makeatletter
newifif@restonecol
makeatother
letalgorithmrelax
letendalgorithmrelax
usepackage[linesnumbered,ruled,vlined]{algorithm2e}%[ruled,vlined]{
usepackage{algpseudocode}
renewcommand{algorithmicrequire}{textbf{Input:}}
renewcommand{algorithmicensure}{textbf{Output:}}

begin{document}

begin{algorithm}

caption{trace column}
LinesNumbered
KwIn{
$v$:当前访问的节点newline
$c$:当前访问节点所要溯源的列
}
KwOut{
$S$ :遍历所找到的根节点的集合
}
textbf{Initialize} $S=emptyset$ ;
If{$v$ instanceof DataSourceNode}{
$n$.used=false;
$n$.id=$v$.id;
$n$.column=position of $c$ in $v$;
$S=Scup {n}$;
}
ElseIf{node instanceof JoinTreeNode}{
prenode[0]=node.input1;
prenode[1]=node.input2;
For{i=0;i<2;i++}{
If{$c$ is from prenode[i]}{
$S=Scup trace$(prenode[i],position of $c$ in prenode[i]);
If{position of $c$ in prenode[i]=position of key in prenode[i]}{
$S=Scup trace$(prenode[1-i],position of $c$ in prenode[1-i]);
break;
}
break;
}
}
}
return $S$newline
end{algorithm}

begin{algorithm}
caption{trace column22}
....as the same code block....
end{algorithm}

end{document}