Class 3
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\chapter{Back to basics}
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\begin{algorithm}
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\caption{Search an element in an array}
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\begin{algorithmic}[1]
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\Function{Search}{$A$: Array($n$), $E$: element}
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\For {($i = 0$; $i < n$; $i++$)}
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\If {$A[i] = E$}
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\State \Return \True
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\EndIf
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\EndFor
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\State \Return \False
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Search an element in an array using a while loop}
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\begin{algorithmic}[1]
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\Function{Search}{$A$: Array($n$), $E$: element}
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\State $i \gets 0$
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\While {$i < n$}
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\If {$A[i] = E$}
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\State \Return \True
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\EndIf
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\State $i \gets i + 1$
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\EndWhile
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\State
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\Return
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\False
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Search an element in an array using a while loop (bis)}
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\begin{algorithmic}[1]
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\Function{Search}{$A$: Array($n$), $E$: element}
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% \Comment{Version ``preffered" by the professor}
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\State $i \gets 0$
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\While {$i < n$ and $A[i] \neq E$}
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\State $i \gets i + 1$
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\EndWhile
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\If {$i = n$}
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\State
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\Return \False \Else \State \Return \True \EndIf
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Count the occurrences of an element in an array}
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\begin{algorithmic}[1]
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\Function{Search}{$A$: Array($n$), $E$: element} \State $c \gets 0$
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\For{($i = 0$; $i < n$; $i++$)} \If {A[i] $ = $ E} \State $c \gets c + 1$ \EndIf
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\EndFor \State \Return $c$ \EndFunction
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\end{algorithmic}
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\end{algorithm}
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@ -1,90 +1,29 @@
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\chapter{Back to basics}
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\begin{algorithm}
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\caption{Search an element in an array}
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\begin{algorithmic}[1]
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\Function{Search}{A: Array(n), E: element}
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\For {(i=0; i < n; i++)}
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\If {A[i] $ = $ E}
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\State \Return \True
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\EndIf
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\EndFor
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\State \Return \False
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Search an element in an array using a while loop}
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\begin{algorithmic}[1]
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\Function{Search}{A: Array(n), E: element}
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\State $i \gets 0$
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\While {$i < n$}
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\If {A[i] $ = $ E}
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\State \Return \True
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\EndIf
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\State $i \gets i + 1$
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\EndWhile
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\State \Return \False
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Search an element in an array using a while loop (bis)}
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\begin{algorithmic}[1]
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\Function{Search}{A: Array(n), E: element}
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\Comment{Version ``preffered" by the professor}
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\State $i \gets 0$
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\While {$i < n$ and $A[i] \neq E$}
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\State $i \gets i + 1$
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\EndWhile
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\If {$i = n$}
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\State \Return \False
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\Else
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\State \Return \True
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\EndIf
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Count the occurences of an element in an array}
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\begin{algorithmic}[1]
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\Function{Search}{A: Array(n), E: element}
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\State $c \gets 0$
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\For{$i = 0$; $i < n$; $i++$}
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\If {A[i] $ = $ E}
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\State $c \gets c + 1$
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\EndIf
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\EndFor
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\State \Return $c$
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\chapter{Motif}
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\chapter{Motif}
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\begin{algorithm}
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\begin{algorithm}
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\caption{Brute-force search of a motif in a sequence}
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\caption{Brute-force search of a motif in a sequence}
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\begin{algorithmic}[1]
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\begin{algorithmic}[1]
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\Function{FindMotif}{S: Array(n), M: Array(m)}
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\Function{FindMotif}{S: Array(n), M: Array(m)} {
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\Returns{list of position}
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\Returns{list of position}
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\State $pos \gets $ empty list
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\State $pos \gets \{\}$
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\State $i \gets 0$
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\State $i \gets 0$
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\While {$i < n - m + 1$}
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\While {$i < n - m + 1$} {
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\State $j \gets 0$
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\State $j \gets 0$
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\While {$j < m$ and S[i+j] $ = $ M[j]}
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\While {$j < m$ and S[i+j] $ = $ M[j]} {
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\State $j++$
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\State $j++$
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}
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\EndWhile
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\EndWhile
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\If {$j = m$}
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\If {$j = m$}
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\State add $i$ to $pos$
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\State $pos \gets pos \cup \{i\}$
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\EndIf
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\EndIf
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\State $i++$
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\State $i++$
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}
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\EndWhile
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\EndWhile
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\State \Return $pos$
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\State \Return $pos$
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}
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\EndFunction
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\EndFunction
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\end{algorithmic}
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\end{algorithmic}
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\label{alg:naive-motif-matching}
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\end{algorithm}
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\end{algorithm}
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\begin{algorithm}
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\begin{algorithm}
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\chapter{Matrices}
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Let $S_{1}$ and $S_{2}$ be two sequences.
