#627535 (Rust) No.199 星を描こう

提出ソース
結果

問題	No.199 星を描こう
コンテスト
ユーザー	nebocco
提出日時	2021-03-11 19:30:03
言語	Rust (1.83.0 + proconio)
結果	AC
実行時間	1 ms / 2,000 ms
コード長	14,648 bytes
コンパイル時間	12,470 ms
コンパイル使用メモリ	404,080 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-10-13 07:14:45
合計ジャッジ時間	13,862 ms
ジャッジサーバーID （参考情報）	judge5 / judge2
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 3
other	AC * 25
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ソースコード

raw source code
fn main() {
	let mut io = IO::new();
    input!{ from io,
		ps: [(f64, f64); 5]
    }
	let pl = ps.iter().map(|&(x, y)| Point::new(x, y)).collect::<Vec<Point>>();
    io.println(
		if convex_hull(&pl).len() == 5 {
			"YES"
		} else {
			"NO"
		}
	);
}

pub fn convex_hull(points: &[Point]) -> Vec<Point> {
	let mut l = points.to_owned();
	l.sort_by(|x, y| x.x().partial_cmp(&y.x()).unwrap());
	let mut res1: Vec<Point> = Vec::new();
	let mut res2: Vec<Point> = Vec::new();
	for &x in &l {
		while res1.len() > 1 && res1[res1.len() - 2].area(&res1[res1.len() - 1], &x) <= 0. {
			res1.pop();
		}
		res1.push(x);
	}
	res1.pop();
	for &x in l.iter().rev() {
		while res2.len() > 1 && res2[res2.len() - 2].area(&res2[res2.len() - 1], &x) <= 0. {
			res2.pop();
		}
		res2.push(x);
	}
	res2.pop();
	res1.extend_from_slice(&res2);
	res1
}

// ------------ geometry start ------------

#[derive(Clone, Copy)]
pub struct Point(f64, f64);

impl Point {
    pub const EPS: f64 = 0.000_000_001;

    pub fn new<T: Into<f64>>(x: T, y: T) -> Self {
        Self(x.into(), y.into())
    }

    #[inline]
    pub fn x(&self) -> f64 { self.0 }

    #[inline]
    pub fn y(&self) -> f64 { self.1 }

    #[inline]
    pub fn arg(&self) -> f64 {
        self.1.atan2(self.0)
    }

    #[inline]
    pub fn norm(&self) -> f64 {
        (self.0.powi(2) + self.1.powi(2)).sqrt()
    }

    #[inline]
    pub fn dist(&self, rhs: &Self) -> f64 {
        (self - rhs).norm()
    }

    #[inline]
    pub fn unit(&self) -> Self {
        assert!(!self.is_zero(), "ゼロベクトルに法線はありませんよ？");
        let d = self.norm();
        Self(self.0 / d, self.1 / d)
    }

    #[inline]
    pub fn normal(&self) -> Self {
        Self(-self.1, self.0)
    }

    #[inline]
    pub fn dot(&self, rhs: &Self) -> f64 {
        self.0 * rhs.0 + self.1 * rhs.1
    }

    #[inline]
    pub fn cross(&self, rhs: &Self) -> f64 {
        self.0 * rhs.1 - self.1 * rhs.0
    }

    #[inline]
    pub fn area(&self, p: &Self, q: &Self) -> f64 {
        (p - self).cross(&(q - self))
    }

    #[inline]
    pub fn rotate(&self, theta: f64) -> Self {
        Self (
            self.0 * theta.cos() - self.1 * theta.sin(),
            self.0 * theta.sin() + self.1 * theta.cos(),
        )
    }
}

pub struct Line(Point, Point);

impl Line {
    pub fn new(p: Point, q: Point) -> Self {
        Self(p, q)
    }

    /// a * x + b * y = c
    pub fn from_equation(a: f64, b: f64, c: f64) -> Self {
        assert!(a.abs() < Point::EPS || a.abs() < Point::EPS, "不当な式ではありませんか？");
        if a.abs() < Point::EPS {
            Self(Point::new(0., c / b), Point::new(1., c / b))
        } else if b.abs() < Point::EPS {
            Self(Point::new(c / a, 0.), Point::new(c / a, 1.))
        } else {
            Self(Point::new(0., c / b), Point::new(c / a, 0.))
        }
    }

