Elsarticle文档类下实现两个算法精确并排对齐的LaTeX技术求助

各位LaTeX大佬好，我目前在用elsarticle文档类撰写论文，需要将两个算法并排展示。我尝试使用minipage环境来实现，但生成的算法没法做到精确的并排对齐（输出效果的截图已附上）。以下是我当前可编译的LaTeX代码，麻烦大家帮忙看看如何调整才能让这两个算法完美对齐？

\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}

目前的输出中两个算法没有精确对齐，麻烦各位帮忙支招调整代码，让它们能完美地并排展示！

备注：内容来源于stack exchange，提问作者Khalid