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$S_{1} = $ ACGUUCC
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$S_{2} = $ GUU
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\begin{table}
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\centering
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\begin{tabular}{c|ccccccc}
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& A & C & G & U & U & C & C \\
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\hline
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G & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\
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U & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\
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U & 0 & 0 & 0 & 1 & 1 & 0 & 0
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\end{tabular}
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\caption{Comparison matrix}
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\end{table}
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Let $n = |S_{1}|$, $m = |S_{2}|$
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The complexity of this algorithm is $\mathcal{O}(n \cdot m)$ to build the matrix, and it requires also to find the diagonals and thus it is a bit less efficient than the \autoref{alg:naive-motif-matching}.
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To find repetitions, we can use a comparison matrix with a single sequence against itself. A repetition would appear as a diagonal of ones, not on the main diagonal.
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Let $S = $ ACGUUACGUU. Let's write the comparison matrix.
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\begin{table}
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\includegraphics{figures/part1/comparison_matrix_repetitions.pdf}
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\caption{Comparison matrix for seq="ACGUUACGUUGUU"}
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\end{table}
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\begin{algorithm}
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\caption{Construct a comparison matrix}
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\begin{algorithmic}[1]
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\Function{ComparisonMatrix}{S: Array(n)}
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\State $M \gets Array(n, n)$
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\For{$i = 0$; $i < n$; $i++$}
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\For{$j=0$; $j < n$; $j++$}
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\If {S[i] $ = $ S[j]}
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\State $M[i][j] = 1$
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\Else
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\State $M[i][j] = 0$
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\EndIf
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\EndFor
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\EndFor
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\State \Return $M$
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Construct the top half of comparison matrix}
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\begin{algorithmic}[1]
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\Function{ComparisonMatrix}{S: Array(n)}
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\State $M \gets Array(n,n)$
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\For{i = 0; i < n; i++}
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\For{j=i; j < n; j++}
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\If {S[i] = S[j]}
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\State M[i][j] = 1
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\Else
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\State M[i][j] = 0
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\EndIf
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\EndFor
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\EndFor
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\State \Return M
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Find repetitions (with the set of visited segments)}
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\begin{algorithmic}[1]
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\Function{FindRepetions}{S: Array(n)}
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\Returns{A list of start and end positions for repeted sequences}
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\State M = \Call{ComparisonMatrix}{S}
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\State pos = \{\}
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\State visited = \{\}
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\For {i_{start} = 0; i_{start} < n; i_{start}++}
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\For {j_{start} = i_{start}+1; j_{start} < n; j_{start}++}
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\If{M[i_{start}][j_{start}] = 1 and (i_{start}, j_{start}) \notin visited}
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\State i = i_{start}
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\State j = j_{start}
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\While {M[i][j] = 1}
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\State i++
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\State j++
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\State visited = visited \cup \{(i, j)\}
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\EndWhile
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\State pos = pos \cup \{(i_{start}, i), (j_{start},j)\}
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\EndIf
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\EndFor
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\EndFor
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Find repetitions with an exploration of diagonals}
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\begin{algorithmic}[1]
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\Function{FindRepetions}{S: Array(n)}
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\Returns{A list of start and end positions for repeted sequences}
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\State M = \Call{ComparisonMatrix}{S}
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\State $pos = \{\}$
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\For {diag = 1; diag < n; diag++}
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\State j = diag
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\State i = 0
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\While {i < n and j < n}
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\If {M[i][j] = 1}
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\State $i_{start} = i$
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\State $j_{start} = j$
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\While {i < n and j < n and M[i][j] = 1 }
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\State i++
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\State j++
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\EndWhile
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\State $pos = pos \cup \{((i_{start},i-1),(j_{start},j-1)\}$
