Edge cases, more comments and formatting
This commit is contained in:
Arne Keller
parent
56a613fb88
commit
573788fbfc
@ -82,7 +82,13 @@ pub(crate) fn dump_route(opt: Opt, house: Point, polys: &[Polygon], route: &[Run
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);
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}
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pub(crate) fn save_svg(opt: Opt, filename: &str, house: Point, polys: &[Polygon], route: &[RunState]) {
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pub(crate) fn save_svg(
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opt: Opt,
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filename: &str,
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house: Point,
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polys: &[Polygon],
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route: &[RunState],
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) {
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let (points, lines, route1, route2_start) = gen_params(opt, house, route);
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fs::write(
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filename,
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@ -103,9 +109,7 @@ fn gen_params(
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Point,
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) {
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let last = route.last().unwrap();
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let points = vec![
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(house, "red"),
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];
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let points = vec![(house, "red")];
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let lines = route
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.iter()
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.map(|x| x.pos)
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@ -115,7 +119,9 @@ fn gen_params(
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.collect::<Vec<_>>();
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let route1 = route.iter().map(|x| x.pos).collect::<Vec<_>>();
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let route2_start = last.pos.translate(0.0, -last.total_distance * (opt.bus/opt.lisa));
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let route2_start = last
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.pos
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.translate(0.0, -last.total_distance * (opt.bus / opt.lisa));
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(points, lines, route1, route2_start)
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}
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@ -127,8 +133,25 @@ pub(crate) fn generate_svg(
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route2_start: Point,
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) -> String {
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let dot_radius = 25.2;
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let width = route1.iter().map(|p| p.x()).chain(polys.iter().map(|x| x.exterior().0.iter().map(|p| p.x)).flatten()).max_by(|a, b| a.partial_cmp(b).unwrap()).unwrap() + dot_radius * 2.0;
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let upper_y = polys.iter().map(|x| x.exterior().0.iter().map(|p| p.y)).flatten().chain(Some(route1.last().unwrap().y())).max_by(|a, b| a.partial_cmp(b).unwrap()).unwrap();
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let width = route1
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.iter()
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.map(|p| p.x())
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.chain(
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polys
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.iter()
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.map(|x| x.exterior().0.iter().map(|p| p.x))
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.flatten(),
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)
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.max_by(|a, b| a.partial_cmp(b).unwrap())
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.unwrap()
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+ dot_radius * 2.0;
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let upper_y = polys
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.iter()
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.map(|x| x.exterior().0.iter().map(|p| p.y))
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.flatten()
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.chain(Some(route1.last().unwrap().y()))
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.max_by(|a, b| a.partial_cmp(b).unwrap())
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.unwrap();
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let mut document = Document::new()
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// view box at (x,y), (w,h)
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.set(
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@ -137,8 +160,8 @@ pub(crate) fn generate_svg(
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-dot_radius,
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-upper_y - dot_radius,
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width,
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-route2_start.y() + upper_y + dot_radius * 2.0
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)
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-route2_start.y() + upper_y + dot_radius * 2.0,
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),
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)
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.set("xmlns:xlink", "http://www.w3.org/1999/xlink");
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32
src/input.rs
32
src/input.rs
@ -60,43 +60,19 @@ fn read_stdin() -> InputData {
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fn _custom_input() -> InputData {
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let mut polys = vec![];
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polys.push(Polygon::new(
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vec![
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[2.0, 0.0],
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[6.0, 0.0],
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[6.0, 6.0],
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[2.0, 5.0],
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]
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.into(),
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vec![[2.0, 0.0], [6.0, 0.0], [6.0, 6.0], [2.0, 5.0]].into(),
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vec![],
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));
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polys.push(Polygon::new(
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vec![
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[1.0, 20.0],
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[2.0, 20.0],
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[2.0, 23.0],
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[1.0, 23.0],
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]
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.into(),
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vec![[1.0, 20.0], [2.0, 20.0], [2.0, 23.0], [1.0, 23.0]].into(),
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vec![],
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));
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polys.push(Polygon::new(
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vec![
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[1.0, 25.0],
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[2.0, 25.0],
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[2.0, 28.0],
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[1.0, 28.0],
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]
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.into(),
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vec![[1.0, 25.0], [2.0, 25.0], [2.0, 28.0], [1.0, 28.0]].into(),
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vec![],
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));
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let mut stick = Polygon::new(
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vec![
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[1.0, 115.0],
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[2.0, 115.0],
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[2.0, 130.0],
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[1.0, 130.0],
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]
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.into(),
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vec![[1.0, 115.0], [2.0, 115.0], [2.0, 130.0], [1.0, 130.0]].into(),
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vec![],
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);
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polys.push(stick.clone());
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96
src/main.rs
96
src/main.rs
@ -7,6 +7,7 @@ use structopt::StructOpt;
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use std::cmp;
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use std::collections::BinaryHeap;
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use std::f64;
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use std::process::exit;
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mod display;
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mod input;
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@ -16,6 +17,7 @@ type Line = geo::Line<f64>;
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type LineString = geo::LineString<f64>;
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type Polygon = geo::Polygon<f64>;
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/// Datenstruktur für Kommandozeilen-Argumente
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#[derive(StructOpt, Clone, Copy)]