    #[inline]
    pub fn projection(&self, p: &Point) -> Point {
        self.0 + (self.0 - self.1) * Point::new(
            (p - self.0).dot(&(self.0 - self.1)) / (self.0 - self.1).norm(),
            0.
        )
    }

    #[inline]
    pub fn reflection(&self, p: &Point) -> Point {
        p + (self.projection(p) - p) * Point::new(2., 0.)
    }

    #[inline]
    pub fn is_orthogonal(&self, rhs: &Self) -> bool {
        (self.1 - self.0).dot(&(rhs.1 - rhs.0)) < Point::EPS
    }

    #[inline]
    pub fn is_parallel(&self, rhs: &Self) -> bool {
        (self.1 - self.0).cross(&(rhs.1 - rhs.0)) < Point::EPS
    }

    pub fn crosspoint(&self, rhs: &Self) -> Option<Point> {
        let d1 = (self.1 - self.0).cross(&(rhs.1 - rhs.0));
        let d2 = (self.1 - self.0).cross(&(rhs.1 - rhs.0));
        if self.is_parallel(rhs) {
            if d1.abs() < Point::EPS && d2.abs() < Point::EPS {
                Some(self.0)
            } else {
                None
            }
        } else {
            Some(rhs.0 + (rhs.1 - rhs.0) * Point::new(d2 / d1, 0.))
        }

    }
}

pub struct Circle {
    pub center: Point,
    pub radius: f64,
}

impl Circle {
    pub fn new<T: Into<f64>>(x: T, y: T, r: T) -> Self {
        Self {
            center: Point::new(x, y),
            radius: r.into()
        }
    }
    #[allow(unused_variables)]
    pub fn intersection(&self, rhs: &Self) -> (Option<Point>, Option<Point>) {
        todo!()
    }
}

// ------------ impl arith start ------------

use std::fmt;

impl fmt::Debug for Point {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "({:.6}, {:.6})", self.x(), self.y())
    }
}

impl fmt::Display for Point {
    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
        write!(f, "({:.6}, {:.6})", self.x(), self.y())
    }
}

impl PartialEq for Point {
    fn eq(&self, rhs: &Self) -> bool {
        (self.0 - rhs.0).abs() < Self::EPS &&
        (self.1 - rhs.1).abs() < Self::EPS
    }
}

impl Eq for Point {}

impl PartialOrd for Point {
    fn partial_cmp(&self, rhs: &Self) -> Option<std::cmp::Ordering> {
        Some(self.cmp(rhs))
    }
}

impl Ord for Point {
    fn cmp(&self, rhs: &Self) -> std::cmp::Ordering {
        if let Some(v) = self.arg().partial_cmp(&rhs.arg()) {
            v
        } else {
            std::cmp::Ordering::Equal
        }
    }
}

impl Add for Point {
    type Output = Point;
    fn add(self, rhs: Self) -> Self {
        Self(self.0 + rhs.0, self.1 + rhs.1)
    }
}

impl Sub for Point {
    type Output = Point;
    fn sub(self, rhs: Self) -> Self {
        Self(self.0 - rhs.0, self.1 - rhs.1)
    }
}

impl Mul for Point {
    type Output = Point;
    fn mul(self, rhs: Self) -> Self {
        Self(
            self.0 * rhs.0 - self.1 * rhs.1,
            self.0 * rhs.1 + self.1 * rhs.0
        )
    }
}

#[allow(clippy::suspicious_arithmetic_impl)]
impl Div for Point {
    type Output = Point;
    fn div(self, rhs: Self) -> Self {
		assert!(!rhs.is_zero(), "ゼロベクトルで割ろうとしていませんか？");
		let d = rhs.0.powi(2) + rhs.1.powi(2);
        Self(
            (self.0 * rhs.0 - self.1 * -rhs.1) / d,
            (self.0 * -rhs.1 + self.1 * rhs.0) / d
        )
    }
}

impl Zero for Point {
    fn zero() -> Self {
        Self(0., 0.)
    }
}

impl<'a> Zero for &'a Point {
    fn zero() -> &'a Point {
        &Point(0., 0.)
    }
}

