Fancy output; initial documentation

.gitignore

@@ -1,3 +1,4 @@
 /target
 **/*.rs.bk
-tmp*.svg
+tmp*.svg
+*.pdf

Cargo.lock

@@ -2,6 +2,7 @@
 name = "Aufgabe1"
 version = "0.1.0"
 dependencies = [
+ "chrono 0.4.6 (registry+https://github.com/rust-lang/crates.io-index)",
  "decorum 0.1.2",
  "geo 0.11.0",
  "svg 0.5.12 (registry+https://github.com/rust-lang/crates.io-index)",
@@ -44,6 +45,16 @@ name = "cfg-if"
 version = "0.1.6"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 
+[[package]]
+name = "chrono"
+version = "0.4.6"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+dependencies = [
+ "num-integer 0.1.39 (registry+https://github.com/rust-lang/crates.io-index)",
+ "num-traits 0.2.6 (registry+https://github.com/rust-lang/crates.io-index)",
+ "time 0.1.42 (registry+https://github.com/rust-lang/crates.io-index)",
+]
+
 [[package]]
 name = "decorum"
 version = "0.1.2"
@@ -96,6 +107,14 @@ name = "libc"
 version = "0.2.47"
 source = "registry+https://github.com/rust-lang/crates.io-index"
 
+[[package]]
+name = "num-integer"
+version = "0.1.39"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+dependencies = [
+ "num-traits 0.2.6 (registry+https://github.com/rust-lang/crates.io-index)",
+]
+
 [[package]]
 name = "num-traits"
 version = "0.2.6"
@@ -122,6 +141,11 @@ dependencies = [
  "proc-macro2 0.4.25 (registry+https://github.com/rust-lang/crates.io-index)",
 ]
 
+[[package]]
+name = "redox_syscall"
+version = "0.1.51"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+
 [[package]]
 name = "rstar"
 version = "0.1.1"
@@ -177,6 +201,16 @@ dependencies = [
  "unicode-xid 0.1.0 (registry+https://github.com/rust-lang/crates.io-index)",
 ]
 
