Side-by-side algorithms in latex - algorithm

Question

I am using "elsarticle" class and need to place two algorithms side by side. I am using minipage fucntion to do this but algorithms are not generated exactly side by side (a picture is attached for your reference). A working latex code is given as:
documentclass[3p]{elsarticle}
\usepackage{hyperref}
%\modulolinenumbers[5]
\usepackage[ruled,linesnumbered]{algorithm2e}
\usepackage{amsfonts}
\usepackage{threeparttable}
\usepackage{tabularx}
%\usepackage{cite}
\usepackage{mathtools}
\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{multirow}
\usepackage{algorithm}
\usepackage{algpseudocode}
\begin{document}
\begin{minipage}{0.5\textwidth}
\begin{algorithm}[H]
% \caption{(X,Y)-only co-Z addition with update ($ZADDU_{(X,Y)}$)}
\caption{ $ZADDU_{(X,Y)}$}
\label{alg1}
%\begin{multicols}{2} % and a label for \ref{} commands
\begin{algorithmic}[1]
\Require{ $R_1 = (X_1, Y_1, Z )$ and $R_2 = (X_2, Y_2, Z)$ }
\Ensure {$(R_3, R_1)\mspace{5mu} = \mspace{5mu}ZADDU_{(X,Y)}(R_1, R_2)$ $\mspace{15mu}$where $R_3= R_1 + R_2=
(X_3, Y_3, Z_3)$ and $R_1 = (\lambda^2{X_1}, \lambda^3 {Y_1}, Z_3)$ with $Z_3=\lambda Z$ for some $\lambda\neq0$}\\
% \tcc{\textbf{Phase A:}}
% $z := 0, R_1 := x$\;
% $R_2 := u_2$\;
%
% \tcc{\textbf{Phase B:}}
$B=(X_1-X_2)^2$;
$E_1 =X_1 U; E_2 = X_2 U$; $C =(Y_1 - Y_2)^2$\\
$D =Y_1 (E_1 - E_2)$; $X_3=C - E_1 - E_2$;
$Y_3=(Y_1 - Y_2)(E_1 - X_3 ) - D$;\\
${X_1}= E_1$; ${Y_1} = D$;
$R_3=(X_3, Y_3)$, $R_3=(X_1, Y_1)$\\
\Return{($R_3,R_1$)}\;
\end{algorithmic}
\end{algorithm}
\end{minipage}
\hfill
\begin{minipage}{0.5\textwidth}
\begin{algorithm}[H]
% \caption{(X,Y)-only conjugate co-Z addition ($ZADDC_{(X,Y)}$)}
\caption{$ZADDC_{(X,Y)}$}
% give the algorithm a caption
\label{alg1}
%\begin{multicols}{2} % and a label for \ref{} commands
\begin{algorithmic}[1]
\Require{ $R_1 = (X_1, Y_1, Z )$ and $R_2 = (X_2, Y_2, Z)$ }
\Ensure {$(R_3, \overline R_3)\mspace{5mu} = \mspace{5mu}ZADDC_{(X,Y)}(R_1, R_2)$$\mspace{10mu}$where $R_3= R_1 + R_2=
(X_3, Y_3, Z_3)$ and $\overline R_3 =R_1 - R_2= (\overline{X_3},\overline {Y_3}, Z_3)$ }\\
% \tcc{\textbf{Phase A:}}
% $z := 0, R_1 := x$\;
% $R_2 := u_2$\;
%
% \tcc{\textbf{Phase B:}}
$B=(X_1-X_2)^2$;
$E_1 =X_1 U; E_2 = X_2 U$; $C =(Y_1 - Y_2)^2$;\\
$D =Y_1 (E_1 - E_2)$; $X_3=C - V_1 - V_2$;
$Y_3=(Y_1 - Y_2)(E_1 - X_3 ) - D$; \\
$\overline{C} = (Y1 + Y2)^2$; $\overline{X_3}= \overline{C} - E_1 - E_2$; $\overline{Y_3} = (Y_1 + Y_2)(E_1 - \overline{X_3} ) - D$;\\
\Return{($R_3,\overline R_3$)}\;
\end{algorithmic}
\end{algorithm}
\end{minipage}
\end{document}
An output picture is attached, any help to align these algorithms side by side would be appreciated a lot.

