結果

問題 No.1078 I love Matrix Construction
ユーザー nebocconebocco
提出日時 2021-02-19 19:49:50
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 311 ms / 2,000 ms
コード長 15,368 bytes
コンパイル時間 12,444 ms
コンパイル使用メモリ 378,468 KB
実行使用メモリ 90,012 KB
最終ジャッジ日時 2024-09-16 15:55:14
合計ジャッジ時間 17,739 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
5,248 KB
testcase_01 AC 0 ms
5,248 KB
testcase_02 AC 24 ms
14,848 KB
testcase_03 AC 78 ms
34,944 KB
testcase_04 AC 120 ms
47,848 KB
testcase_05 AC 104 ms
40,064 KB
testcase_06 AC 21 ms
14,336 KB
testcase_07 AC 8 ms
6,656 KB
testcase_08 AC 96 ms
40,668 KB
testcase_09 AC 4 ms
5,376 KB
testcase_10 AC 311 ms
90,012 KB
testcase_11 AC 128 ms
50,500 KB
testcase_12 AC 226 ms
74,100 KB
testcase_13 AC 277 ms
83,136 KB
testcase_14 AC 157 ms
58,304 KB
testcase_15 AC 228 ms
79,084 KB
testcase_16 AC 6 ms
5,632 KB
testcase_17 AC 1 ms
5,376 KB
testcase_18 AC 16 ms
11,392 KB
testcase_19 AC 43 ms
23,552 KB
testcase_20 AC 44 ms
22,912 KB
testcase_21 AC 2 ms
5,376 KB
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ソースコード

diff # 

fn main() {
	let mut io = IO::new();
    input!{ from io,
		n: usize,
		s: [Usize1; n],
		t: [Usize1; n],
		u: [usize; n],
    }
	let mut sat = TwoSat::new(n*n);
	for i in 0..n {
		let f = (u[i] & 1) == 1;
		let g = (u[i] & 2) == 2;
		for j in 0..n {
			sat.add_clause(s[i] * n + j, !f, j * n + t[i], !g);
		}
	}
	if let Some(l) = sat.solve() {
		for h in l.chunks(n) {
			io.iterln(h.iter().map(|&x| x as i32), " ");
		}
	} else {
		io.println(-1);
	}
}

// ------------ 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);

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);

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; $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 ------------
0