Cfrgtkky

begin{document}

usepackage{savesym}

usepackage{program}

savesymbol{AND}

savesymbol{OR}

savesymbol{NOT}

savesymbol{TO}

savesymbol{COMMENT}

savesymbol{BODY}

savesymbol{IF}

savesymbol{ELSE}

savesymbol{ELSIF}

savesymbol{FOR}

savesymbol{WHILE}





usepackage{algorithm}

usepackage{algorithmic}

begin{algorithm}

    caption{Initialization} label{algorithm: cds bw}

textbf{Input:}

    V, E, S, Stextsubscript{ai}, P, Ptextsubscript{ai}, Rtextsubscript{s}, ptextsubscript{a},rtextsubscript{asp}, 

    $a in V$, ${stextsubscript{i} in stextsubscript{ai}}$ , $r in  R$\

    hspace*{algorithmicindent} textbf{Output:} 

    Wtextsubscript{r} ($r in R$), Ptextsubscript{va} ($a in V$)

    begin{algorithmic}[1]

        State $UA gets V$ 

        State $T gets 0$

        State $Makspan gets 0$

        State $SrtS gets Sort(S)$

        State $rXs gets SrtS$

        For{$s in S$}

        State $Wr gets Compute$

        EndFor   

        For{ $a in V$}

        State $Ptextsubscript{va} gets Compute$

        EndFor          

end{algorithmic}

end{algorithm}

As we wrote in the comments, your document has many issues. You should probably familiarize yourself with the common structure for LaTeX documents. As Johannes_B wrote: "First a document class, then loading packages, then begin the document and now you can start the algorithm." More details here.

Your particular example is easy to fix once you stick to these rules.

%this comes first

documentclass{article}



%then this

usepackage{algpseudocode}

usepackage{algorithm}

%I dont know what all this is for

%usepackage{program}

%usepackage{savesym}

%savesymbol{AND}

%savesymbol{OR}

%savesymbol{NOT}

%savesymbol{TO}

%savesymbol{COMMENT}

%savesymbol{BODY}

%savesymbol{IF}

%savesymbol{ELSE}

%savesymbol{ELSIF}

%savesymbol{FOR}

%savesymbol{WHILE}



%everything you begin, you also have to end

begin{document}

    begin{algorithm}

            caption{Initialization} label{algorithm: cds bw}

            textbf{Input:}

            V, E, S, Stextsubscript{ai}, P, Ptextsubscript{ai}, Rtextsubscript{s}, ptextsubscript{a},rtextsubscript{asp}, 

            $a in V$, ${stextsubscript{i} in stextsubscript{ai}}$ , $r in  R$\

            hspace*{algorithmicindent} textbf{Output:} 

            Wtextsubscript{r} ($r in R$), Ptextsubscript{va} ($a in V$)

            begin{algorithmic}

                    State $UA gets V$ 

                    State $T gets 0$

                    State $Makspan gets 0$

                    State $SrtS gets Sort(S)$

                    State $rXs gets SrtS$

                    For{$s in S$}

                    State $Wr gets Compute$

                    EndFor   

                    For{ $a in V$}

                    State $Ptextsubscript{va} gets Compute$

                    EndFor          

            end{algorithmic}

    end{algorithm}

end{document}