How to add input and output before algorithm procedure

Answer:

To add input and output before MyProcedure a possibility is to add the text before \begin{algorithmic} with starred hspace \hspace*{}(see 6.3.3 Horizontal Space) and the indentation \algorithmicindent (see 4.1 Blocks and loops). LaTeX normally removes horizontal space at the beginning of a line, to preserve this space, use the starred version.

 ...
 \hspace*{\algorithmicindent} \textbf{Input} \\
 \hspace*{\algorithmicindent} \textbf{Output} 
 \begin{algorithmic}[1]
 ...

Complete full MWE: A minimal working example (MWE) starts with \documentclass and ends with \end{document}.

To complete the MWE and to avoid the following error:

! Undefined control sequence. \BState ->\State \algbackskip l.24 \BState

You have to use the following definition (the solution is from @Werner see: Undefined control sequence.\BState ->\State \algbackskip \BState):

\makeatletter
% Reinsert missing \algbackskip
\def\algbackskip{\hskip-\ALG@thistlm}
\makeatother

MWE:

\documentclass{article}
\usepackage{algorithm}
\usepackage[noend]{algpseudocode}

\makeatletter
% Reinsert missing \algbackskip
\def\algbackskip{\hskip-\ALG@thistlm}
\makeatother

\begin{document}
    \begin{algorithm}
    \caption{My algorithm}\label{euclid}
    \hspace*{\algorithmicindent} \textbf{Input} \\
    \hspace*{\algorithmicindent} \textbf{Output} 
    \begin{algorithmic}[1]
    \Procedure{MyProcedure}{}
%    \Procedure{MyProcedure}{$x,y$}
%     % Input:
%     \Comment{Input: x}
%     % Output:
%     \Comment{Output:y}
    \State $\textit{stringlen} \gets \textit{length of } \textit{string}$
    \State $i \gets \textit{patlen}$
    \BState \emph{top}:
    \If {$i > \textit{stringlen}$} \Return false
    \EndIf
    \State $j \gets \textit{patlen}$
    \BState \emph{loop}:
    \If {$\textit{string}(i) = \textit{path}(j)$}
    \State $j \gets j-1$.
    \State $i \gets i-1$.
    \State \textbf{goto} \emph{loop}.
    \State \textbf{close};
    \EndIf
    \State $i \gets i+\max(\textit{delta}_1(\textit{string}(i)),\textit{delta}_2(j))$.
    \State \textbf{goto} \emph{top}.
    \EndProcedure
    \end{algorithmic}
    \end{algorithm}
\end{document} 

Alternative: You can add the input and output after MyProcedure with \Procedure{MyProcedure}{$x,y$} ...

or \Comment{Input: x}/\Comment{Output: y}.

If one is using the algorithmic environment, one can make \REQUIRE and \ENSURE to print Input and Output by adding in the preamble:

\renewcommand{\algorithmicrequire}{\textbf{Input:}}
\renewcommand{\algorithmicensure}{\textbf{Output:}}