+[[package]]
+name = "time"
+version = "0.1.42"
+source = "registry+https://github.com/rust-lang/crates.io-index"
+dependencies = [
+ "libc 0.2.47 (registry+https://github.com/rust-lang/crates.io-index)",
+ "redox_syscall 0.1.51 (registry+https://github.com/rust-lang/crates.io-index)",
+ "winapi 0.3.6 (registry+https://github.com/rust-lang/crates.io-index)",
+]
+
 [[package]]
 name = "unicode-xid"
 version = "0.1.0"
@@ -207,13 +241,16 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 "checksum backtrace-sys 0.1.28 (registry+https://github.com/rust-lang/crates.io-index)" = "797c830ac25ccc92a7f8a7b9862bde440715531514594a6154e3d4a54dd769b6"
 "checksum cc 1.0.28 (registry+https://github.com/rust-lang/crates.io-index)" = "bb4a8b715cb4597106ea87c7c84b2f1d452c7492033765df7f32651e66fcf749"
 "checksum cfg-if 0.1.6 (registry+https://github.com/rust-lang/crates.io-index)" = "082bb9b28e00d3c9d39cc03e64ce4cea0f1bb9b3fde493f0cbc008472d22bdf4"
+"checksum chrono 0.4.6 (registry+https://github.com/rust-lang/crates.io-index)" = "45912881121cb26fad7c38c17ba7daa18764771836b34fab7d3fbd93ed633878"
 "checksum failure 0.1.5 (registry+https://github.com/rust-lang/crates.io-index)" = "795bd83d3abeb9220f257e597aa0080a508b27533824adf336529648f6abf7e2"
 "checksum failure_derive 0.1.5 (registry+https://github.com/rust-lang/crates.io-index)" = "ea1063915fd7ef4309e222a5a07cf9c319fb9c7836b1f89b85458672dbb127e1"
 "checksum libc 0.2.47 (registry+https://github.com/rust-lang/crates.io-index)" = "48450664a984b25d5b479554c29cc04e3150c97aa4c01da5604a2d4ed9151476"
+"checksum num-integer 0.1.39 (registry+https://github.com/rust-lang/crates.io-index)" = "e83d528d2677f0518c570baf2b7abdcf0cd2d248860b68507bdcb3e91d4c0cea"
 "checksum num-traits 0.2.6 (registry+https://github.com/rust-lang/crates.io-index)" = "0b3a5d7cc97d6d30d8b9bc8fa19bf45349ffe46241e8816f50f62f6d6aaabee1"
 "checksum pdqselect 0.1.0 (registry+https://github.com/rust-lang/crates.io-index)" = "4ec91767ecc0a0bbe558ce8c9da33c068066c57ecc8bb8477ef8c1ad3ef77c27"
 "checksum proc-macro2 0.4.25 (registry+https://github.com/rust-lang/crates.io-index)" = "d3797b7142c9aa74954e351fc089bbee7958cebbff6bf2815e7ffff0b19f547d"
 "checksum quote 0.6.10 (registry+https://github.com/rust-lang/crates.io-index)" = "53fa22a1994bd0f9372d7a816207d8a2677ad0325b073f5c5332760f0fb62b5c"
+"checksum redox_syscall 0.1.51 (registry+https://github.com/rust-lang/crates.io-index)" = "423e376fffca3dfa06c9e9790a9ccd282fafb3cc6e6397d01dbf64f9bacc6b85"
 "checksum rstar 0.1.1 (registry+https://github.com/rust-lang/crates.io-index)" = "64ffe043929ee67d46694af1a4851f6bbe571b52a55677ba1686222dc35fd449"
 "checksum rustc-demangle 0.1.13 (registry+https://github.com/rust-lang/crates.io-index)" = "adacaae16d02b6ec37fdc7acfcddf365978de76d1983d3ee22afc260e1ca9619"
 "checksum serde 1.0.84 (registry+https://github.com/rust-lang/crates.io-index)" = "0e732ed5a5592c17d961555e3b552985baf98d50ce418b7b655f31f6ba7eb1b7"
@@ -221,6 +258,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
 "checksum svg 0.5.12 (registry+https://github.com/rust-lang/crates.io-index)" = "a863ec1f8e7cfd4ea449f77445cca06aac240b9a677ccf12b0f65ef020db52c7"
 "checksum syn 0.15.26 (registry+https://github.com/rust-lang/crates.io-index)" = "f92e629aa1d9c827b2bb8297046c1ccffc57c99b947a680d3ccff1f136a3bee9"
 "checksum synstructure 0.10.1 (registry+https://github.com/rust-lang/crates.io-index)" = "73687139bf99285483c96ac0add482c3776528beac1d97d444f6e91f203a2015"
+"checksum time 0.1.42 (registry+https://github.com/rust-lang/crates.io-index)" = "db8dcfca086c1143c9270ac42a2bbd8a7ee477b78ac8e45b19abfb0cbede4b6f"
 "checksum unicode-xid 0.1.0 (registry+https://github.com/rust-lang/crates.io-index)" = "fc72304796d0818e357ead4e000d19c9c174ab23dc11093ac919054d20a6a7fc"
 "checksum winapi 0.3.6 (registry+https://github.com/rust-lang/crates.io-index)" = "92c1eb33641e276cfa214a0522acad57be5c56b10cb348b3c5117db75f3ac4b0"
 "checksum winapi-i686-pc-windows-gnu 0.4.0 (registry+https://github.com/rust-lang/crates.io-index)" = "ac3b87c63620426dd9b991e5ce0329eff545bccbbb34f3be09ff6fb6ab51b7b6"

Cargo.toml

@@ -4,7 +4,11 @@ version = "0.1.0"
 authors = ["arne"]
 edition = "2018"
 
+[profile.release]
+codegen-units = 1
+
 [dependencies]
 geo = { path = "/home/arne/Documents/Code/Github/geo/geo" }
 svg = "0.5.11"
 decorum = { path = "/home/arne/Documents/Code/Github/decorum" }
+chrono = "0.4.6"

