# i want to write an algorithm but things went wrong

\begin{algorithm}
\hspace*{\algorithmicindent} \textbf{Input:}  V, E, S, S\textsubscript {ai}, P, P\textsubscript{ai}, R\textsubscript{s}, p\textsubscript{a},r\textsubscript{asp}, $a \in V$, ${s\textsubscript{i} \in s\textsubscript{ai}}$ , $r \in R$\\
\hspace*{\algorithmicindent} \textbf{Output:} W\textsubscript{r} ($r \in R$), P \textsubscript{va} ($a \in V$)
\begin{algorithmic}%[1]
\caption{Initialization} \label{algorithm: cds bw}
%   \Ensure
%   \Require A connected graph $G(V, E)$
\State $UA \gets V \State$T \gets 0\\
\State $Makspan \gets 0\\ \State$SrtS \gets Sort(S)\\
\State $rXs \gets SrtS\\ \item for$s \in S do
\State $Wr \gets Compute \EndFor \end{algorithmic} \end{algorithm}  these are the erros. Command \item invalid in math mode. \State$T \gets 0\\
Something's wrong--perhaps a missing \item. \State
Something's wrong--perhaps a missing \item. \State
Command \item invalid in math mode. \State
Missing $inserted. \State Missing } inserted. \State Extra }, or forgotten \endgroup. \State Command \item invalid in math mode. \State$Makspan \gets 0\\
Something's wrong--perhaps a missing \item. \State
Something's wrong--perhaps a missing \item. \State
Command \item invalid in math mode. \State
Missing $inserted. \State Missing } inserted. \State Extra }, or forgotten \endgroup. \State Command \item invalid in math mode. \State$SrtS \gets Sort(S)\\
Something's wrong--perhaps a missing \item. \State
Something's wrong--perhaps a missing \item. \State
Command \item invalid in math mode. \State
Missing $inserted. \State Missing } inserted. \State Extra }, or forgotten \endgroup. \State Command \item invalid in math mode. \State$rXs \gets SrtS\\
Something's wrong--perhaps a missing \item. \item
Something's wrong--perhaps a missing \item. \item
Command \item invalid in math mode. \item
Missing $inserted. \item f Missing } inserted. \item f Extra }, or forgotten \endgroup. \item f Command \item invalid in math mode. \State Something's wrong--perhaps a missing \item. \State Something's wrong--perhaps a missing \item. \State Missing$ inserted. \State $Wr \gets Missing$ inserted.
Missing } inserted.
Extra }, or forgotten \endgroup.
Missing number, treated as zero. \EndFor
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• A quick guess you are entering the math mode by means of the dollar in the \State commands but you don't really leave it. same for the \item. – albert Oct 24 '18 at 16:19
• As it is possible to add line from one statement to another i.e. ruled, vlined etc – Iftikhar Ahmad Oct 24 '18 at 18:12
• @albert please guide me in this regard – Iftikhar Ahmad Oct 25 '18 at 8:19
• I think the answer from Werner gives the answers. – albert Oct 25 '18 at 8:38

Here are some corrections:

1. Use \State without a closing \\.

2. When opening math mode, also close it $...$.

3. Use \For{<condition>}...\EndFor.

4. \caption should be outside the algorithmic environment.

\documentclass{article}

\usepackage{algorithm,algpseudocode}

\begin{document}

\begin{algorithm}
\caption{Initialization} \label{algorithm: cds bw}
\hspace*{\algorithmicindent} \textbf{Input:}
V, E, S, S\textsubscript{ai}, P, P\textsubscript{ai}, R\textsubscript{s}, p\textsubscript{a},r\textsubscript{asp},
$a \in V$, ${s\textsubscript{i} \in s\textsubscript{ai}}$ , $r \in R$\\
\hspace*{\algorithmicindent} \textbf{Output:}
W\textsubscript{r} ($r \in R$), P \textsubscript{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
\end{algorithmic}
\end{algorithm}

\end{document}