Levenshtein edit distance

Each sequence can contain up to 12 characters.

    \begin{algorithm}
    \caption{LevenshteinDistance}
    \begin{algorithmic}
    \FUNCTION{LevenshteinDistance}{A, B, m, n}
        \STATE $dp[0][j] \gets j$ for $0 \leq j \leq n$
        \STATE $dp[i][0] \gets i$ for $0 \leq i \leq m$
        \FOR{$i \gets 1$ \TO $m$}
            \FOR{$j \gets 1$ \TO $n$}
                \STATE $cost \gets 0$ if $A[i - 1] = B[j - 1]$, otherwise $1$
                \STATE $dp[i][j] \gets \min(dp[i - 1][j] + 1, dp[i][j - 1] + 1, dp[i - 1][j - 1] + cost)$
            \ENDFOR
        \ENDFOR
        \RETURN $dp[m][n]$
    \ENDFUNCTION
    \end{algorithmic}
    \end{algorithm}