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#[structopt(name = "aufgabe1", about = "Implementierung für Aufgabe 1")]
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struct Opt {
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@ -36,19 +38,21 @@ struct Opt {
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bus: f64,
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}
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/// Möglicher Zustand von Lisas Rennen
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#[derive(Debug, Clone, Copy, PartialEq)]
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struct RunState {
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/// Theoretisch mögliche Wartezeit
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delay: f64,
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/// Theoretisch mögliche Startposition des Busses
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bus: f64,
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/// Lisas Position
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pos: Point,
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// Bisher zurückgelegte Strecke
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total_distance: f64,
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}
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/// Trait-Implementierung, damit die Struktur in BinaryHeaps passt
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impl cmp::Eq for RunState {}
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impl cmp::Ord for RunState {
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fn cmp(&self, other: &Self) -> cmp::Ordering {
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self.delay.partial_cmp(&other.delay).unwrap()
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self.bus.partial_cmp(&other.bus).unwrap()
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}
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}
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impl cmp::PartialOrd for RunState {
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@ -60,13 +64,30 @@ impl cmp::PartialOrd for RunState {
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fn main() {
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// Kommandozeilen-Argumente einlesen
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let opt = Opt::from_args();
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// (unwahrscheinlich)
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if opt.lisa >= opt.bus {
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eprintln!("Lisa sollte lieber zur Schule rennen, als den Bus zu nehmen.");
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exit(1);
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}
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// (noch unwahrscheinlicher)
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if opt.bus <= 0.0 {
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if opt.lisa > 0.0 {
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eprintln!("Lisa sollte lieber zur Schule rennen, da der Bus vermutlich eine Panne hat oder im Rückwärtsgang ist.");
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} else {
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eprintln!("Lisa kann nicht laufen.");
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}
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exit(1);
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} else if opt.lisa <= 0.0 {
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eprintln!("Lisa muss den Busfahrer bitten, zu ihrem Haus zu fahren.");
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exit(1);
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}
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// Geschwindigkeiten in m/s umrechnen
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let bus_speed = opt.bus / 3.6;
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let lisa_speed = opt.lisa / 3.6;
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// Startzeitpunkt berechnen
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let calc_time = |total_distance, y| {
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NaiveTime::from_hms(7, 30, 0)
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- Duration::seconds(((total_distance * (opt.bus/opt.lisa) - y) / bus_speed) as i64)
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- Duration::seconds(((total_distance * (opt.bus / opt.lisa) - y) / bus_speed) as i64)
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};
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// Ankuftszeit berechnen
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let calc_end_time = |total_distance, y| {
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@ -88,12 +109,15 @@ fn main() {
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// Startzustand: Lisa ist an ihrem Haus, zurückgelegte Distanz ist Null
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let start = RunState {
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pos: house,
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delay: max_possible_delay(&opt, 0.0, house),
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bus: best_bus_pos(&opt, 0.0, house),
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total_distance: 0.0,
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};
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// bestmöglicher Fall: Lisa geht direkt zum Bus
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let meeting_point = Point::new(0.0, house.y() + (opt.lisa/opt.bus).asin().tan() * house.x());
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let meeting_point = Point::new(
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0.0,
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house.y() + (opt.lisa / opt.bus).asin().tan() * house.x(),
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);
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eprintln!(
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"Theoretisches Maximum: {:?}",
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calc_time(distance(meeting_point, house), meeting_point.y())
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@ -104,14 +128,14 @@ fn main() {
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states.push(vec![start]);
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// beste Lösung speichern
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let mut best_delay = f64::NEG_INFINITY;
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let mut best_bus = f64::NEG_INFINITY;
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let mut best = vec![];
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// Zwischenlösungen speichern
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let save_prefix = "tmp_";
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let save_prefix = "route_";
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let mut save_counter = 0;
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// weitersuchen, bis kein besserer Zustand mehr vorhanden ist
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while states.peek().map(|x| x[0].delay > best_delay) == Some(true) {
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while states.peek().map(|x| x[0].bus > best_bus) == Some(true) {
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// besten Zustand einlesen
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let state = states.pop().unwrap();
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let last = &state[0];
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@ -132,14 +156,15 @@ fn main() {
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{
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// Lisa könnte zu dieser Ecke rennen
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let total_distance = last.total_distance + distance(last.pos, next);
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let delay = max_possible_delay(&opt, total_distance, next);
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if delay > best_delay {
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let bus = best_bus_pos(&opt, total_distance, next);
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// theoretisch möglicher Startzeitpunkt ist nach bestem gefundenem Startzeitpunkt
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if bus > best_bus {
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let mut route = state.clone();
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route.insert(
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0,
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RunState {
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pos: next,
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delay,
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bus,
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total_distance,
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},
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);
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@ -147,29 +172,29 @@ fn main() {
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}
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}
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// versuche, direkt zum Bus zu gehen
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// Lisa trifft Bus mit 60°-Winkel
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// Lisa trifft Bus in einem bestimmten Winkel (meist 60°)
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let next = Point::new(
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0.0,
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last.pos.y() + (opt.lisa/opt.bus).asin().tan() * last.pos.x(),
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last.pos.y() + (opt.lisa / opt.bus).asin().tan() * last.pos.x(),
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);
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let line = Line::new(last.pos, next);
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// freier Weg?
