Line in algorithm2e environment wrapping late

Question

I am having a small issue where where the line

Let $s$ be the highest-ranked student in $h$'s preference list which $h$ has not yet requested to be a resident\

in my algorithm is wrapping a little too late. The boundary should be the same as the line under "Homework 1" provided by fancyhdr I believe. Below is that complete portion of me tex file. Could anyone assist me in getting that line to wrap earlier? If I force it with a newline then it will also give an incorrect line numbering for the algorithm environment so that quick fix isn't an option I am willing to settle with.

\begin{enumerate}
...
\item[\textbf{4.}] 
    Below is an algorithm to find a stable assignment of students to hospitals:

    \begin{algorithm}[H]
        \SetKwData{List}{list}
        \SetKwFunction{Remove}{Remove}
        \SetKwFunction{Insert}{Insert}
        \SetKwInOut{Input}{input}

        \Input{A set of hospitals $H$ where each $h \in H$ has a list of students $h.\List$ with a capacity equivalent to number of positions available \\ A set of students $S$}
        Initially $s$ is free for all $s \in S$ and $h.\List$ is empty for all $h \in H$. \\
        \While{there exists $h \in H$ such that $h.\List$ is not full}
        {
            Choose such a hospital $h$\\
            \While{$h.\List$ is not full}
            {
                Let $s$ be the highest-ranked student in $h$'s preference list which $h$ has not yet requested to be a resident\\
            }
        }
    \end{algorithm}
...
\end{enumerate}

Answer 1

According to the algorithm2e code, [H]-style algorithms are set as a minipage of width \hsize (in algorithm2e.sty):

%%% environment for {algorithm}[H]
\newenvironment{algocf@Here}{\noindent%
  \def\@captype{algocf}% if not defined, caption exit with an error
  \begin{minipage}{\hsize}%
}{%
  \end{minipage}%\par%
}%

Changing this to a minipage of width \linewidth saves the day. Use etoolbox to patch \algocf@Here:

\documentclass{article}
\usepackage{showframe,etoolbox}% http://ctan.org/pkg/{showframe,etoolbox}
\usepackage{algorithm2e}% http://ctan.org/pkg/algorithm2e

\makeatletter
\patchcmd{\algocf@Here}{\hsize}{\linewidth}{}{}
\makeatother
\begin{document}
\begin{enumerate}
\item[\textbf{4.}] 
    Below is an algorithm to find a stable assignment of students to hospitals:

    \begin{algorithm}[H]
        \SetKwData{List}{list}
        \SetKwFunction{Remove}{Remove}
        \SetKwFunction{Insert}{Insert}
        \SetKwInOut{Input}{input}

        \Input{A set of hospitals~$H$ where each $h \in H$ has a list of students $h.\List$ with a capacity equivalent to number of positions available \\
          A set of students~$S$}
        Initially~$s$ is free for all $s \in S$ and $h.\List$ is empty for all $h \in H$\;
        \While{there exists $h \in H$ such that $h.\List$ is not full}
        {
            Choose such a hospital~$h$\;
            \While{$h.\List$ is not full}
            {
                Let~$s$ be the highest-ranked student in~$h$'s preference list which~$h$ has not yet requested to be a resident
            }
        }
    \end{algorithm}
\end{enumerate}
\end{document}

\patchcmd{<cmd>}{<search>}{<replace>}{<success>}{<failure>} replaces <search> in <cmd> with <replace> - in this case, \hsize with \linewidth. \linewidth gives a true representation of the width of a line inside a list (in your case, an enumerate). For a discussion on the difference in these lengths, see Difference between \textwidth, \linewidth and \hsize.