\documentclass{memoir}

\let\MEMOIRnewfloat\newfloat
\let\newfloat\relax
\usepackage{algorithm}
\usepackage{algpseudocode}
\let\newfloat\MEMOIRnewfloat

\renewcommand{\algorithmiccomment}[1]{// #1}

\begin{document}

\listofalgorithms

\begin{algorithm}
\caption{EuclidĄ¯s algorithm}\label{euclid}
\begin{algorithmic}[1]
\Procedure{Euclid}{$a,b$}\Comment{The g.c.d. of a and b}
\State $r\gets a\bmod b$
\While{$r\not=0$}\Comment{We have the answer if r is 0}
\State $a\gets b$
\State $b\gets r$
\State $r\gets a\bmod b$
\EndWhile\label{euclidendwhile}
\State \textbf{return} $b$\Comment{The g.c.d. is b}
\EndProcedure
\end{algorithmic}
\end{algorithm}

\end{document}