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if none_intersect(&polys, &line) {
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let line_length = line.end_point().euclidean_distance(&line.start_point());
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let total_distance = last.total_distance + line_length;
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let delay = max_possible_delay(&opt, total_distance, line.end_point());
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if delay > best_delay {
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let bus = best_bus_pos(&opt, total_distance, line.end_point());
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if bus > best_bus {
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// neue beste Wartezeit
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let mut route = state.clone();
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route.insert(
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0,
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RunState {
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pos: next,
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delay,
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bus,
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total_distance,
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},
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);
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// Verbesserung anzeigen und speichern
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// Verbesserung anzeigen und evtl. speichern
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eprintln!(
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"Verbesserung: {:?} ({:?}+ Möglichkeiten verbleiben)",
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calc_time(total_distance, line.end.y),
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@ -177,7 +202,7 @@ fn main() {
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);
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best = route;
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best.reverse();
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best_delay = delay;
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best_bus = bus;
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if opt.save_intermediates {
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display::save_svg(
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opt,
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@ -233,12 +258,15 @@ fn main() {
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}
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}
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/// Schneidet die Linie keines der Polygone?
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/// (Berührungen erlaubt)
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fn none_intersect(polys: &[Polygon], line: &Line) -> bool {
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let mut middle = line.start;
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middle.x += line.dx() / 2.0;
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middle.y += line.dy() / 2.0;
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let middle: Point = middle.into();
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'poly: for p in polys {
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// Alle Seitenlinien des Polygons
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for l in p.exterior().lines().chain(vec![Line::new(
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p.exterior().0[0],
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*p.exterior().0.last().unwrap(),
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@ -246,7 +274,7 @@ fn none_intersect(polys: &[Polygon], line: &Line) -> bool {
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if (l.start == line.start && l.end == line.end)
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|| (l.start == line.end && l.end == line.start)
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{
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// point is on polygon border
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// Linie liegt auf Kante des Polygons
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continue 'poly;
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}
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if l.start == line.start
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@ -254,25 +282,43 @@ fn none_intersect(polys: &[Polygon], line: &Line) -> bool {
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|| l.start == line.end
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|| l.end == line.start
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{
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continue; // would always intersect with itself
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continue; // Linie schneidet sich immer selbst
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}
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if l.intersects(line) {
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return false;
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}
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}
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// falls Mittelpunkt in Polygon:
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if p.euclidean_distance(&middle) == 0.0 {
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// schneidet Polygon
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return false;
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}
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// (dieser Fall tritt auf, wenn die Linie von einer Polygon-Ecke zu einer anderen Ecke verläuft)
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}
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true
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}
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/// Euklidische Distanz zweier Punkte
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fn distance(a: Point, b: Point) -> f64 {
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((a.x() - b.x()).powi(2) + (a.y() - b.y()).powi(2)).sqrt()
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}
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fn max_possible_delay(opt: &Opt, total_distance: f64, lisa: Point) -> f64 {
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let x_l = lisa.x();
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let y_l = lisa.y();
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y_l - (((opt.bus/opt.lisa).powi(2) - 1.0) * x_l.powi(2)).sqrt() - total_distance * (opt.bus/opt.lisa)
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/// Mit dieser Funktion kann man bestimmen, wo der Bus zu Lisas Startzeit war.
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/// Die Funktion nimmt an, dass Lisa, von ihrer aktuellen Position aus, den Bus ohne Umwege erreichen kann.
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/// Sehr hilfreich als Heuristik, da sie nie schlechter als das eigentliche Ergebnis sein kann.
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fn best_bus_pos(opt: &Opt, total_distance: f64, lisa: Point) -> f64 {
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let x_l = lisa.x(); // a
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let y_l = lisa.y(); // b
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// y-Koordinate des Busses: d
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// Länge, die Lisa noch laufen muss: l
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// Verhältnis beider Geschwindigkeiten: x = bus / lisa
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// l^2 = sqrt(a^2 + (b - xl - d)^2)
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// die quadratische Gleichung hat zwei Lösungen (siehe Dok.)
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// nach der ABC-Formel muss b^2 - 4ac = 0 sein, damit die Gleichung nur eine Lösung hat:
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// (2xb-2xd)^2 - 4*((1-x^2)*(-a^2-b^2-d^2+2bd)) = 0
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// (eine WolframAlpha-Eingabe später..)
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// d = sqrt(a^2 * (x^2 - 1)) + b
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// in dieser Berechnung wird auch die bereits zurückgelegte Strecke berücksichtigt:
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y_l - (((opt.bus / opt.lisa).powi(2) - 1.0) * x_l.powi(2)).sqrt()
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- total_distance * (opt.bus / opt.lisa)
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}
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