DokumentationAufgabe1.tex

@@ -0,0 +1,157 @@
+\documentclass[a4paper,10pt,ngerman]{scrartcl}
+\usepackage{babel}
+\usepackage[T1]{fontenc}
+\usepackage[a4paper,margin=2.5cm]{geometry}
+
+% automatische Quotes
+\usepackage{csquotes}
+\MakeOuterQuote{"}
+
+% Die nächsten drei Felder bitte anpassen:
+\newcommand{\Name}{Arne Keller} % Teamname oder eigenen Namen angeben
+\newcommand{\TeilnahmeId}{50966}
+\newcommand{\Aufgabe}{Aufgabe 1: Lisa rennt}
+
+% Kopf- und Fußzeilen
+\usepackage{scrlayer-scrpage, lastpage}
+\setkomafont{pageheadfoot}{\textrm}
+\lohead{\Aufgabe}
+\chead{\thepage{}/\pageref{LastPage}}
+\rohead{\Name/Teilnahme-Id: \TeilnahmeId}
+\cfoot{}
+
+% Für mathematische Befehle und Symbole
+\usepackage{amsmath,amsthm,amssymb}
+
+% Für Bilder
+\usepackage{graphicx,subcaption,float}
+\usepackage{tkz-euclide}
+\usetkzobj{all}
+
+% Für Algorithmen
+%\usepackage{algpseudocode}
+
+% Für Quelltext
+\usepackage{listings}
+\usepackage{color}
+\definecolor{mygreen}{rgb}{0,0.6,0}
+\definecolor{mygray}{rgb}{0.5,0.5,0.5}
+\definecolor{mymauve}{rgb}{0.58,0,0.82}
+\lstset{
+  keywordstyle=\color{blue},commentstyle=\color{mygreen},
+  stringstyle=\color{mymauve},rulecolor=\color{black},
+  basicstyle=\footnotesize\ttfamily,numberstyle=\tiny\color{mygray},
+  captionpos=b, % sets the caption-position to bottom
+  keepspaces=true, % keeps spaces in text
+  numbers=left, numbersep=5pt, showspaces=false,showstringspaces=false,
+  showtabs=false, stepnumber=2, tabsize=2, title=\lstname
+}
+\lstdefinelanguage{Rust}{
+  keywords={break, match, continue, else, for, fn, if, return, self, let, mut, loop, while, extern, crate, use, static, enum, struct, impl, as, type, derive, mod},
+  morecomment=[l]{//},
+  morecomment=[s]{/*}{*/},
+  morestring=[b]",
+  sensitive=true
+}
+
+% Diese beiden Pakete müssen als letztes geladen werden
+%\usepackage{hyperref} % Anklickbare Links im Dokument
+%\usepackage{cleveref}
+
+% Daten für die Titelseite
+\title{\Aufgabe}
+\author{\Name\\Teilnahme-ID: \TeilnahmeId}
+\date{29. April 2019}
+
+
+\begin{document}
+\maketitle
+\tableofcontents
+
+\section{Lösungsidee}
+Zunächst kann man feststellen, dass der letzte Abschnitt jeder Route zum Bus immer exakt gerade ist. In einer Kurve würde Lisa weiter laufen, ohne am Ende auf der y-Achse weiter zu sein. Es gibt keinen, einen oder zwei Treffpunkte, bei denen Lisa (ohne zu warten) den Bus erwischt:
+
+\begin{figure}[H]
+\centering
+\begin{subfigure}{.33\textwidth}
+	\centering
+	\begin{tikzpicture}
+		\tkzInit[xmax=3.5,ymax=7.5]
+		\tkzAxeXY
+		\tkzGrid
+		\tkzDefPoint(0,0){B}
+		\tkzDefPoint(1.25,3.5){L}
+		\tkzDefPoint(0,2.83333){M1}
+		\tkzDefPoint(0,6.5){M2}
+
+		\tkzDrawSegment(L,M1)
+		\tkzDrawSegment(L,M2)
+		\tkzDrawPoints(B,L,M1,M2)
+
+		\tkzLabelPoints(B,L,M1,M2)
+	\end{tikzpicture}
+	\caption{Zwei Treffpunkte}
+	\label{abb:fall1}
+\end{subfigure}%
+\begin{subfigure}{.33\textwidth}
+	\centering
+	\begin{tikzpicture}
+		\tkzInit[xmax=3.5,ymax=7.5]
+		\tkzAxeXY
+		\tkzGrid
+		\tkzDefPoint(0,0){B}
+		\tkzDefPoint(2.020725942,3.5){L}
+		\tkzDefPoint(0,4.614){M}
+
+		\tkzDrawSegment(L,M)
+		\tkzDrawPoints(B,L,M)
+
+		\tkzLabelPoints[yshift=14pt](M)
+		\tkzLabelPoints(B,L)
+	\end{tikzpicture}
+	\caption{Ein Treffpunkt}
+	\label{abb:fall1}
+\end{subfigure}%
+\begin{subfigure}{.33\textwidth}
+	\centering
+	\begin{tikzpicture}
+		\tkzInit[xmax=3.5,ymax=7.5]
+		\tkzAxeXY
+		\tkzGrid
+		\tkzDefPoint(0,0){B}
+		\tkzDefPoint(3,3.5){L}
+
+		\tkzDrawPoints(B,L)
+
+		\tkzLabelPoints(B,L)
+	\end{tikzpicture}
+	\caption{Kein Treffpunkt}
+	\label{abb:fall1}
+\end{subfigure}
+\caption{Mögliche Treffpunktanzahlen}
+\label{fig:treffpunkte}
+\end{figure}
+
+\begin{proof}
+	Sei Lisa bei $L(x_{L},y_{L})$ und der Bus bei $B(x_{B},y_{B})$. $M(x_{M},y_{M})$ sei der Treffpunkt von Lisa mit dem Bus. $d$ sei der Weg, den Lisa zu diesem Punkt geht.
+	\begin{align*}
+		d &= \sqrt{(x_{L}-x_{M})^2 + (y_{L}-y_{M})^2} &&\text{(Satz des Pythagoras)} \\
+		&= \sqrt{x_{L}^2 + (y_{L}-y_{M})^2} &&\text{($x_{B} = x_{M} = 0$)} \\
+		d^2 &= x_{L}^2 + (y_{L}-y_{M})^2 \\
+		&= x_{L}^2 + (y_{L}-y_{B}-2d)^2 &&\text{($y_{M} = y_{B} + 2d$)} \\
+		&= x_{L}^2 + y_{L}^2 + y_{B}^2 + 4d^2 - 2y_{B}y_{M} - 4dy_{L} + 4dy_{B} \\
+		-3d^2 + 4\cdot(y_{B}-y_{L})\cdot{}d &= x_{L}^2 + y_{L}^2 + y_{B}^2 - 2y_{B}y_{M} \\
+		d &= \frac{a\pm\sqrt{a^2 + 12\cdot{}(-x_{L}^2 - y_{L}^2 - y_{B}^2 + 2y_{B}y_{M})}}{-6} &&\text{($a = 4\cdot(y_{B}-y_{L})$)}\qedhere
+	\end{align*}
+\end{proof}
+
+Für diese Gleichung gibt es maximal zwei nicht-negative Lösungen.
+
+\section{Umsetzung}
+
+\section{Beispiele}
+
+\section{Quellcode}
+\lstinputlisting[frame=single,language=Rust,breaklines=true]{src/main.rs}
+
+\end{document}