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\EndIf
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\State i++
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\State j++
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\State
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\EndWhile
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\EndFor
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Find repetitions with an exploration of diagonals, without nested while}
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\begin{algorithmic}[1]
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\Function{FindRepetions}{S: Array(n)}
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\Returns{A list of start positions for repeted sequences and match length}
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\State M = \Call{ComparisonMatrix}{S}
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\State $pos = \{\}$
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\For {diag = 1; diag < n; diag++}
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\State j = diag
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\State i = 0
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\State l = 0
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\While {i < n and j < n}
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\If {M[i][j] = 1}
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\State l++
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\Else
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\If {l > 0}
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\State $pos = pos \cup \{((i-l,j-l,l)\}$
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\State l = 0
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\EndIf
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\EndIf
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\State i++
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\State j++
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\EndWhile
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\If {$l > 0$}
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\State $pos = pos \cup \{((i-l,j-l,l)\}$
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\EndIf
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\EndFor
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\State \Return pos
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\begin{algorithm}
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\caption{Find repetitions}
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\begin{algorithmic}[1]
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\Function{FindRepetions}{S: Array(n)}
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\Returns{A list of start and end positions for repeted sequences}
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\State M = \Call{ComparisonMatrix}{S}
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\State pos = \{\}
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\For {$i_{start} = 0$; $i_{start} < n$; $i_{start}++$}
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\For {$j_{start} = i_{start}+1$; $j_{start} < n$; $j_{start}++$}
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\If{$M[i_{start}][j_{start}] = 1$}
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\State $i = i_{start}$
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\State $j = j_{start}$
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\While {M[i][j] = 1}
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\State M[i][j] = 0 \Comment{Ensure that the segment is not explored again}
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\State i++
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\State j++
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\EndWhile
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\State $pos = pos \cup \{((i_{start}, i-1), (j_{start},j-1))\}$
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\EndIf
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\EndFor
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\EndFor
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\EndFunction
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\end{algorithmic}
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\end{algorithm}
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\section{Automata}
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An automaton is a tuple $\langle S, s_{0}, T, \Sigma,f\langle$
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\begin{itemize}
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\item $S$ the set of states
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\item $s_{0}$ the initial state
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\item $T$ the set of terminal states
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\item $\Sigma$ the alphabet
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\item $f$ the transition function $f: (s_{1}, c) \to s_{2}$
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\end{itemize}
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\paragraph{Example} Given the language $L$ on the alphabet $\Sigma = \{A, C, T\}$, $L = \{A^{*}, CTT, CA^{*}\}$
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\begin{definition}[Deterministic automaton]
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An automaton is deterministic, if for each couple $(p, a) \in S \times \Sigma$ it exists at most a state $q$ such as $f(p, q) = q$
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\end{definition}
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\begin{definition}[Complete automaton]
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An automaton is complete, if for each couple $(p, a) \in S \times \Sigma$ it exists at least a state $q$ such as $f(p, q) = q$.
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\end{definition}
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\begin{algorithm}
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\caption{Check wether a word belong to a language for which we have an automaton}
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\begin{algorithmic}[1]
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\Function{WordInLanguage}{W: Array(n), A: $\langle S, s_{0}, T, \Sigma,f \rangle$}
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\Returns{A Boolean valued to \True{} if the word is recognized by the language automaton}
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\State $s \gets s_{0}$
|
||||||
|
\State $i \gets 0$
|
||||||
|
\While {i < n} {
|
||||||
|
|
||||||
|
\State $a \gets W[i]$
|
||||||
|
\If {$\exists f(s, a)$} {
|
||||||
|
\State $s \gets f(s, a)$
|
||||||
|
\Else
|
||||||
|
\State \Return \False
|
||||||
|
}
|
||||||
|
\EndIf
|
||||||
|
\State i++
|
||||||
|
}
|
||||||
|
\EndWhile
|
||||||
|
\If {$s \in T$} {
|
||||||
|
\State \Return \True
|
||||||
|
}
|
||||||
|
\Else {
|
||||||
|
|
||||||
|
\State \Return \False
|
||||||
|
}
|
||||||
|
\EndIf
|
||||||
|
\EndFunction
|
||||||
|
\end{algorithmic}
|
||||||
|
\end{algorithm}
|
||||||
|
|
||||||
|
\section{Suffix Automaton}
|
||||||
|
|
||||||
|
Let $S = $ AACTACT
|
||||||
|
|
||||||
|
A suffix automata recognize all suffix of a given sequence.
