\begin{algorithm}
\caption{Modified Counting Sort with Constant Extra Space}
\begin{algorithmic}
\INPUT a sequence $A$ of $n$ elements ranging from $0$ to $k$
\OUTPUT a sorted sequence $A$
\STATE let $B[0..k]$ be a new array initialized with all 0's
\STATE let $C[0..k]$ be a new array initialized with all 0's
\FOR{$i = 1$ \TO $n$}
\STATE $B[A[i]] = B[A[i]] + 1$
\STATE $C[A[i]] = C[A[i]] + 1$
\ENDFOR
\STATE \COMMENT{$B[i], C[i]$ now contains the number of elements equal to $i$}
\FOR{$i = 1$ \TO $k$}
\STATE $C[i] = C[i] + C[i-1]$
\ENDFOR
\STATE \COMMENT{$C[i]$ now contains the number of elements less than or equal to $i$}
\FOR{$i = 0$ \TO $k$}
\WHILE{$B[i] > 0$}
\STATE $B[i] = B[i] - 1$
\STATE $A[C[i] - B[i]] = i$
\ENDWHILE
\ENDFOR
\end{algorithmic}
\end{algorithm}