\documentclass{scrartcl}
\RequirePackage{algorithm}
\RequirePackage{algorithmicx}
\RequirePackage[noEnd=false]{algpseudocodex}
\newcommand{\algorithmautorefname}{Algorithm} % Allow autoref.
% Define macros to typeset boolean in pseudocode environments
\algnewcommand{\True}{\textbf{\texttt{true}}}
\algnewcommand{\False}{\textbf{\texttt{false}}}
\algnewcommand{\NIL}{\textbf{\texttt{NIL}}}
\algnewcommand{\NULL}{\textbf{\texttt{null}}}
\input{definitions.tex}

\begin{document}

\begin{algorithm}
    \caption{Construct a longest common subsequence matrix keeping the path in memory}
    \begin{algorithmic}[1]
        \Function{LCSQ\_Matrix\_Path}{$S_{1}$: Array($n$), $S_{2}$: Array($m$)}
        \State $M \gets $ Array($m+1$, $n+1$)
        \State $P \gets $ Array($m+1$, $n+1$)
        \For {($i = 0$; $i < n+1$, $i++$)}
            \State $M[i][0] \gets 0$
        \EndFor
        \For {($j = 0$; $j < m+1$; $j+$)}
            \State $M[0][j] \gets 0$
        \EndFor
        \For{($i = 1$; $i < n+1$; $i++$)}
        \For{($j = 1$; $j < m+1$; $j++$)}
        \If {$i = 1$ or $j = 0$}
        \State $M[i][j] = 0$
        \Else
        \If {$S_{1}[i-1] = S_{2}[j-1]$}
            \State $M[i][j] \gets M[i-1][j-1] + 1$
            \State $P[i][j] \gets '\nwarrow'$
        \ElsIf {$M[i][j-1] \geq M[i-1][j]$}
            \State $M[i][j] \gets M[i][j-1]$
            \State $P[i][j] \gets '\leftarrow'$
            \Else
            \State $M[i][j] \gets M[i-1][j]$
            \State $P[i][j] \gets '\downarrow'$
        \EndIf
\EndIf
        \EndFor
        \EndFor
        \State \Return $M, P$
        \EndFunction
    \end{algorithmic}
\end{algorithm}

\iffalse
	\begin{algorithm}
		\caption{Backtrack the longest common subsequence}
		\begin{algorithmic}[1]
			\Function{LCSQ}{$S_{1}$: Array($n$), $S_{2}$: Array($m$)}
			\State $M, P \gets $ \Call{LCSQ\_Matrix}{$S_{1}$, $S_{2}$}
			\State $L \gets Array(M[n][m])$
			\State $k \gets 0$
			\State $i \gets n$
			\State $j \gets m$
			\While{$i > 0$ and $j > 0$}
			\If {$P[i][j] = '\nwarrow' $}
			\State $L[k] \gets S_{1}[i]$
			\State $i--$
			\State $j--$
			\State $k++$
			\ElsIf {$P[i][j] = '\leftarrow'$}
			\State $j--$
			\Else
			\State $i--$
			\EndIf
			\EndWhile
			\State \Return $L$
			\EndFunction
		\end{algorithmic}
	\end{algorithm}

	\begin{algorithm}
		\caption{Recursive reconstruction of the longest common subsequence}
		\begin{algorithmic}[1]
			\Procedure{LCSQ}{$S_{1}$: Array($n$), $S_{2}$: Array($m$)}
			\State $M, P \gets $ \Call{LCSQ\_Matrix}{$S_{1}$, $S_{2}$}
			\State $i \gets n$
			\State $j \gets m$
			\State \Call{Aux}{$P$, $S_{1}$, $i$, $j$}
			\EndProcedure

			\Procedure{Aux}{$P$: Array($n+1$, $m+1$), $S_{1}$: Array($n$), $i$, $j$}
			\If {$P[i][j] = '\nwarrow' $}
			\State $l \gets S_{1}[i]$
			\State \Call{Aux}{$P$, $S_{1}$, $i-1$, $j-1$}
			\State \texttt{print}($l$)
			\ElsIf {$P[i][j] = '\leftarrow'$}
			\State \Call{Aux}{$P$, $S_{1}$, $i$, $j-1$}
			\Else
			\State \Call{Aux}{$P$, $S_{1}$, $i-1$, $j$}
			\EndIf
			\EndProcedure
		\end{algorithmic}
	\end{algorithm}
\fi
\end{document}

\end{document}