|
||||||
|
|
||||||
|
|
||||||
|
The suffix language of $S$ is $\{S, ACTACT, CTACT, TACT, ACT, CT, T\}$.
|
||||||
|
|
||||||
|
|
||||||
|
\begin{figure}
|
||||||
|
\centering
|
||||||
|
\includegraphics{figures/part1/minimal_suffix_automaton_exercise.pdf}
|
||||||
|
\caption{Suffix automaton for $S = $ AACTACT}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\begin{figure}
|
||||||
|
\centering
|
||||||
|
\includegraphics{figures/part1/minimal_suffix_automaton_exercise_bis.pdf}
|
||||||
|
\caption{Suffix automaton for $S = $ TCATCATT}
|
||||||
|
\end{figure}
|
||||||
|
|
||||||
|
\end{definition}
|
||||||
|
\begin{algorithm}
|
||||||
|
\begin{algorithm}
|
||||||
|
\caption{Check if a sequences matches a motif, from a suffix automaton $\mathcal{O}(m)$}
|
||||||
|
\begin{algorithmic}[1]
|
||||||
|
\Function{CheckMotifInSuffixAutomaton}{W: Array(m), A: $\langle S, s_{0}, T, \Sigma,f \rangle$}
|
||||||
|
\Returns{Boolean valued to \True{} if the motif is in the sequence}
|
||||||
|
\State $s \gets s_{0}$
|
||||||
|
\State $i \gets 0$
|
||||||
|
\While {i < m and $\exists f(s, W[i])$}
|
||||||
|
\State $s \gets f(s, W[i])$
|
||||||
|
\State i++
|
||||||
|
\EndWhile
|
||||||
|
\If {i=n}
|
||||||
|
\State \Return \True
|
||||||
|
\Else
|
||||||
|
\State \Return \False
|
||||||
|
\EndIf
|
||||||
|
\EndFunction
|
||||||
|
\end{algorithmic}
|
||||||
|
\end{algorithm}
|
||||||
|
|
||||||
|
The complexity of the pattern matching algorithm is $\mathcal{O}(n + m)$, because building the automaton is $\mathcal{O}(m)$
|
||||||
|
\end{algorithm}
|
||||||
|
|
@ -1,3 +1,3 @@
|
||||||
\newcommand{\Returns}[1]{
|
\newcommand{\Returns}[1]{
|
||||||
\State \textbf{Returns} #1
|
\State \textbf{returns} #1
|
||||||
}
|
}
|
||||||
|
|
|
||||||
Binary file not shown.
