\section{Befunge}

\definition{}
\textit{Befunge} is another esoteric programming langauge, designed to be very difficult to compile. \par
It consists of a \say{field} of instructions, a two-dimensional program counter, and a stack of values. \par

\vspace{2mm}

The program counter starts in the top-left corner of the field, moving right. \par
It executes any instruction it encounters.
The instructions \texttt{>}, \texttt{<}, \texttt{\^}, and \texttt{v} can be used to direct the program counter,
and \texttt{\_} and \texttt{|} are used for control flow.



\vfill

An instruction reference is below:
\begin{itemize}[itemsep=2mm]
	\item \texttt{+} Addition: Pop two values $a$ and $b$, then push the result of $a+b$
	\item \texttt{-} Subtraction: Pop two values $a$ and $b$, then push the result of $b-a$
	\item \texttt{*} Multiplication: Pop two values $a$ and $b$, then push the result of $a \times b$
	\item \texttt{/} Integer division: Pop two values $a$ and $b$, then push the result of $b \div a$, rounded down.
	\item \texttt{\%} Modulo: Pop two values $a$ and $b$, then push the remainder of the integer division of $b \div a$.
	\item \texttt{!} Logical NOT: Pop a value. If the value is zero, push 1; otherwise, push zero.
	\item \texttt{ \`} Greater than: Pop two values $a$ and $b$, then push 1 if $b>a$, otherwise zero.
	\item \texttt{>} Program counter direction right
	\item \texttt{<} Program counter direction left
	\item \texttt{\textasciicircum} Program counter direction up
	\item \texttt{v} Program counter direction down
	\item \texttt{?} Random program counter direction
	\item \texttt{\_} Horizontal \texttt{if}: pop a value; set direction to right if value=0, set to left otherwise
	\item \texttt{|} Vertical \texttt{if}: pop a value; set direction to down if value=0, set to up otherwise
	\item \texttt{"} Toggle string mode (push each character's ASCII value all the way up to the next ")
	\item \texttt{:} Duplicate top stack value
	\item \texttt{\textbackslash} Swap top stack values
	\item \texttt{\$} Pop top of stack and discard
	\item \texttt{.} Pop top of stack and output as integer
	\item \texttt{,} Pop top of stack and output as ASCII character
	\item \texttt{\#} Bridge: jump over next command in the current direction of the current PC
	\item \texttt{g} A "get" call (a way to retrieve data in storage). Pop two values y and x, then push the ASCII value of the character at that position in the program. If (x,y) is out of bounds, push 0
	\item \texttt{p} A "put" call (a way to store a value for later use). Pop three values y, x and v, then change the character at the position (x,y) in the program to the character with ASCII value v
	\item \texttt{\&} Get integer from user and push it
	\item \texttt{\~{}} Get character from user and push it
	\item \texttt{@} End program
	\item \texttt{0}-\texttt{9} Push corresponding number onto the stack
\end{itemize}

\vspace{2mm}

Note that the \texttt{p} instruction allows us to write self-modifying code.

\vfill
\pagebreak

\problem{}
Write a program that prints \say{\texttt{Hello World}}.

\problem{}
Write a program that prints the alphabet

\problem{}
Write a program that generates a random sequence of numbers (\texttt{0}-\texttt{9}).

\vfill



\problem{}
Write a program that does not contain the string \say{\texttt{Hello World}}, \par
but writes that string somewhere inside its source.

\problem{}
Replace the \texttt{x}s in the following program
so that the loop runs forever. \par
Do not use any control-flow instructions
(\texttt{>}, \texttt{<}, \texttt{\textasciicircum{}}, \texttt{v}, \texttt{\_}, \texttt{|}, \texttt{\#}, or \texttt{?}) \par
\hint{
	Start by replacing all the \texttt{x}s with spaces. \par
	You may not need all the \texttt{x}s, feel free to use a smaller rectangle.
}

\vspace{2mm}

\begin{center}
	\texttt{>xxxxxxxxv \\
		x ~ ~ ~ ~x \\
		x ~ ~ ~ ~x \\
		x ~ ~ ~ ~x \\
		x ~ ~ ~ ~x \\
		x ~ ~ ~ ~x \\
		x ~ ~ ~ ~x \\
		x ~ ~ ~ ~x \\
		\textasciicircum{}xxxxxxxx@
}
\end{center}

\begin{solution}
	The intended solution is self-modifying code:

	\begin{center}
		\texttt{>69*6+97pv\\
			p ~ ~ ~ ~8\\
			7 ~ ~ ~ ~8\\
			9 ~ ~ ~ ~*\\
			* ~ ~ ~ ~0\\
			8 ~ ~ ~ ~0\\
			8 ~ ~ ~ ~p\\
			\textasciicircum{}p00-2*88@
		}
	\end{center}

\end{solution}


\vfill


\problem{Bonus}
Write a quine. (i.e, write a program that outputs itself)

\begin{solution}
	\texttt{01->1\# +\# :\# 0\# g\# ,\# :\# 5\# 8\# *\# 4\# +\# -\# \_@}
\end{solution}

\vfill
\pagebreak