#625299 (Rust) No.650 行列木クエリ

提出ソース
結果

問題	No.650 行列木クエリ
ユーザー	nebocco
提出日時	2021-03-05 19:51:56
言語	Rust (1.77.0 + proconio)
結果	AC
実行時間	57 ms / 2,000 ms
コード長	15,064 bytes
コンパイル時間	12,640 ms
コンパイル使用メモリ	406,708 KB
実行使用メモリ	23,552 KB
最終ジャッジ日時	2024-10-06 22:14:34
合計ジャッジ時間	14,426 ms
ジャッジサーバーID （参考情報）	judge3 / judge1
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	17 ms 6,912 KB
testcase_02	AC	56 ms 23,552 KB
testcase_03	AC	1 ms 5,248 KB
testcase_04	AC	18 ms 6,912 KB
testcase_05	AC	57 ms 23,424 KB
testcase_06	AC	1 ms 5,248 KB
testcase_07	AC	1 ms 5,248 KB
testcase_08	AC	16 ms 7,040 KB
testcase_09	AC	41 ms 23,384 KB
testcase_10	AC	1 ms 5,248 KB
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ソースコード

raw source code
fn main() {
	let mut io = IO::new();
    input!{ from io,
		n: usize,
		ed: [(usize, usize); n-1],
		q: usize
    }
	let mut hld = HeavyLightDecomposition::new(n);
	for &(u, v) in &ed {
		hld.add_edge(u, v);
	}
	hld.build(0);
	let mut seg = SegmentTree::<Mat>::new(n);
	for _ in 0..q {
		let c = io.scan::<char>();
		if c == 'x' {
			let (i, (a0, a1, a2, a3)) = io.scan::<(usize, (i64, i64, i64, i64))>();
			seg.set(hld.id(ed[i].0).max(hld.id(ed[i].1)), Mat(a0, a1, a2, a3));

		} else {
			let (u, v) = io.scan::<(usize, usize)>();
			let (rng1, rng2) = hld.for_each_edge(u, v);
			assert!(rng1.is_empty());
			let mut res = Mat::zero();
			for x in rng2 {
				res = res + seg.fold(x);
			}
			io.println(((res.0, res.1), (res.2, res.3)));
		}
	}
}

const MOD: i64 = 1_000_000_007;

#[derive(Clone, PartialEq, Debug)]
struct Mat(i64, i64, i64, i64);

impl Associative for Mat {}

impl Add for Mat {
	type Output = Self;
	fn add(self, rhs: Self) -> Self {
		Self(
			(self.0 * rhs.0 + self.1 * rhs.2) % MOD,
			(self.0 * rhs.1 + self.1 * rhs.3) % MOD,
			(self.2 * rhs.0 + self.3 * rhs.2) % MOD,
			(self.2 * rhs.1 + self.3 * rhs.3) % MOD
		)
	}
}

impl Zero for Mat {
	fn zero() -> Self { Self(1, 0, 0, 1) }
}

use std::ops::Bound::{Excluded, Included, Unbounded};
use std::ops::RangeBounds;

/// 区間を配列サイズに収まるように丸める。
///
/// 与えられた区間 `r` と `0..len` の共通部分を、有界な半開区間として返す。
///
/// # Examples
/// ```
/// use bibliotheca::utils::bounds::bounds_within;
///
/// assert_eq!(bounds_within(.., 7), 0..7);
/// assert_eq!(bounds_within(..=4, 7), 0..5);
/// ```
pub fn bounds_within<R: RangeBounds<usize>>(r: R, len: usize) -> Range<usize> {
    let e_ex = match r.end_bound() {
        Included(&e) => e + 1,
        Excluded(&e) => e,
        Unbounded => len,
    }
    .min(len);
    let s_in = match r.start_bound() {
        Included(&s) => s,
        Excluded(&s) => s + 1,
        Unbounded => 0,
    }
    .min(e_ex);
    s_in..e_ex
}


// ------------ Segment Tree start ------------

pub struct SegmentTree<T: Monoid> {
    n: usize,
	size: usize,
	node: Vec<T>
}

impl<T: Monoid> SegmentTree<T> {
	pub fn new(n: usize) -> Self {
		let size = n.next_power_of_two();
		let node = vec![T::zero(); size * 2];
		SegmentTree {
			n, size, node
		}
	}

	pub fn set(&mut self, mut i: usize, x: T) {
		i += self.size;
		self.node[i] = x;
		self.fix(i);
	}

	fn fix(&mut self, mut i: usize) {
        while i > 0 {
			i >>= 1;
			self.node[i] = self.node[i << 1].clone() + self.node[(i << 1) + 1].clone();
		}
    }

	pub fn fold<R: RangeBounds<usize>>(&self, rng: R) -> T {
		let Range { start, end } = bounds_within(rng, self.size);
		let mut vl = T::zero();
		let mut vr = T::zero();
		let mut l = start + self.size;
		let mut r = end + self.size;
		while l < r {
			if l & 1 == 1 {
				vl = vl + self.node[l].clone();
				l += 1;
			}
			if r & 1 == 1 {
				r -= 1;
				vr = self.node[r].clone() + vr;
			}
			l >>= 1;
			r >>= 1;
		}
		vl + vr
    }