macro_rules! binop_ref {
    ($(impl $imp:ident, $method:ident)*) => {
        $(
            impl<'a> $imp<Point> for &'a Point {
                type Output = Point;
                fn $method(self, other: Point) -> Self::Output {
                    $imp::$method(*self, other)
                }
            }

            impl<'a> $imp<&'a Point> for Point {
                type Output = Point;
                fn $method(self, other: &Point) -> Self::Output {
                    $imp::$method(self, *other)
                }
            }

            impl<'a> $imp<&'a Point> for &'a Point {
                type Output = Point;
                fn $method(self, other: &Point) -> Self::Output {
                    $imp::$method(*self, *other)
                }
            }
        )*
    };
}

binop_ref! {
	impl Add, add
	impl Sub, sub
	impl Mul, mul
	impl Div, div
}

// ------------ impl arith end ------------
// ------------ geometry end ------------


// ------------ algebraic traits start ------------
use std::marker::Sized;
use std::ops::*;

/// 元
pub trait Element: Sized + Clone + PartialEq {}
impl<T: Sized + Clone + PartialEq> Element for T {}

/// 結合性
pub trait Associative: Magma {}

/// マグマ
pub trait Magma: Element + Add<Output=Self> {}
impl<T: Element + Add<Output=Self>> Magma for T {}

/// 半群
pub trait SemiGroup: Magma + Associative {}
impl<T: Magma + Associative> SemiGroup for T {}

/// モノイド
pub trait Monoid: SemiGroup + Zero {}
impl<T: SemiGroup + Zero> Monoid for T {}

pub trait ComMonoid: Monoid + AddAssign {}
impl<T: Monoid + AddAssign> ComMonoid for T {}

/// 群
pub trait Group: Monoid + Neg<Output=Self> {}
impl<T: Monoid + Neg<Output=Self>> Group for T {}

pub trait ComGroup: Group + ComMonoid {}
impl<T: Group + ComMonoid> ComGroup for T {}

/// 半環
pub trait SemiRing: ComMonoid + Mul<Output=Self> + One {}
impl<T: ComMonoid + Mul<Output=Self> + One> SemiRing for T {}

/// 環
pub trait Ring: ComGroup + SemiRing {}
impl<T: ComGroup + SemiRing> Ring for T {}

pub trait ComRing: Ring + MulAssign {}
impl<T: Ring + MulAssign> ComRing for T {}

/// 体
pub trait Field: ComRing + Div<Output=Self> + DivAssign {}
impl<T: ComRing + Div<Output=Self> + DivAssign> Field for T {}

/// 加法単元
pub trait Zero: Element {
    fn zero() -> Self;
    fn is_zero(&self) -> bool {
        *self == Self::zero()
    }
}

/// 乗法単元
pub trait One: Element {
    fn one() -> Self;
    fn is_one(&self) -> bool {
        *self == Self::one()
    }
}

macro_rules! impl_integer {
    ($($T:ty,)*) => {
        $(
            impl Associative for $T {}

            impl Zero for $T {
                fn zero() -> Self { 0 }
                fn is_zero(&self) -> bool { *self == 0 }
            }

            impl<'a> Zero for &'a $T {
                fn zero() -> Self { &0 }
                fn is_zero(&self) -> bool { *self == &0 }
            }

            impl One for $T {
                fn one() -> Self { 1 }
                fn is_one(&self) -> bool { *self == 1 }
            }

            impl<'a> One for &'a $T {
                fn one() -> Self { &1 }
                fn is_one(&self) -> bool { *self == &1 }
            }
        )*
    };
}

impl_integer! {
    i8, i16, i32, i64, i128, isize,
    u8, u16, u32, u64, u128, usize,
}
// ------------ algebraic traits end ------------