|
|
@ -0,0 +1,21 @@
|
||||||
|
\documentclass[tikz]{standalone}
|
||||||
|
|
||||||
|
\usepackage{tikz}
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
\usetikzlibrary{automata,positioning}
|
||||||
|
|
||||||
|
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid, auto]
|
||||||
|
|
||||||
|
\node[state, initial] (q_0) {$q_{0}$};
|
||||||
|
\node[state,right=of q_0] (q_1) {$q_{1}$};
|
||||||
|
\node[state,below=of q_0] (q_2) {$q_{2}$};
|
||||||
|
\node[state,accepting, right=of q_2] (q_3) {$q_{3}$};
|
||||||
|
|
||||||
|
\path[->] (q_0) edge node {A} (q_1)
|
||||||
|
edge node {G} (q_3)
|
||||||
|
(q_0) edge node {C} (q_2)
|
||||||
|
(q_2) edge node {C} (q_3);
|
||||||
|
\end{tikzpicture}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
|
|
@ -0,0 +1,69 @@
|
||||||
|
function comparison_matrix(seq)
|
||||||
|
matrix = {}
|
||||||
|
for i=1,#seq do
|
||||||
|
matrix[i] = {}
|
||||||
|
for j=1,#seq do
|
||||||
|
if seq[i] == seq[j] then
|
||||||
|
matrix[i][j] = 1
|
||||||
|
else
|
||||||
|
matrix[i][j] = 0
|
||||||
|
end
|
||||||
|
end
|
||||||
|
end
|
||||||
|
return matrix
|
||||||
|
end
|
||||||
|
|
||||||
|
function split_char(seq)
|
||||||
|
t = {}
|
||||||
|
seq:gsub(".",function(c) table.insert(t,c) end)
|
||||||
|
return t
|
||||||
|
end
|
||||||
|
|
||||||
|
function repr_matrix(matrix)
|
||||||
|
repr = ""
|
||||||
|
for i=1,#matrix do
|
||||||
|
for j=1,#matrix do
|
||||||
|
repr = repr .. matrix[i][j] .. " "
|
||||||
|
end
|
||||||
|
repr = repr .. "\n"
|
||||||
|
end
|
||||||
|
return repr
|
||||||
|
end
|
||||||
|
function comparison_matrix_tabular(matrix, seq1, seq2)
|
||||||
|
seq2 = seq2 or seq1
|
||||||
|
n=#seq1
|
||||||
|
m=#seq2
|
||||||
|
repr = [[\begin{tabular}{]] .. string.rep("c", n+1) .. "} \n"
|
||||||
|
repr = repr .. " "
|
||||||
|
for i=1,n do
|
||||||
|
repr = repr .. "& " .. seq1[i] .. " "
|
||||||
|
end
|
||||||
|
repr = repr .. "\\\\ \n "
|
||||||
|
for j=1,m do
|
||||||
|
repr = repr .. seq2[j] .. " "
|
||||||
|
for i=1,n do
|
||||||
|
repr = repr .. "& " .. matrix[i][j] .. " "
|
||||||
|
end
|
||||||
|
repr = repr .. " \\\\ \n "
|
||||||
|
end
|
||||||
|
repr = repr .. [[\end{tabular}]]
|
||||||
|
return repr
|
||||||
|
end
|
||||||
|
|
||||||
|
function main()
|
||||||
|
seq = split_char("ACGUUACGUUGUU")
|
||||||
|
|
||||||
|
matrix = comparison_matrix(seq)
|
||||||
|
|
||||||
|
print(comparison_matrix_tabular(matrix, seq))
|
||||||
|
end
|
||||||
|
|
||||||
|
function repr_comparison_matrix(seq)
|
||||||
|
seq = split_char(seq)
|
||||||
|
matrix = comparison_matrix(seq)
|
||||||
|
return comparison_matrix_tabular(matrix, seq)
|
||||||
|
end
|
||||||
|
|
||||||
|
main()
|
||||||
|
|
||||||
|
return { comparison_matrix=comparison_matrix, comparison_matrix_tabular, repr_comparison_matrix=repr_comparison_matrix }
|
||||||
Binary file not shown.
|
|
@ -0,0 +1,14 @@
|
||||||
|
\documentclass[tikz]{standalone}
|
||||||
|
|
||||||
|
\usepackage{tikz}
|
||||||
|
\usepackage{luatextra}
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
|
||||||
|
\directlua{
|
||||||
|
lib = require("comparison_matrix_repetitions")
|
||||||
|
seq="ACGUUACGUUGUU"
|
||||||
|
tex.print(lib.repr_comparison_matrix(seq))
|
||||||
|
}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
|
|
@ -0,0 +1,24 @@
|
||||||
|
\documentclass[tikz]{standalone}
|
||||||
|
|
||||||
|
\usepackage{tikz}
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
\usetikzlibrary{automata,positioning}
|
||||||
|
|
||||||
|
\iffalse
|
||||||
|
$\Sigma = \{A, C, T\}$, $L = \{A^{*}, CTT, CA^{*}\}$
|
||||||
|
\fi
|
||||||
|
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid, auto]
|
||||||
|
% TODO
|
||||||
|
\node[state, initial] (q_0) {$q_{0}$};
|
||||||
|
\node[state,right=of q_0] (q_1) {$q_{1}$};
|
||||||
|
\node[state,below=of q_0] (q_2) {$q_{2}$};
|
||||||
|
\node[state,accepting, right=of q_2] (q_3) {$q_{3}$};
|
||||||
|
|
||||||
|
\path[->] (q_0) edge node {A} (q_1)
|
||||||
|
edge node {G} (q_3)
|
||||||
|
(q_0) edge node {C} (q_2)
|
||||||
|
(q_2) edge node {C} (q_3);
|
||||||
|
\end{tikzpicture}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
Binary file not shown.
