結果

問題 No.483 マッチ並べ
ユーザー nebocco
提出日時 2021-03-08 20:49:56
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 2 ms / 2,000 ms
コード長 15,939 bytes
コンパイル時間 17,773 ms
コンパイル使用メモリ 383,684 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-10-10 11:34:55
合計ジャッジ時間 15,444 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 * 53
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

fn main() {
    let mut io = IO::new();
    input!{ from io,
        n: usize,
        l: [(Usize1, Usize1, Usize1, Usize1); n]
    }
    let m = 100;
    let mut sat = TwoSat::new(n);
    let mut g = vec![Vec::new(); m*m];
    for (i, &(a, b, c, d)) in l.iter().enumerate() {
        let u = a * m + b;
        let v = c * m + d;
        for &(j, x) in &g[u] {
            sat.add_clause(i, false, j, x);
        }
        for &(j, x) in &g[v] {
            sat.add_clause(i, true, j, x);
        }
        g[u].push((i, false));
        g[v].push((i, true));
    }
    let ans = if sat.solve().is_some() {
        "YES"
    } else {
        "NO"
    };
    io.println(ans);
}
// * verified: https://judge.yosupo.jp/submission/26465
// ------------ 2-SAT start ------------
// * verified: https://judge.yosupo.jp/submission/26463
// ------------ Strongly Connected Components start ------------
// ! DirectedGraph::reverse() is too heavy
pub trait SCC {
    fn strongly_connected(&self) -> (usize, Vec<usize>);
    fn groups(&self) -> Vec<Vec<usize>>;
}
impl<C: Cost> SCC for DirectedGraph<C> {
    fn strongly_connected(&self) -> (usize, Vec<usize>) {
        fn _scc_dfs<C: Cost>(graph: &DirectedGraph<C>, x: usize, res: &mut [Option<usize>]) {
            for y in graph.edges_from(x) {
                if res[y.to].is_none() {
                    res[y.to] = res[x];
                    _scc_dfs(graph, y.to, res);
                }
            }
        }
        let n = self.size();
        let post_backward = Traversal::post_order(&self.backward);
        let mut res: Vec<Option<usize>> = vec![None; n];
        let mut cnt = 0;
        for &x in post_backward.index.iter().rev() {
            if res[x].is_none() {
                res[x] = Some(cnt);
                _scc_dfs(self, x, &mut res);
                cnt += 1;
            }
        }
        (
            cnt,
            res.iter().map(|x| cnt - 1 - x.unwrap()).collect(),
        )
    }
    fn groups(&self) -> Vec<Vec<usize>> {
        let (c, g) = self.strongly_connected();
        let mut res = vec![Vec::new(); c];
        for (i, &x) in g.iter().enumerate() {
            res[x].push(i);
        }
        res
    }
}
// ------------ Strongly Connected Components end ------------
pub struct TwoSat(DirectedGraph<Void>);
impl TwoSat {
    pub fn new(n: usize) -> Self {
        Self(DirectedGraph::new(2 * n))
    }
    pub fn add_clause(&mut self, i: usize, f: bool, j: usize, g: bool) {
        self.0.add_edge(2 * i + !f as usize, 2 * j + g as usize, Void());
        self.0.add_edge(2 * j + !g as usize, 2 * i + f as usize, Void());
    }
    pub fn solve(&self) -> Option<Vec<bool>> {
        self.0
            .strongly_connected().1
            .chunks_exact(2)
            .map(|v| {
                use std::cmp::Ordering::*;
                match v[0].cmp(&v[1]) {
                    Equal => None,
                    Less => Some(true),
                    Greater => Some(false),
                }
            })
            .collect()
    }
}
// ------------ 2-SAT end ------------
#[derive(Debug, Clone)]
pub struct Traversal {
    pub index: Vec<usize>,
    pub time: Vec<usize>,
}
impl Traversal {
    pub fn pre_order<C: Cost>(graph: &[Vec<Edge<C>>]) -> Self {
        fn _dfs<C: Cost>(graph: &[Vec<Edge<C>>], x: usize, res: &mut PermutationBuilder) {
            res.visit(x);
            for &y in graph[x].iter() {
                if !res.on_stack(y.to) {
                    _dfs(graph, y.to, res);
                }
            }
        }
        let n = graph.len();
        let mut res = PermutationBuilder::new(n);
        for i in 0..n {
            if !res.on_stack(i) {
                _dfs(graph, i, &mut res);
            }
        }
        res.build()
    }
    pub fn post_order<C: Cost>(graph: &[Vec<Edge<C>>]) -> Self {
        fn _dfs<C: Cost>(graph: &[Vec<Edge<C>>], x: usize, ckd: &mut [bool], res: &mut PermutationBuilder) {
            for &y in graph[x].iter() {
                if !std::mem::replace(&mut ckd[y.to], true) {
                    _dfs(graph, y.to, ckd, res);
                }
            }
            res.visit(x);