// ------------ io module start ------------
use std::io::{stdout, BufWriter, Read, StdoutLock, Write};

pub struct IO {
	iter: std::str::SplitAsciiWhitespace<'static>,
	buf: BufWriter<StdoutLock<'static>>,
}

impl IO {
	pub fn new() -> Self {
		let mut input = String::new();
		std::io::stdin().read_to_string(&mut input).unwrap();
		let input = Box::leak(input.into_boxed_str());
		let out = Box::new(stdout());
		IO {
			iter: input.split_ascii_whitespace(),
			buf: BufWriter::new(Box::leak(out).lock()),
		}
	}
	fn scan_str(&mut self) -> &'static str {
		self.iter.next().unwrap()
	}
	pub fn scan<T: Scan>(&mut self) -> <T as Scan>::Output {
		<T as Scan>::scan(self)
	}
	pub fn scan_vec<T: Scan>(&mut self, n: usize) -> Vec<<T as Scan>::Output> {
		(0..n).map(|_| self.scan::<T>()).collect()
	}
	pub fn print<T: Print>(&mut self, x: T) {
		<T as Print>::print(self, x);
	}
	pub fn println<T: Print>(&mut self, x: T) {
		self.print(x);
		self.print("\n");
	}
	pub fn iterln<T: Print, I: Iterator<Item = T>>(&mut self, mut iter: I, delim: &str) {
		if let Some(v) = iter.next() {
			self.print(v);
			for v in iter {
				self.print(delim);
				self.print(v);
			}
		}
		self.print("\n");
	}
	pub fn flush(&mut self) {
		self.buf.flush().unwrap();
	}
}

impl Default for IO {
	fn default() -> Self {
		Self::new()
	}
}

pub trait Scan {
	type Output;
	fn scan(io: &mut IO) -> Self::Output;
}

macro_rules! impl_scan {
	($($t:tt),*) => {
		$(
			impl Scan for $t {
				type Output = Self;
				fn scan(s: &mut IO) -> Self::Output {
					s.scan_str().parse().unwrap()
				}
			}
		)*
	};
}

impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String, f32, f64);

impl Scan for char {
	type Output = char;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().next().unwrap()
	}
}

pub enum Bytes {}
impl Scan for Bytes {
	type Output = &'static [u8];
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().as_bytes()
	}
}

pub enum Chars {}
impl Scan for Chars {
	type Output = Vec<char>;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().collect()
	}
}

pub enum Usize1 {}
impl Scan for Usize1 {
	type Output = usize;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan::<usize>().wrapping_sub(1)
	}
}

impl<T: Scan, U: Scan> Scan for (T, U) {
	type Output = (T::Output, U::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan> Scan for (T, U, V) {
	type Output = (T::Output, U::Output, V::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan, W: Scan> Scan for (T, U, V, W) {
	type Output = (T::Output, U::Output, V::Output, W::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s), W::scan(s))
	}
}

pub trait Print {
	fn print(w: &mut IO, x: Self);
}

macro_rules! impl_print_int {
	($($t:ty),*) => {
		$(
			impl Print for $t {
				fn print(w: &mut IO, x: Self) {
					w.buf.write_all(x.to_string().as_bytes()).unwrap();
				}
			}
		)*
	};
}

impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize, f32, f64);

impl Print for u8 {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(&[x]).unwrap();
	}
}

impl Print for &[u8] {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(x).unwrap();
	}
}

impl Print for &str {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl Print for String {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl<T: Print, U: Print> Print for (T, U) {
	fn print(w: &mut IO, (x, y): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
	}
}

impl<T: Print, U: Print, V: Print> Print for (T, U, V) {
	fn print(w: &mut IO, (x, y, z): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
		w.print(" ");
		w.print(z);
	}
}

mod neboccoio_macro {
	#[macro_export]
	macro_rules! input {
		(@start $io:tt @read @rest) => {};

		(@start $io:tt @read @rest, $($rest: tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @rest mut $($rest:tt)*) => {
			input!(@start $io @read @mut [mut] @rest $($rest)*)
		};

		(@start $io:tt @read @rest $($rest:tt)*) => {
			input!(@start $io @read @mut [] @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [[$kind:tt; $len1:expr]; $len2:expr] $($rest:tt)*) => {
			let $($mut)* $var = (0..$len2).map(|_| $io.scan_vec::<$kind>($len1)).collect::<Vec<Vec<$kind>>>();
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($rest:tt)*) => {
			let $($mut)* $var = $io.scan_vec::<$kind>($len);
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => {
			let $($mut)* $var = $io.scan::<$kind>();
			input!(@start $io @read @rest $($rest)*)
		};

		(from $io:tt $($rest:tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};
	}
}

// ------------ io module end ------------
yukicoder

結果

ソースコード
