usepackage[linesnumbered,ruled,vlined]{algorithm2e}

renewcommand{labelenumi}{(Roman{enumi})}

begin{algorithm}
DontPrintSemicolon % Some LaTeX compilers require you to use dontprintsemicolon    instead
KwIn{a,b,c,d}
KwOut{e,r}
Calculate $x$, and $y$    Check,
renewcommand{labelenumi}{(Roman{enumi})}
begin{enumerate}[noitemsep,nolistsep]
item If  $k geq n$, then the  $m_{2}$.
item If  $h geq j$, then  $m_{1}$.
end{enumerate}
Otherwise,    Initialisation: textit{$g(0)=nj$}    $i=0$    Compute $n_{2}$,
[
n(i)=frac {a}{b(i)sqrt{3v}}
]    Update $b$,
[
b(i+1)=( -frac{1}{2(g(i)/D}+1)
]    $i=i+1$,    Repeat textit{Steps 3 to 6}, till $|a(i+1)-a(i) |<epsilon$
caption{algo of g}
label{algo:b}
end{algorithm}

documentclass{article}
usepackage[linesnumbered,ruled,vlined]{algorithm2e}

begin{document}

begin{algorithm}
%DontPrintSemicolon % Some LaTeX compilers require you to use dontprintsemicolon    instead
KwIn{a,b,c,d}
KwOut{e,r}
Calculate $x$, and $y$    Check, linebreak
%renewcommand{labelenumi}{(Roman{enumi})}
%begin{enumerate}[noitemsep,nolistsep]
%item
 (I) If  $k geq n$, then the  $m_{2}$.
linebreak
%item
(II) If  $h geq j$, then  $m_{1}$.    %end{enumerate}
Otherwise,    Initialisation: textit{$g(0)=nj$}    $i=0$    Compute $n_{2}$,
[
n(i)=frac {a}{b(i)sqrt{3v}}
]    Update $b$,
[
b(i+1)=( -frac{1}{2(g(i)/D}+1)
]    $i=i+1$,    Repeat textit{Steps 3 to 6}, till $|a(i+1)-a(i) |<epsilon$
caption{algo of g}
label{algo:b}
end{algorithm}

end{document}

documentclass{article}
usepackage[linesnumbered,ruled,vlined]{algorithm2e}% http://ctan.org/pkg/algorithm2e
DontPrintSemicolon
begin{document}

begin{algorithm}
  KwIn{$a$, $b$, $c$, $d$}
  KwOut{$e$, $r$}
  Calculate~$x$ and~$y$;
  lIf{$k geq n$}{$m_2$};
  lIf{$h geq j$}{$m_1$};
  Else{%
    Repeat{$|a(i+1)-a(i)| < epsilon$}{%
      Initialisation: $g(0) = nj$;label{stepA}
      $i=0$;
      Compute~$n_2$
      [
        n(i) = frac{a}{b(i)sqrt{3v}}
      ]
      nl Update~$b$
      [
        b(i+1) = (-frac{1}{2(g(i)/D} + 1)
      ]
      nl $i = i + 1$;
    }
  }
  caption{My algorithm}
  label{algo:b}
end{algorithm}

end{document}

{
begin{enumerate}[noitemsep,nolistsep]
item If  $k geq n$, then the  $m_{2}$.
item If  $h geq j$, then  $m_{1}$.
end{enumerate}
}