|
|
@ -0,0 +1,62 @@
|
||||||
|
\documentclass[tikz]{standalone}
|
||||||
|
|
||||||
|
\usepackage{tikz}
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
\usetikzlibrary{automata,positioning}
|
||||||
|
|
||||||
|
\iffalse
|
||||||
|
$S = $ AACTACT
|
||||||
|
The suffix language of $S$ is $\{S, ACTACT, CTACT, TACT, ACT, CT, T\}$.
|
||||||
|
|
||||||
|
\fi
|
||||||
|
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid, auto]
|
||||||
|
% TODO
|
||||||
|
\node[state, initial] (q_0) {$q_{0}$};
|
||||||
|
\node[state,right=of q_0] (q_1) {$q_{1}$};
|
||||||
|
\node[state,right=of q_1] (q_2) {$q_{2}$};
|
||||||
|
\node[state,right=of q_2] (q_3) {$q_{3}$};
|
||||||
|
\node[state,right=of q_3] (q_4) {$q_{4}$};
|
||||||
|
\node[state,right=of q_4] (q_5) {$q_{5}$};
|
||||||
|
\node[state,right=of q_5] (q_6) {$q_{6}$};
|
||||||
|
\node[state,accepting,right=of q_6] (q_7) {$q_{7}$};
|
||||||
|
|
||||||
|
% Fix for CT
|
||||||
|
\node[state,below=of q_2] (q_8) {$q_{8}$};
|
||||||
|
\node[state,right=of q_8,accepting,yshift=-2cm] (q_9) {$q_{9}$};
|
||||||
|
|
||||||
|
% Fix for T
|
||||||
|
% \node[state,above=of q_2,yshift=2cm,accepting] (q_10) {$q_{10}$};
|
||||||
|
% S itself
|
||||||
|
\path[->] (q_0) edge node {A} (q_1)
|
||||||
|
(q_1) edge node {A} (q_2)
|
||||||
|
(q_2) edge node {C} (q_3)
|
||||||
|
(q_3) edge node {T} (q_4)
|
||||||
|
(q_4) edge node {A} (q_5)
|
||||||
|
(q_5) edge node {C} (q_6)
|
||||||
|
(q_6) edge node {T} (q_7);
|
||||||
|
|
||||||
|
% First suffix: ACTACT
|
||||||
|
\path[->] (q_1) edge[bend left=30] node {C} (q_8)
|
||||||
|
(q_9) edge[bend right=30] node {A} (q_5);
|
||||||
|
|
||||||
|
% Second suffix: CTACT
|
||||||
|
\path[->] (q_0) edge[bend right=30] node {C} (q_8)
|
||||||
|
(q_8) edge node {T} (q_9);
|
||||||
|
|
||||||
|
% Third suffix: TACT
|
||||||
|
% \path[->] (q_0) edge[bend left=30] node {T} (q_10)
|
||||||
|
%(q_10) edge[bend left=30] node {A} (q_5);
|
||||||
|
|
||||||
|
|
||||||
|
% Fourth suffix: ACT
|
||||||
|
% \path[->] (q_)
|
||||||
|
|
||||||
|
% Fifth suffix: CT
|
||||||
|
|
||||||
|
% Fix for T
|
||||||
|
\path[->] (q_0) edge[bend right=40] node {T} (q_9);
|
||||||
|
|
||||||
|
\end{tikzpicture}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
Binary file not shown.
