#import "@local/handout:0.1.0": *
#import "@preview/cetz:0.3.1"

#show: handout.with(
  title: [Warm-Up: What's an AST?],
  by: "Mark",
  subtitle: "Based on a true story.",
)

#problem()
Say we have a valid string of simple arithmetic that contains \
no unary operators (like $3!$ or $-4$) and no parenthesis:

#v(2mm)
$
  3 + 9 times 8 div 5 and 6
$
#v(2mm)

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

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

#v(2mm)

#align(
  center,
  cetz.canvas({
    import cetz.draw: *

    // spell:off
    content((0, 0), $+$, name: "r")
    content((-0.5, -1), $3$, name: "a")
    content((0.5, -1), $div$, name: "b")
    content((-0.3, -2), $times$, name: "ba")
    content((1.3, -2), $and$, name: "bb")
    content((-0.8, -3), $9$, name: "baa")
    content((0.2, -3), $8$, name: "bab")
    content((0.8, -3), $5$, name: "bba")
    content((1.8, -3), $6$, name: "bbb")
    // spell:on

    // Zero-sized arrows are a hack for offset.
    set-style(
      stroke: (thickness: 0.3mm),
      mark: (
        start: (
          symbol: "|",
          offset: 0.25,
          width: 0mm,
          length: 0mm,
        ),
        end: (
          symbol: "|",
          offset: 0.25,
          width: 0mm,
          length: 0mm,
        ),
      ),
    )

    // spell:off
    line("r", "a")
    line("r", "b")
    line("b", "ba")
    line("b", "bb")
    line("ba", "baa")
    line("ba", "bab")
    line("bb", "bba")
    line("bb", "bbb")
    // spell:on
  }),
)