documentclass[a4paper,fleqn]{cas-sc}
usepackage{cite}
usepackage{multirow}
%usepackage[utf8x]{inputenc}
usepackage{mathrsfs}
usepackage{amssymb,amsthm}
usepackage{caption}
captionsetup[figure]{position=below, margin=1cm, labelfont=bf, labelsep=period, skip=12pt, justification=justified}
usepackage{multicol}
usepackage{graphicx}
usepackage{subfigure}
usepackage{float}
usepackage{etoolbox}
usepackage{booktabs}
%usepackage[table]{xcolor}
%usepackage{float}
%usepackage[cmex10]{amsmath}
%usepackage{url}
usepackage[T1]{fontenc}
usepackage{soul}
letlabelindentrelax
usepackage{enumitem}
usepackage{array}
usepackage{longtable}
usepackage{epstopdf}
%usepackage{amsmath}
usepackage{textcomp}
usepackage{multirow}
usepackage{pdflscape}
%usepackage{rotating}
%restylefloat*{figure} %% create a line before and after an image
floatstyle{plain}
captionsetup{labelsep=space,justification=centering,singlelinecheck=on}
usepackage{mathcomp}
usepackage{lscape}
%usepackage{float}
usepackage{longtable}
usepackage{lineno}
setlengthcolumnsep{25pt}

newcommand{PreserveBackslash}[1]{lettemp = \#1let\ = temp}
newcolumntype{C}[1]{>{PreserveBackslashcentering}p{#1}}
newcolumntype{R}[1]{>{PreserveBackslashraggedleft}p{#1}}
newcolumntype{L}[1]{>{PreserveBackslashraggedright}p{#1}}
setcounter{page}{1}
twocolumn
%% %%%%%%
%%% Packages to add the vertical line with in algorithm:pseudocode
usepackage{algorithm}
usepackage[noend]{algpseudocode}
usepackage{etoolbox}

makeatletter
% start with some helper code
% This is the vertical rule that is inserted
newcommand*{algrule}[1][algorithmicindent]{%
    makebox[#1][l]{%
        hspace*{.2em}% <------------- This is where the rule starts from
        vrule height .75baselineskip depth .25baselineskip
    }
}

newcountALG@printindent@tempcnta
defALG@printindent{%
    ifnum theALG@nested>0% is there anything to print
    ifxALG@textALG@x@notext% is this an end group without any text?
    % do nothing
    else
    unskip
    % draw a rule for each indent level
    ALG@printindent@tempcnta=1
    loop
    algrule[csname ALG@ind@theALG@printindent@tempcntaendcsname]%
    advance ALG@printindent@tempcnta 1
    ifnum ALG@printindent@tempcnta<numexprtheALG@nested+1relax
    repeat
    fi
    fi
}
% the following line injects our new indent handling code in place of the default spacing
patchcmd{ALG@doentity}{noindenthskipALG@tlm}{ALG@printindent}{}{errmessage{failed to patch}}
patchcmd{ALG@doentity}{item[]nointerlineskip}{}{}{} % no spurious vertical space
% end vertical rule patch for algorithmicx
makeatother
usepackage{textcomp}
defBibTeX{{rm Bkern-.05em{sc ikern-.025em b}kern-.08em
        Tkern-.1667emlower.7exhbox{E}kern-.125emX}}

begin{document}

end{document}