|
|
@ -0,0 +1,50 @@
|
||||||
|
\documentclass[tikz]{standalone}
|
||||||
|
|
||||||
|
\usepackage{tikz}
|
||||||
|
|
||||||
|
\begin{document}
|
||||||
|
\usetikzlibrary{automata,positioning}
|
||||||
|
|
||||||
|
\iffalse
|
||||||
|
$S = $ TCATCATT
|
||||||
|
The suffix language of $S$ is $\{TCATCATT, CATCATT, ATCATT, TCATT, CATT, ATT, AT, T\}$.
|
||||||
|
\fi
|
||||||
|
\begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid, auto]
|
||||||
|
\node[state, initial] (q_0) {$q_{0}$};
|
||||||
|
\node[state,right=of q_0,accepting] (q_1) {$q_{1}$};
|
||||||
|
\node[state,right=of q_1] (q_2) {$q_{2}$};
|
||||||
|
\node[state,right=of q_2] (q_3) {$q_{3}$};
|
||||||
|
\node[state,right=of q_3] (q_4) {$q_{4}$};
|
||||||
|
\node[state,right=of q_4] (q_5) {$q_{5}$};
|
||||||
|
\node[state,right=of q_5] (q_6) {$q_{6}$};
|
||||||
|
\node[state,right=of q_6] (q_7) {$q_{7}$};
|
||||||
|
\node[state,right=of q_7,accepting] (q_8) {$q_{8}$};
|
||||||
|
|
||||||
|
\path[->] (q_0) edge node {T} (q_1)
|
||||||
|
(q_1) edge node {C} (q_2)
|
||||||
|
(q_2) edge node {A} (q_3)
|
||||||
|
(q_3) edge node {T} (q_4)
|
||||||
|
(q_4) edge node {C} (q_5)
|
||||||
|
(q_5) edge node {A} (q_6)
|
||||||
|
(q_6) edge node {T} (q_7)
|
||||||
|
(q_7) edge node {T} (q_8);
|
||||||
|
|
||||||
|
% CATCATT
|
||||||
|
\path[->] (q_0) edge[bend right=40] node {C} (q_2);
|
||||||
|
|
||||||
|
% ATCATT
|
||||||
|
\path[->] (q_0) edge[bend right=50] node {A} (q_3);
|
||||||
|
|
||||||
|
% TCATT
|
||||||
|
\path[->] (q_4) edge[bend right=30] node {T} (q_8);
|
||||||
|
|
||||||
|
% CATT
|
||||||
|
|
||||||
|
% ATT
|
||||||
|
%\path[->] (q_0) edge[bend right=50] node {A} (q_6);
|
||||||
|
|
||||||
|
% TT
|
||||||
|
\path[->] (q_1) edge[bend left=30] node {T} (q_8);
|
||||||
|
|
||||||
|
\end{tikzpicture}
|
||||||
|
\end{document}
|
||||||
|
|
@ -0,0 +1,657 @@
|
||||||
|
<?xml version="1.0" encoding="UTF-8"?>
|
||||||
|
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" width="612" height="792" viewBox="0 0 612 792">
|
||||||
|
<defs>
|
||||||
|
<g>
|
||||||
|
<g id="glyph-0-0">
|
||||||
|
</g>
|
||||||
|
<g id="glyph-0-1">
|
||||||
|
<path d="M 7.140625 0 L 7.140625 -0.3125 L 6.96875 -0.3125 C 6.375 -0.3125 6.234375 -0.375 6.125 -0.703125 L 3.96875 -6.9375 C 3.921875 -7.0625 3.890625 -7.140625 3.734375 -7.140625 C 3.578125 -7.140625 3.546875 -7.078125 3.5 -6.9375 L 1.4375 -0.984375 C 1.25 -0.46875 0.859375 -0.3125 0.3125 -0.3125 L 0.3125 0 L 1.328125 -0.03125 L 2.484375 0 L 2.484375 -0.3125 C 1.984375 -0.3125 1.734375 -0.5625 1.734375 -0.8125 C 1.734375 -0.84375 1.75 -0.953125 1.75 -0.96875 L 2.21875 -2.265625 L 4.671875 -2.265625 L 5.203125 -0.75 C 5.21875 -0.703125 5.234375 -0.640625 5.234375 -0.609375 C 5.234375 -0.3125 4.671875 -0.3125 4.40625 -0.3125 L 4.40625 0 C 4.765625 -0.03125 5.46875 -0.03125 5.84375 -0.03125 Z M 4.5625 -2.578125 L 2.328125 -2.578125 L 3.4375 -5.828125 Z M 4.5625 -2.578125 "/>
|
||||||
|
</g>
|
||||||
|
<g id="glyph-0-2">
|
||||||
|
<path d="M 6.625 -2.328125 C 6.625 -2.421875 6.625 -2.5 6.5 -2.5 C 6.390625 -2.5 6.390625 -2.4375 6.375 -2.328125 C 6.296875 -0.90625 5.234375 -0.09375 4.140625 -0.09375 C 3.53125 -0.09375 1.578125 -0.421875 1.578125 -3.40625 C 1.578125 -6.375 3.53125 -6.71875 4.140625 -6.71875 C 5.21875 -6.71875 6.109375 -5.8125 6.3125 -4.359375 C 6.328125 -4.21875 6.328125 -4.1875 6.46875 -4.1875 C 6.625 -4.1875 6.625 -4.21875 6.625 -4.421875 L 6.625 -6.78125 C 6.625 -6.953125 6.625 -7.03125 6.515625 -7.03125 C 6.484375 -7.03125 6.4375 -7.03125 6.359375 -6.90625 L 5.859375 -6.171875 C 5.5 -6.53125 4.984375 -7.03125 4.03125 -7.03125 C 2.15625 -7.03125 0.5625 -5.4375 0.5625 -3.40625 C 0.5625 -1.34375 2.171875 0.21875 4.03125 0.21875 C 5.65625 0.21875 6.625 -1.171875 6.625 -2.328125 Z M 6.625 -2.328125 "/>
|
||||||
|
</g>
|
||||||
|
<g id="glyph-0-3">