    /// (j, t) => pred(j-1) = true, pred(j) = false
    pub fn partition(&self, pred: impl Fn(usize, &T) -> bool) -> (usize, T) {
        assert!(pred(0, &T::zero()), "need to be pred(0, T::zero())");
        if pred(self.n - 1, &self.node[1]) {
            return (self.n - 1, self.node[1].clone())
        }
        let mut j = 1;
        let mut current = T::zero();
        let mut idx = 0;
        let mut f = self.size;
        while j < self.size {
            j <<= 1;
            f >>= 1;
            let next = current.clone() + self.node[j].clone();
            if pred(idx + f - 1, &next) {
                current = next;
                j |= 1;
                idx += f;
            }
        }
        (idx, current)
    }
}

impl<T: Monoid> From<Vec<T>> for SegmentTree<T> {
	fn from(vec: Vec<T>) -> Self {
        let n = vec.len();
		let size = n.next_power_of_two();
		let mut node = vec![T::zero(); size << 1];
		for (i, e) in vec.iter().cloned().enumerate() {
			node[i + size] = e;
		}
		for i in (1..size).rev() {
			node[i] = node[i << 1].clone() + node[(i << 1) + 1].clone();
		}
		SegmentTree {
			n, size, node
		}
	}
}

impl<T: Monoid> Index<usize> for SegmentTree<T> {
	type Output = T;
	fn index(&self, i: usize) -> &Self::Output {
		assert!(i < self.size, "index out of range: length is {}, but given {}.", self.size, i);
		&self.node[i + self.size]
	}
}

// ------------ Segment Tree 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 ------------



// ------------ Heavy Light Decomposition start ------------

use std::ops::Range;

pub struct HeavyLightDecomposition {
	graph: Vec<Vec<usize>>,
	index: Vec<usize>, // 新しい頂点番号
	parent: Vec<usize>, // 親
	head: Vec<usize>, // 属するHeavy Pathの根
	range: Vec<usize>, // 部分木の開区間右端
}

impl HeavyLightDecomposition {
	pub fn new(n: usize) -> Self {
		Self {
			graph: vec![Vec::new(); n],
			index: Vec::new(),
			parent: Vec::new(),
			head: Vec::new(),
			range: Vec::new(),
		}
	}

	pub fn add_edge(&mut self, u: usize, v: usize) {
		self.graph[u].push(v);
		self.graph[v].push(u);
	}

	pub fn build(&mut self, root: usize)  {
		let graph = &mut self.graph;
		let n = graph.len();
		let mut index = vec![0; n];
		let mut parent = vec![n; n];
		let mut head = vec![root; n];
		let mut range = vec![0; n];
		let mut siz = vec![1; n];
		let mut st = Vec::new();
		st.push(root);
		while let Some(v) = st.pop() {
			if v < n {
				st.push(!v);
				if let Some(k) = graph[v].iter().position(|&u| u == parent[v]) {
					graph[v].swap_remove(k);
				}
				graph[v].iter().for_each(|&u| { parent[u] = v; st.push(u); });
			} else {
				let v = !v;
				for i in 0..graph[v].len() {
					let u = graph[v][i];
					siz[v] += siz[u];
					if siz[graph[v][0]] < siz[u] {
						graph[v].swap(0, i);
					}
				}
			}
		}
		st.push(root);
		let mut c = 0;
		while let Some(v) = st.pop() {
			if v < n {
				st.push(!v);
				index[v] = c; c += 1;
				for &u in graph[v].iter().skip(1) {
					head[u] = u;
					st.push(u);
				}
				if let Some(&u) = graph[v].get(0) {
					head[u] = head[v];
					st.push(u);
				}
			} else {
				range[!v] = c;
			}
		}
		self.index = index;
		self.parent = parent;
		self.head = head;
		self.range = range;
	}

	pub fn lca(&self, mut u: usize, mut v: usize) -> usize {
		let parent = &self.parent;
		let head = &self.head;
		let index = &self.index;

		while head[u] != head[v] {
			if index[u] < index[v] {
				v = parent[head[v]];
			} else {
				u = parent[head[u]];
			}
		}
		if index[u] < index[v] {
			u
		} else {
			v
		}
	}

	fn for_each(&self, mut u: usize, mut v: usize, b: usize) -> (Vec<Range<usize>>, Vec<Range<usize>>) {
		let parent = &self.parent;
		let head = &self.head;
		let index = &self.index;

		let mut up = Vec::new();
		let mut down = Vec::new();
		while head[u] != head[v] {
			if index[u] < index[v] {
				let h = head[v];
				down.push(index[h]..index[v] + 1);
				v = parent[h];
			} else {
				let h = head[u];
				up.push(index[h]..index[u] + 1);
				u = parent[h];
			}
		}
		if index[u] < index[v] {
			down.push(index[u] + b .. index[v] + 1);
		} else if index[v] + b < index[u] + 1 {
			up.push(index[v] + b .. index[u] + 1);
		}

		down.reverse();
		(up, down)
	}

	pub fn id(&self, v: usize) -> usize {
		self.index[v]
	}

	pub fn for_each_vertex(&self, u: usize, v: usize) -> (Vec<Range<usize>>, Vec<Range<usize>>) {
		self.for_each(u, v, 0)
	}
	pub fn for_each_edge(&self, u: usize, v: usize) -> (Vec<Range<usize>>, Vec<Range<usize>>) {
		self.for_each(u, v, 1)
	}
	pub fn subtree_range(&self, v: usize) -> Range<usize> {
		self.index[v]..self.range[v]
	}
}

// ------------ Heavy Light Decomposition 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);

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

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

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

テストケース

ソースコード
