sequence-algorithms/content/chapters/part1/1.tex

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\chapter{Back to basics}
\begin{algorithm}
\caption{Search an element in an array}
\begin{algorithmic}[1]
\Function{Search}{A: Array(n), E: element}
\For {(i=0; i < n; i++)}
\If {A[i] $ = $ E}
\State \Return \True
\EndIf
\EndFor
\State \Return \False
\EndFunction
\end{algorithmic}
\end{algorithm}
\begin{algorithm}
\caption{Search an element in an array using a while loop}
\begin{algorithmic}[1]
\Function{Search}{A: Array(n), E: element}
\State $i \gets 0$
\While {$i < n$}
\If {A[i] $ = $ E}
\State \Return \True
\EndIf
\State $i \gets i + 1$
\EndWhile
\State \Return \False
\EndFunction
\end{algorithmic}
\end{algorithm}
\begin{algorithm}
\caption{Search an element in an array using a while loop (bis)}
\begin{algorithmic}[1]
\Function{Search}{A: Array(n), E: element}
\Comment{Version ``preffered" by the professor}
\State $i \gets 0$
\While {$i < n$ and $A[i] \neq E$}
\State $i \gets i + 1$
\EndWhile
\If {$i = n$}
\State \Return \False
\Else
\State \Return \True
\EndIf
\EndFunction
\end{algorithmic}
\end{algorithm}
\begin{algorithm}
\caption{Count the occurences of an element in an array}
\begin{algorithmic}[1]
\Function{Search}{A: Array(n), E: element}
\State $c \gets 0$
\For{$i = 0$; $i < n$; $i++$}
\If {A[i] $ = $ E}
\State $c \gets c + 1$
\EndIf
\EndFor
\State \Return $c$
\EndFunction
\end{algorithmic}
\end{algorithm}
\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{list of position}
\State $pos \gets $ empty list
\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 add $i$ to $pos$
\EndIf
\State $i++$
\EndWhile
\State \Return $pos$
\EndFunction
\end{algorithmic}
\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}