Answer 1

A couple of problems:
missing \ in front of documentclass
incompatible package. Your document will produce the error
Command \listofalgorithms already defined. ...s}{\listof{algorithm}{\listalgorithmname}}
You should never ignore error messages. After an error latex only recovers enough to syntax check the rest of the document, not necessarily producing sensible output
you are placing two minipages with .5\textwidth each besides each other. This will fill the entire line leaving no space for all the additional spaces added by your unescaped line endings. Either make your minipages smaller or add % at the end of lines so they don't act like spaces
use unique labels for your algorithms
the hyperref package should be loaded as one of the last packages. Don't load it directly at the start of your preamble
and just from your picture I would guess that in your real document you are missing an empty line before the minipages
\documentclass[3p]{elsarticle}
%\modulolinenumbers[5]
\usepackage[ruled,linesnumbered]{algorithm2e}
\usepackage{amsfonts}
\usepackage{threeparttable}
\usepackage{tabularx}
%\usepackage{cite}
\usepackage{mathtools}
\DeclarePairedDelimiter\ceil{\lceil}{\rceil}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{multirow}
%\usepackage{algorithm}
\usepackage{algpseudocode}
\usepackage{hyperref}
\begin{document}
\noindent\begin{minipage}{0.5\textwidth}
\begin{algorithm}[H]
% \caption{(X,Y)-only co-Z addition with update ($ZADDU_{(X,Y)}$)}
\caption{ $ZADDU_{(X,Y)}$}
\label{alg1}
%\begin{multicols}{2} % and a label for \ref{} commands
\begin{algorithmic}[1]
\Require{ $R_1 = (X_1, Y_1, Z )$ and $R_2 = (X_2, Y_2, Z)$ }
\Ensure {$(R_3, R_1)\mspace{5mu} = \mspace{5mu}ZADDU_{(X,Y)}(R_1, R_2)$ $\mspace{15mu}$where $R_3= R_1 + R_2=
(X_3, Y_3, Z_3)$ and $R_1 = (\lambda^2{X_1}, \lambda^3 {Y_1}, Z_3)$ with $Z_3=\lambda Z$ for some $\lambda\neq0$}\\
% \tcc{\textbf{Phase A:}}
% $z := 0, R_1 := x$\;
% $R_2 := u_2$\;
%
% \tcc{\textbf{Phase B:}}
$B=(X_1-X_2)^2$;
$E_1 =X_1 U; E_2 = X_2 U$; $C =(Y_1 - Y_2)^2$\\
$D =Y_1 (E_1 - E_2)$; $X_3=C - E_1 - E_2$;
$Y_3=(Y_1 - Y_2)(E_1 - X_3 ) - D$;\\
${X_1}= E_1$; ${Y_1} = D$;
$R_3=(X_3, Y_3)$, $R_3=(X_1, Y_1)$\\
\Return{($R_3,R_1$)}\;
\end{algorithmic}
\end{algorithm}
\end{minipage}%
%\hfill
\begin{minipage}{0.5\textwidth}
\begin{algorithm}[H]
% \caption{(X,Y)-only conjugate co-Z addition ($ZADDC_{(X,Y)}$)}
\caption{$ZADDC_{(X,Y)}$}
% give the algorithm a caption
\label{alg2}
%\begin{multicols}{2} % and a label for \ref{} commands
\begin{algorithmic}[1]
\Require{ $R_1 = (X_1, Y_1, Z )$ and $R_2 = (X_2, Y_2, Z)$ }
\Ensure {$(R_3, \overline R_3)\mspace{5mu} = \mspace{5mu}ZADDC_{(X,Y)}(R_1, R_2)$$\mspace{10mu}$where $R_3= R_1 + R_2=
(X_3, Y_3, Z_3)$ and $\overline R_3 =R_1 - R_2= (\overline{X_3},\overline {Y_3}, Z_3)$ }\\
% \tcc{\textbf{Phase A:}}
% $z := 0, R_1 := x$\;
% $R_2 := u_2$\;
%
% \tcc{\textbf{Phase B:}}
$B=(X_1-X_2)^2$;
$E_1 =X_1 U; E_2 = X_2 U$; $C =(Y_1 - Y_2)^2$;\\
$D =Y_1 (E_1 - E_2)$; $X_3=C - V_1 - V_2$;
$Y_3=(Y_1 - Y_2)(E_1 - X_3 ) - D$; \\
$\overline{C} = (Y1 + Y2)^2$; $\overline{X_3}= \overline{C} - E_1 - E_2$; $\overline{Y_3} = (Y_1 + Y_2)(E_1 - \overline{X_3} ) - D$;\\
\Return{($R_3,\overline R_3$)}\;
\end{algorithmic}
\end{algorithm}
\end{minipage}%
\end{document}