src/display.rs

@@ -4,17 +4,49 @@ use svg::node::element::{AnimateMotion, Circle, MotionPath};
 use svg::Document;
 use svg::Node;
 
-use std::io;
+use std::fs;
 
 use super::*;
 
-pub(crate) fn dump_svg(
+pub(crate) fn dump_route(house: Point, polys: &[Polygon], route: &Vec<RunState>) {
+	let (points, lines, route1, route2_start) = gen_params(house, route);
+	print!("{}", generate_svg(&points, &lines, polys, &route1, route2_start));
+}
+
+pub(crate) fn save_svg(filename: &str, house: Point, polys: &[Polygon], route: &Vec<RunState>) {
+	let (points, lines, route1, route2_start) = gen_params(house, route);
+	fs::write(filename, generate_svg(&points, &lines, polys, &route1, route2_start)).unwrap();
+}
+
+fn gen_params(house: Point, route: &Vec<RunState>) -> (Vec<(Point, &'static str)>, Vec<(Line, &'static str)>, Vec<Point>, Point) {
+	let first = route.first().unwrap();
+	let last = route.last().unwrap();
+	let best_delay = last.delay;
+	let points = vec![
+		(house, "red"),
+		(first.bus.translate(0.0.into(), best_delay), "yellow"),
+		(last.bus, "orange"),
+	];
+	let lines = route
+		.iter()
+		.map(|x| x.pos)
+		.collect::<LineString>()
+		.lines()
+		.map(|x| (x, "gray"))
+		.collect::<Vec<_>>();
+
+	let route1 = route.iter().map(|x| x.pos).collect::<Vec<_>>();
+	let route2_start = first.bus.translate(0.0.into(), best_delay);
+	(points, lines, route1, route2_start)
+}
+
+pub(crate) fn generate_svg(
 	points: &[(Point, &'static str)],
 	lines: &[(Line, &'static str)],
 	polys: &[Polygon],
 	route1: &[Point],
 	route2_start: Point,
-) {
+) -> String {
 	let mut document = Document::new()
 		// view box at (0, -200), w*h (200, 200)
 		.set("viewBox", (0, -1100, 2100, 2100))
@@ -125,5 +157,5 @@ pub(crate) fn dump_svg(
 	dot1.append(motion1);
 	document.append(dot1);
 