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<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="281.658887" y="127.92"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-0" x="20.922" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-3" x="27.029098" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="48.050269" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="67.33794" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="86.794976" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="106.401451" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="125.828599" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="145.255747" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="164.543418" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="184.000454" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="203.60693" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="223.034078" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="242.630591" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="262.237066" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="281.664214" y="139.875"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-0" x="21.096" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-4" x="27.203098" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="48.044941" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="67.332612" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="86.799611" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="106.396124" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="125.823272" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="145.25042" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="164.538091" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="184.005089" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="203.601602" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="223.02875" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="242.635226" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="262.231739" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="281.658887" y="151.831"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-0" x="21.096" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-4" x="27.203098" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="48.044941" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="67.332612" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="86.799611" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="106.396124" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="125.823272" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="145.25042" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="164.538091" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="184.005089" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="203.601602" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="223.02875" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-6" x="242.635226" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="262.231739" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-5" x="281.658887" y="163.786"/>
|
||||||
|
</g>
|
||||||
|
<g fill="rgb(0%, 0%, 0%)" fill-opacity="1">
|
||||||
|
<use xlink:href="#glyph-0-0" x="26.491" y="175.741"/>
|
||||||
|
</g>
|
||||||
|
</svg>
|
||||||
|
After Width: | Height: | Size: 27 KiB |
|
|
@ -0,0 +1,15 @@
|
||||||
|
defaultIndent: " "
|
||||||
|
specialBeginEnd:
|
||||||
|
If:
|
||||||
|
begin: '\\If'
|
||||||
|
middle: '\\ElsIf'
|
||||||
|
end: '\\EndIf'
|
||||||
|
lookForThis: 1
|
||||||
|
While:
|
||||||
|
begin: '\\While'
|
||||||
|
end: '\\EndWhile'
|
||||||
|
lookForThis: 1
|
||||||
|
For:
|
||||||
|
begin: '\\For'
|
||||||
|
end: '\\EndFor'
|
||||||
|
specialBeforeCommand: 1
|
||||||
|
|
@ -0,0 +1,15 @@
|
||||||
|
\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}
|
||||||
|
|
||||||
|
\end{document}
|
||||||
Loading…
Reference in New Issue