANA". Note that the substring occurrences overlap; yet no longer common substring can be obtained by 'uniting' them. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:LongestSubstring.pdf * File:LongestSubstring svg.svg |
LaTeX source code |
|---|
\documentclass[12pt]{article}
\setlength{\unitlength}{1mm}
\usepackage[pdftex]{color}
\usepackage[paperwidth=36\unitlength,paperheight=16\unitlength]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{36\unitlength}
\setlength{\textheight}{16\unitlength}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}
% colors
\definecolor{fANA} {rgb}{0.00,0.70,0.00}
\definecolor{fADA} {rgb}{0.00,0.00,0.70}
\definecolor{fANAx} {rgb}{0.50,0.99,0.50}
\definecolor{fADAx} {rgb}{0.50,0.50,0.99}
%\definecolor{bANA} {rgb}{0.80,0.99,0.80}
%\definecolor{bADA} {rgb}{0.80,0.80,0.99}
%\definecolor{bAxA} {rgb}{0.60,0.99,0.99}
\begin{document}
\begin{picture}(33,13)%
% substring backgrounds
%\textcolor{bANA}{\put( 4,0){\makebox(0,0)[bl]{\rule{10mm}{3mm}}}}%
%\textcolor{bAxA}{\put(14,0){\makebox(0,0)[bl]{\rule{ 5mm}{3mm}}}}%
%\textcolor{bADA}{\put(19,0){\makebox(0,0)[bl]{\rule{10mm}{3mm}}}}%
%
%\textcolor{bADA}{\put( 4,10){\makebox(0,0)[bl]{\rule{10mm}{3mm}}}}%
%\textcolor{bAxA}{\put(14,10){\makebox(0,0)[bl]{\rule{ 5mm}{3mm}}}}%
%\textcolor{bANA}{\put(19,10){\makebox(0,0)[bl]{\rule{10mm}{3mm}}}}%
%
% strings
\put( 0,0){\makebox(0,0)[bl]{\sf C}}%
\put( 5,0){\makebox(0,0)[bl]{\sf A}}%
\put(10,0){\makebox(0,0)[bl]{\sf N}}%
\put(15,0){\makebox(0,0)[bl]{\sf A}}%
\put(20,0){\makebox(0,0)[bl]{\sf D}}%
\put(25,0){\makebox(0,0)[bl]{\sf A}}%
\put(30,0){\makebox(0,0)[bl]{\sf S}}%
%
\put( 0,10){\makebox(0,0)[bl]{\sf B}}%
\put( 5,10){\makebox(0,0)[bl]{\sf A}}%
\put(10,10){\makebox(0,0)[bl]{\sf D}}%
\put(15,10){\makebox(0,0)[bl]{\sf A}}%
\put(20,10){\makebox(0,0)[bl]{\sf N}}%
\put(25,10){\makebox(0,0)[bl]{\sf A}}%
\put(30,10){\makebox(0,0)[bl]{\sf T}}%
%
% substring matches
\textcolor{fANA}{\put( 4,3.5){\line(0,1){0.5}}}%
\textcolor{fANA}{\put(19,3.5){\line(0,1){0.5}}}%
%
\textcolor{fANA}{\put(14,8){\line(0,1){0.5}}}%
\textcolor{fANA}{\put(29,8){\line(0,1){0.5}}}%
%
\textcolor{fANAx}{\put( 4,4){\line(5,2){10}}}%
\textcolor{fANAx}{\put(19,4){\line(5,2){10}}}%
%
\textcolor{fADA}{\put(14,4.5){\line(0,1){0.5}}}%
\textcolor{fADA}{\put(29,4.5){\line(0,1){0.5}}}%
%
\textcolor{fADA}{\put( 4,9){\line(0,1){0.5}}}%
\textcolor{fADA}{\put(19,9){\line(0,1){0.5}}}%
%
\textcolor{fADAx}{\put(14,5){\line(-5,2){10}}}%
\textcolor{fADAx}{\put(29,5){\line(-5,2){10}}}%
%
% substrings
\thicklines%
\textcolor{fANA}{\put( 4,4){\line(1,0){15}}}%
\textcolor{fANA}{\put(14,8){\line(1,0){15}}}%
\textcolor{fADA}{\put(14,5){\line(1,0){15}}}%
\textcolor{fADA}{\put( 4,9){\line(1,0){15}}}%
\end{picture}
\end{document}
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