-	svg::write(io::stdout(), &document).unwrap();
+	document.to_string()
 }

src/main.rs

@@ -1,23 +1,25 @@
 use geo::prelude::*;
 
+use chrono::{Duration, NaiveTime};
+
 use std::cmp;
 use std::collections::BinaryHeap;
 
 mod display;
 mod input;
 
-type Point = geo::Point<f32>;
+type Point = geo::Point<f64>;
-type Line = geo::Line<f32>;
+type Line = geo::Line<f64>;
-type LineString = geo::LineString<f32>;
+type LineString = geo::LineString<f64>;
-type Polygon = geo::Polygon<f32>;
+type Polygon = geo::Polygon<f64>;
 
-// 30 km/h = 1 units/unit
+// 30 km/h = 8+1/3 meters/second
-// 15 km/h = 0.5 units/unit
+// 15 km/h = 4+1/6 meters/second
 
 #[derive(Debug, Clone, PartialEq)]
 struct RunState {
 	/// Theoretically possible maximum delay
-	delay: f32,
+	delay: f64,
 	/// Our current location
 	pos: Point,
 	/// Current location of the bus, not including any delays
@@ -36,7 +38,11 @@ impl cmp::PartialOrd for RunState {
 }
 
 fn main() {
-	let bus = Point::new(0.0, -2000.0);
+	// starting at 07:00, bus is 15 km away
+	let start_time = NaiveTime::from_hms(7, 0, 0);
+	let bus = Point::new(0.0, -15000.0);
+	let bus_speed = 30.0 / 3.6;
+	let delay_to_time = |delay| start_time + Duration::seconds((delay / bus_speed) as i64);
 
 	let data = input::read_input();
 	let house = data.start;
@@ -58,25 +64,27 @@ fn main() {
 		delay: max_possible_delay(bus, house),
 	};
 
-	eprintln!("# Max. delay possible: {:?}", start.delay);
+	eprintln!("# Max. delay possible: {:?}", delay_to_time(start.delay));
 
 	let mut states = BinaryHeap::new();
 	states.push(vec![start]);
 
 	let mut best_delay = 0.0;
 	let mut best = vec![];
+	let save_prefix = "tmp3_";
+	let mut save_counter = 0;
 
 	while states.peek().map(|x| x[0].delay > best_delay) == Some(true) {
-		eprintln!(". {:?} states left:", states.len());
+		//eprintln!(". {:?} states left:", states.len());
 		let s = states.pop().unwrap();
 		let last = &s[0]; //s.last().unwrap();
-		eprintln!("{},{}", last.pos.x(), last.pos.y());
+		//eprintln!("{},{}", last.pos.x(), last.pos.y());
 
 		// new states
 		let mut all = vec![];
 