        }
        let n = graph.len();
        let mut ckd = vec![false; n];
        let mut res = PermutationBuilder::new(n);
        for i in 0..n {
            if !std::mem::replace(&mut ckd[i], true) {
                _dfs(graph, i, &mut ckd, &mut res);
            }
        }
        res.build()
    }
}
#[derive(Debug, Clone)]
struct PermutationBuilder {
    index: Vec<usize>,
    time: Vec<usize>,
}
impl PermutationBuilder {
    fn new(n: usize) -> Self {
        Self {
            index: Vec::with_capacity(n),
            time: vec![n; n],
        }
    }
    fn build(self) -> Traversal {
        Traversal {
            index: self.index,
            time: self.time,
        }
    }
    #[allow(dead_code)]
    fn is_empty(&self) -> bool {
        self.time.is_empty()
    }
    fn len(&self) -> usize {
        self.time.len()
    }
    fn time(&self) -> usize {
        self.index.len()
    }
    fn visit(&mut self, x: usize) {
        assert!(!self.on_stack(x));
        self.time[x] = self.time();
        self.index.push(x);
    }
    fn on_stack(&self, x: usize) -> bool {
        self.time[x] != self.len()
    }
}
// ------------ Graph impl start ------------
pub trait Cost:
    Element
    + Clone + Copy + std::fmt::Display
    + Eq + Ord
    + Zero + One
    + Add<Output = Self> + AddAssign
    + Sub<Output = Self>
    + Neg<Output = Self>
{
    const MAX: Self;
}
#[derive(Copy, Clone)]
pub struct Edge<C = Void> {
    // pub from: usize,
    pub to: usize,
    pub cost: C,
    pub id: usize
}
pub struct UndirectedGraph<C>(pub Vec<Vec<Edge<C>>>, pub usize);
pub struct DirectedGraph<C>{
    pub forward: Vec<Vec<Edge<C>>>,
    pub backward: Vec<Vec<Edge<C>>>,
    pub count: usize,
}
pub trait Graph<C: Element> {
    fn new(size: usize) -> Self;
    fn size(&self) -> usize;
    fn add_edge(&mut self, u: usize, v: usize, cost: C);
    fn edges_from(&self, v: usize) -> std::slice::Iter<Edge<C>>;
}
impl<C: Element> Graph<C> for UndirectedGraph<C> {
    fn new(size: usize) -> Self {
        Self(vec![Vec::<Edge<C>>::new(); size], 0)
    }
    fn size(&self) -> usize {
        self.0.len()
    }
    fn add_edge(&mut self, u: usize, v: usize, cost: C) {
        self.0[u].push(Edge{ to: v, cost: cost.clone(), id: self.1 });
        self.0[v].push(Edge{ to: u, cost: cost.clone(), id: self.1 });
        self.1 += 1;
    }
    fn edges_from(&self, v: usize) -> std::slice::Iter<Edge<C>> {
        self.0[v].iter()
    }
}
impl<C: Element> Graph<C> for DirectedGraph<C> {
    fn new(size: usize) -> Self {
        Self {
            forward: vec![Vec::<Edge<C>>::new(); size],
            backward: vec![Vec::<Edge<C>>::new(); size],
            count: 0
        }
    }
    fn size(&self) -> usize {
        self.forward.len()
    }
    fn add_edge(&mut self, u: usize, v: usize, cost: C) {
        self.forward[u].push(Edge{ to: v, cost: cost.clone(), id: self.count });
        self.backward[v].push(Edge{ to: u, cost: cost.clone(), id: self.count });
        self.count += 1;
    }
    fn edges_from(&self, v: usize) -> std::slice::Iter<Edge<C>> {
        self.forward[v].iter()
    }
}
impl<C: Element> DirectedGraph<C> {
    pub fn edges_to(&self, u: usize) -> std::slice::Iter<Edge<C>> {
        self.backward[u].iter()
    }
    pub fn reverse(&self) -> Self {
        Self {
            forward: self.backward.clone(),
            backward: self.forward.clone(),
            count: self.count,
        }
    }
}
macro_rules! impl_cost {
    ($($T:ident,)*) => {
        $(
            impl Cost for $T { const MAX: Self = std::$T::MAX; }
        )*
    };
}
impl_cost! {
    i8, i16, i32, i64, i128, isize,
}
#[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord)]
pub struct Void();
impl std::fmt::Display for Void {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "")
    }
}
impl Zero for Void {
    fn zero() -> Self { Void() }
    fn is_zero(&self) -> bool { true }
}
impl One for Void {
    fn one() -> Self { Void() }
    fn is_one(&self) -> bool { true }
}
impl Add for Void {
    type Output = Self;
    fn add(self, _: Self) -> Self { Void() }
}
impl AddAssign for Void {
    fn add_assign(&mut self, _: Self) {}
}
impl Sub for Void {
    type Output = Self;
    fn sub(self, _: Self) -> Self { Void() }
}
impl Neg for Void {
    type Output = Self;
    fn neg(self) -> Self { Void() }
}
impl Cost for Void { const MAX: Self = Void(); }
// ------------ Graph impl 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 ------------
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