handouts/Misc/Warm-Ups/ast.tex

\documentclass[
	solutions,
	hidewarning,
	singlenumbering,
	nopagenumber
]{../../resources/ormc_handout}

\usepackage[linguistics]{forest}



\title{Warm-Up: What's an AST?}
\subtitle{Prepared by Mark on \today. \\ Based on a true story.}

\begin{document}

	\maketitle

	Say you have a valid string of simple arithmetic that contains no unary operators (like $3!$ or $-4$) and no parenthesis:
	$$
	3 + 9 \times 8 \div 5 \land 6
	$$

	You may assume that all numbers and operators in this string consist of exactly one character. \\

	Devise an algorithm that turns this string into a tree (as shown below), respecting the order of operations $[\land, \times, \div, +, -]$.

	\begin{center}
	\begin{forest}
		[$+$
			[3]
			[$\div$
				[$\times$[9][8]]
				[$\land$[5][6]]
			]
		]
	\end{forest}
	\end{center}

\end{document}