 		// attempt to go to any other vertex/point
-		for next in &points {
+		for next in points.iter().filter(|next| !s.iter().any(|x| x.pos == (**next).into())) {
 			let next = Point::from(*next);
 			if next != last.pos && none_intersect(&polys, &Line::new(last.pos, next)) {
 				// could run to that point
@@ -94,82 +102,58 @@ fn main() {
 				all.push(route);
 			}
 		}
-		// attempt to go to the bus, with varying delays
+		// attempt to go to the bus
-		let mut bus_reached = false;
+		let bus = last.bus;
-		for delay in float_range(last.delay.into(), 0.0) {
+		let range = to_bus(bus, last.pos);
-			let bus = last.bus.translate(0.0.into(), delay);
+		if range.len() == 2 {
-			let range = to_bus(bus, last.pos);
+			let range = Line::new(range[0], range[1]);
-			if range.len() == 2 {
+			for percent in float_range(0.0, 1.0) {
-				bus_reached = true; // TODO: what if effectively unreachable?
+				let mut next = range.start;
-				let range = Line::new(range[0], range[1]);
+				next.x += range.dx() * percent;
-				for percent in float_range(0.0, 1.0) {
+				next.y += range.dy() * percent;
-					let mut next = range.start;
+				let next = Point::from(next);
-					next.x += range.dx() * percent;
+				let line = Line::new(last.pos, next);
-					next.y += range.dy() * percent;
+				if none_intersect(&polys, &line) {
-					let next = Point::from(next);
+					let delay = line.end.y - bus.y() - line.end_point().euclidean_distance(&line.start_point()) * 2.0;
-					if none_intersect(&polys, &Line::new(last.pos, next)) {
+					if delay > best_delay {
-						if delay > best_delay {
+						// new high score!
-							// new high score!
+						let mut route = s.clone();
-							let mut route = s.clone();
+						route.insert(
-							route.insert(
+							0,
-								0,
+							RunState {
-								RunState {
+								pos: next,
-									pos: next,
+								bus: next,
-									bus: next,
+								delay,
-									delay,
+							},
-								},
+						);
-							);
+						eprintln!("# New best delay {:?} ({:?} states left)", delay_to_time(delay), states.len());
-							eprintln!("# New best delay {:?}", delay);
+						best = route;
-							best = route;
+						best.reverse();
-							best.reverse();
+						best_delay = delay;
-							best_delay = delay;
+						display::save_svg(&format!("{}{}.svg", save_prefix, save_counter), house, &polys, &best);
-						} else {
+						save_counter += 1;
-							// not worth it
+					} else {
-						}
+						// not worth it
 					}
 				}
 			}
-		}
-		if bus_reached {
-			//eprintln!("-> adding all to queue");
 			states.extend(all);
 		}
 	}
-	eprintln!("d = {:?}", best_delay);
+	eprintln!("d = {:?}", delay_to_time(best_delay));
 	let route = best;
 	eprintln!("Route:");
 	for s in &route {
 		eprintln!("{:.02},{:.02}", s.pos.x(), s.pos.y());
 	}
-	let first = route.first().unwrap();
+	display::dump_route(house, &polys, &route);
-	let last = route.last().unwrap();
-	let points = vec![
-		(house, "red"),
-		(first.bus.translate(0.0.into(), best_delay), "yellow"),
-		(last.bus, "orange"),
-	];
-	let lines = route
-		.iter()
-		.map(|x| x.pos)
-		.collect::<LineString>()
-		.lines()
-		.map(|x| (x, "gray"))
-		.collect::<Vec<_>>();
-
-	display::dump_svg(
-		&points,
-		&lines,
-		&polys,
-		&route.iter().map(|x| x.pos).collect::<Vec<_>>(),
-		first.bus.translate(0.0.into(), best_delay),
-	);
 }
 
 /// [a; b]
-fn float_range(a: f32, b: f32) -> impl Iterator<Item = f32> {
+fn float_range(a: f64, b: f64) -> impl Iterator<Item = f64> {
-	const STEPS: usize = 25;
+	const STEPS: usize = 1000;
 	let d = b - a;
-	(0..=STEPS).map(move |s| a + ((s as f32) * d) / STEPS as f32)
+	(0..=STEPS).map(move |s| a + ((s as f64) * d) / STEPS as f64)
 }
 
 fn none_intersect(polys: &[Polygon], line: &Line) -> bool {
@@ -236,11 +220,11 @@ fn none_intersect(polys: &[Polygon], line: &Line) -> bool {
 	true
 }
 
-fn distance(a: Point, b: Point) -> f32 {
+fn distance(a: Point, b: Point) -> f64 {
 	((a.x() - b.x()).powi(2) + (a.y() - b.y()).powi(2)).sqrt()
 }
 
-fn max_possible_delay(bus: Point, start: Point) -> f32 {
+fn max_possible_delay(bus: Point, start: Point) -> f64 {
 	let a = start.x();
 	let b = start.y();
 	let c = bus.x();