algorithm2e fully justified input / output blocks

Question

I would like to fully justify the input/output blocks in the algorithm2e environment. How can this be achieved?
I cannot find anything regarding this matter in the documentation. To be precise, I would like to keep the indentation as it is, just have the text block fully justified. (I tried just using ragged2e and simply putting justify in the beginning of the input contents, but that did weird things.)
MWE (ignore the algorithm):
documentclass{article}
usepackage[algoruled, linesnumbered]{algorithm2e}
SetKwInOut{Input}{Input}
DontPrintSemicolon
begin{document}
begin{algorithm}
    caption{Getting things done}
    Input{Many things with longish names that make the ragged right look ugly in my opinion. Many things with longish names that make the ragged right look ugly in my opinion. Many things with longish names that make the ragged right look ugly in my opinion.}
    For{$k=1$ KwTo $N$}{
        tcp{Do something}
        $x_k^- = A_{k-1} x_{k-1}^+ + B_{k-1} u_{k-1}$ ;
        $P_{k}^- = A_{k-1} P_{k-1}^+ A_{k-1}^T + Q_{k-1}$ ;
        tcp{And now do something else}
        $K_k = P_{k}^- C_k^T (C_k P_{k}^- C_k^T + R_{k})^{-1}$ ;
        $x_{k}^+ = x_{k}^- + K_{k}(y_{k}-C_k x_{k}^-)$ ;
        $P_{k}^+ = (I - K_{k} C_k) P_{k}^-$ ;
    }
end{algorithm}
end{document}

muzimuzhi Z · Accepted Answer

Try this:
documentclass{article}
usepackage[algoruled, linesnumbered]{algorithm2e}
usepackage{ragged2e}
usepackage{xpatch}

makeatletter
xpatchcmdSetKwInOut
  {hangafter=1parbox[t]}
  {hangafter=1justifyparbox[t]}
  {}{fail}
makeatother

SetKwInOut{Input}{Input}
DontPrintSemicolon

begin{document}
begin{algorithm}
    caption{Getting things done}
    Input{Many things with longish names that make the ragged right look ugly in my opinion. Many things with longish names that make the ragged right look ugly in my opinion. Many things with longish names that make the ragged right look ugly in my opinion.}
    For{$k=1$ KwTo $N$}{
        tcp{Do something}
        $x_k^- = A_{k-1} x_{k-1}^+ + B_{k-1} u_{k-1}$ ;
        $P_{k}^- = A_{k-1} P_{k-1}^+ A_{k-1}^T + Q_{k-1}$ ;
        tcp{And now do something else}
        $K_k = P_{k}^- C_k^T (C_k P_{k}^- C_k^T + R_{k})^{-1}$ ;
        $x_{k}^+ = x_{k}^- + K_{k}(y_{k}-C_k x_{k}^-)$ ;
        $P_{k}^+ = (I - K_{k} C_k) P_{k}^-$ ;
    }
end{algorithm}
end{document}

Some explanations:
When calling SetKwInOut{Input}{Input}, it defines Input by
% here #1 is first arg of SetKwInOut, here it is "Input"
algocf@newcommand{#1}[1]{%
    ifthenelse{boolean{algocf@hanginginout}}{relax}{algocf@seteveryparhanging{relax}}%
    ifthenelse{boolean{algocf@inoutnumbered}}{relax}{algocf@seteveryparnl{relax}}%
    % The following line control the output of Input{##1}.
    % This paragraph starts at parbox, hence the change of paragraph
    % indent (justify) should be inserted before parbox.
    {letalgocf@newinouthangindent=inoutindenthangafter=1parbox[t]{inoutsize}{KwSty{#2algocf@typohfill:}}~##1par}%
    algocf@linesnumbered% reset the numbering of the lines
    ifthenelse{boolean{algocf@hanginginout}}{relax}{algocf@reseteveryparhanging}%
}

algorithm2e fully justified input / output blocks

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