\chapter{Motif}

\begin{algorithm}
    \caption{Brute-force search of a motif in a sequence}
    \begin{algorithmic}[1]
        \Function{FindMotif}{$S$: Array($n$), $M$: Array($m$)}
        \Returns{a list of position}
        \State $pos \gets \{\}$
        \State $i \gets 0$
        \While {$i < n - m + 1$}
            \State $j \gets 0$
            \While {$j < m$ and $S[i+j] = M[j]$}
                \State $j++$
            \EndWhile
            \If {$j = m$}
                \State $pos \gets pos \cup \{i\}$
            \EndIf
            \State $i++$
        \EndWhile
        \State \Return $pos$
        \EndFunction
    \end{algorithmic}
    \label{alg:naive-motif-matching}
\end{algorithm}

\begin{algorithm}
    \caption{Knuth-Morris-Pratt algorithm}
    \begin{algorithmic}[1]
        \Function{KMP\_Search}{$S$: Array($n$), $M$: Array($m$)}
        \Returns{Integer}
        \State $table \gets$ \Call{KMP\_Table}{$M$}
        \State $c \gets 0$ \Comment{Count the number of matches}
        \State $i \gets 0$
        \State $j \gets 0$
        \While {$i < n$}
            \If{$S[i] = M[i]$}
                \State $i \gets i + 1$
                \State $j \gets j + 1$
            \EndIf
            \If {$j = m$}
                \State $c \gets c + 1$
                \State $j \gets table[j-1]$
            \ElsIf {$j < n$ and $M[j] \neq S[i]$}
                \If {$j \neq 0$}
                    \State $j \gets table[j-1]$
                    \Else
                    \State $i \gets i + 1$
                \EndIf
            \EndIf`
        \EndWhile
        \State \Return $c$
        \EndFunction

        \Function{KMP\_Table}{M: Array(m)}
        \State \textbf{Returns} Array(m)
        \State $previous \gets 0$
        \State $table \gets $ array of zeros of size m
        \For {$i = 0$; $i < m$; $i++$}
            \If {$M[i] = M[previous]$}
                \State $previous \gets previous + 1$
                \State $table[i] \gets previous$
                \State $i \gets i + 1$
                \Else
                \If {$previous = 0$}
                    \State $previous \gets table[previous - 1]$
                    \Else
                    \State $table[i] \gets 0$
                    \State $i \gets 1$
                \EndIf
            \EndIf
        \EndFor
        \EndFunction
    \end{algorithmic}
\end{algorithm}