You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
47 lines
1.9 KiB
47 lines
1.9 KiB
\item \lect Use propositional logic to solve Sudoku. Rules: A Sudoku grid consists of a 9x9 square, which is partitioned into nine 3x3 squares. The goal of the game is to write one number from 1 to 9 in each cell in such a way, that each row, each column, and each 3x3-square contains each number exactly once. Usually several numbers are already given.
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
%%%% source: https://texample.net/tikz/examples/sudoku/
|
|
%%%% Author: Roberto Bonvallet, published 2012-02-01, last accessed 2021-02-14, modified
|
|
\newcounter{row}
|
|
\newcounter{col}
|
|
\newcommand\setrow[9]{
|
|
\setcounter{col}{1}
|
|
\foreach \n in {#1, #2, #3, #4, #5, #6, #7, #8, #9} {
|
|
\edef\x{\value{col} - 0.5}
|
|
\edef\y{9.5 - \value{row}}
|
|
\node[anchor=center] at (\x, \y) {\n};
|
|
\stepcounter{col}
|
|
}
|
|
\stepcounter{row}
|
|
}
|
|
|
|
\begin{center}
|
|
\begin{tikzpicture}[scale=.35]
|
|
\begin{scope}
|
|
\draw (0, 0) grid (9, 9);
|
|
\draw[very thick, scale=3] (0, 0) grid (3, 3);
|
|
|
|
\setcounter{row}{1}
|
|
\setrow { }{6}{ } {7}{ }{ } {1}{5}{ }
|
|
\setrow { }{ }{3} {9}{ }{ } {8}{ }{ }
|
|
\setrow { }{ }{2} {3}{ }{ } { }{4}{9}
|
|
|
|
\setrow { }{ }{7} { }{ }{4} { }{ }{ }
|
|
\setrow { }{4}{ } { }{9}{ } { }{8}{ }
|
|
\setrow { }{ }{ } {1}{ }{ } {4}{ }{ }
|
|
|
|
\setrow {6}{7}{ } { }{ }{9} {3}{ }{ }
|
|
\setrow { }{ }{9} { }{ }{2} {5}{ }{ }
|
|
\setrow { }{2}{8} { }{ }{7} { }{6}{ }
|
|
|
|
\node[anchor=center] at (4.5, -1) {Sudoku};
|
|
\end{scope}
|
|
\end{tikzpicture}
|
|
\end{center}
|
|
|
|
In order to model SUDOKU using propositional logic, we first need to define the propositional variables that we
|
|
want to use in our formula. We define variables $x_{ijk}$ for every row $i$,
|
|
for every column $j$, and for every value $k$. This encoding yields to 729 variables ranging from $x_{111}$ to $x_{999}$.
|
|
Using this variables, define the constraints for the rows, the columns, the 3x3-squares and the predefined numbers. \\
|
|
\vspace{0.5cm}
|