How to write algorithm like this in latex

Question

I want to write an algorithm in a latex. There are various ways to write, but I want to write in the way given below. I have tried but I am not able to do anything similar to the given in the image.

see my code:

\documentclass{article}
\usepackage[utf8]{inputenc}   

\begin{document}

Algorithm \\

Input : 

Output : \\

1. $T \leftarrow $ an set of size $S$ \\
2. \textbf{if} $x = 0$\\

3. \hspace{1cm} \textbf{return}

\end{document}

Question : Some of the problems, I am facing are the color of the background, line numbering, spacing etc

Answer 1

based on nice @CaptainNabla answer:

\documentclass{article}
\usepackage{geometry}
\usepackage{enumitem}
\usepackage[framemethod=tikz]{mdframed}

\usepackage{lipsum}
\begin{document}

\begin{mdframed}[hidealllines=true,backgroundcolor=gray!20]
\parindent=0pt
\parskip=2pt  % <-- gives more spaces between paragraphs

\underline{\textsc{ALLSUBSETSUMS}$^\#(S,u)$:}

\medskip      % for additional vertical space 
 \textsf{INPUT:} A set $S$ of $n$ positive integers and an upper bound integer $u$.

\textsf{OUTPUT:} The set of all subset sums with cardinality information of $S$ up to $u$.
\begin{enumerate}[nosep]
    \item \textbf{if} $S=\{x\}$
    \item \hspace{1cm} \textbf{return} $\{(0,0),(x,1)\}$
    \item $T \leftarrow$ an arbitrary subset of $S$ of size $[n/2]$
    \item \textbf{return} \textsc{ALLSUBSETSUMS}$^{\#}(T,u)\bigoplus_u$\textsc{ALLSUBSETSUMS}$^{\#}(S\setminus T,u)$
\end{enumerate}
\end{mdframed}

\lipsum[1]

\end{document}

gives:

Answer 2

The background color can be adjusted as stated here. Then its just a matter of playing around with some fonts:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[framemethod=tikz]{mdframed}

\begin{document}

\begin{mdframed}[hidealllines=true,backgroundcolor=gray!20]
\noindent
\underline{\textsc{AllSubsetSums}\(^\#(S,u)\):}\\

\noindent\textsf{INPUT:} A set \(S\) of \(n\) positive integers and an upper bound integer \(u\).\\
\textsf{OUTPUT:} The set of all subset sums with cardinality information of \(S\) up to \(u\).

\begin{enumerate}
    \item \textbf{if} \(S=\{x\}\)
    \item \hspace{1cm} \textbf{return} \(\{(0,0),(x,1)\}\)
    \item \(T \leftarrow\) an arbitrary subset of \(S\) of size \([n/2]\)
    \item \textbf{return} \textsc{AllSubsetSums}\(^\#(T,u)\oplus_u\)\textsc{AllSubsetSums}\(^\#(S\setminus T,u)\)
\end{enumerate}
\end{mdframed}

\end{document}

which gives

Its not perfect and requires still a lot of fiddling, especially if you have a lot of different algorithms. Then it might be better to redefine the paragraph command...