72 lines
1.5 KiB
Typst
72 lines
1.5 KiB
Typst
#import "@local/handout:0.1.0": *
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#import "@preview/cetz:0.4.2"
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#show: handout.with(
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title: [Warm-Up: What's an AST?],
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by: "Mark",
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subtitle: "Based on a true story.",
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)
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#problem()
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Say we have a valid string of simple arithmetic that contains \
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no unary operators (like $3!$ or $-4$) and no parenthesis:
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#v(2mm)
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$
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3 + 9 times 8 div 5 and 6
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$
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#v(2mm)
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You may assume that all numbers and operators in this string consist of exactly one character. \
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Devise an algorithm that turns such strings into a tree (as shown below), \
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respecting the order of operations $[and, times, div, +, -]$.
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#v(2mm)
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#align(center, cetz.canvas({
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import cetz.draw: *
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// spell:off
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content((0, 0), $+$, name: "r")
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content((-0.5, -1), $3$, name: "a")
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content((0.5, -1), $div$, name: "b")
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content((-0.3, -2), $times$, name: "ba")
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content((1.3, -2), $and$, name: "bb")
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content((-0.8, -3), $9$, name: "baa")
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content((0.2, -3), $8$, name: "bab")
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content((0.8, -3), $5$, name: "bba")
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content((1.8, -3), $6$, name: "bbb")
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// spell:on
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// Zero-sized arrows are a hack for offset.
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set-style(
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stroke: (thickness: 0.3mm),
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mark: (
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start: (
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symbol: "|",
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offset: 0.25,
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width: 0mm,
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length: 0mm,
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),
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end: (
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symbol: "|",
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offset: 0.25,
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width: 0mm,
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length: 0mm,
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),
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),
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)
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// spell:off
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line("r", "a")
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line("r", "b")
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line("b", "ba")
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line("b", "bb")
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line("ba", "baa")
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line("ba", "bab")
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line("bb", "bba")
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line("bb", "bbb")
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// spell:on
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}))
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