65 lines
2.2 KiB
TeX
65 lines
2.2 KiB
TeX
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\chapter{Section alignment}
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\section{Needleman - Wunsch algorithm}
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\begin{algorithm}
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\caption{Needleman-Wunsch Algorithm}
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\begin{algorithmic}[1]
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\Procedure{FillMatrix}{$S_{1}$: Array($m$), $S_{2}$: Array($n$)}
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\Comment{$sub(a, b)$ is the substitution score, $del(a)$ and $ins(a)$ are the deletion and insertion penalty, in regard with the reference $S_{1}$ sequence}
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\State $M = $ Array($m+1$, $n+1$)
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\Comment{Initialize the matrix first column and first row}
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\State $P = $ Array($m$, $n$) \Comment{Store the direction of the cell we chose to build the next cell up on.}
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\For {($i = 0$; $i < m+1$; $i++$)}
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\State $M[i][0] = i * del(S_{1}[i])$
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\EndFor
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\For {($j = 0$; $j < n+1$; $j++$)}
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\State $M[0][j] = j * ins(S_{2}[j])$
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\EndFor
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\Comment{Fill the remaining matrix}
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\For {($i = 1$; $i < m+1$; $i++$)}
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\For {($j = 1$; $j < n+1$; $j++$)}
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\State $delete = M[i-1][j] + del(S_{1}[i-1])$
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\State $insert = M[i][j-1] + ins(S_{2}[j-1])$
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\State $substitute = M[i-1][j-1] + sub(S_{1}[i-1], S_{2}[j-1])$
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\State $choice = \max \{delete, insert, substitute\}$
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\If {$substitute = choice$}
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\State $P[i-1][j-1] = '\nwarrow'$
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\ElsIf {$insertion = choice$}
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\State $P[i-1][j-1] = '\uparrow'$
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\Else
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\State $P[i-1][j-1] = '\leftarrow'$
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\EndIf
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\State $M[i][j] = choice$
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\EndFor
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\EndFor
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\EndProcedure
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\Procedure{ShowAlignment}{$S_{1}$: Array($m$), $S_{2}$: Array($n$)}
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\State $extend_{1} = ''$
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\State $extend_{2} = ''$
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\State $i = m$
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\State $j = n$
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\While{$i > 0$ and $j > 0$}
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\If {$P[i-1][j-1] = '\nwarrow'$}
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\State $extend_{1} = S_{1}[i-1] \circ extend_{1}$
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\State $extend_{2} = S_{2}[j-1] \circ extend_{2}$
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\State $i--$
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\State $j--$
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\ElsIf {$P[i-1][j-1] = '\uparrow'$}
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\State $extend_{1} = S_{1}[i-1] \circ extend_{1}$
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\State $extend_{2} =\quad '-' \circ extend_{2}$
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\State $i--$
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\Else
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\State $extend_{1} =\quad '-' \circ extend_{1}$
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\State $extend_{2} = S_{2}[j-1] \circ extend_{2}$
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\State $j--$
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\EndIf
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\EndWhile
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\State \Call{print}{$extend_{1}$}
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\State \Call{print}{$extend_{2}$}
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\EndProcedure
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\State \Call{FillMatrix}{$S_{1}$, $S_{2}$}
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\State \Call ShowAlignment($S_{1}$, $S_{2}$)
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\end{algorithmic}
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\end{algorithm}
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