#876975 (Rust) No.2336 Do you like typical problems?

• 問題: No.2336 Do you like typical problems?
• ユーザー: akakimidori
• 提出日時: 2023-06-02 21:48:26
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 898 ms / 2,000 ms
• コード長: 12,541 bytes
• コンパイル時間: 18,978 ms
• コンパイル使用メモリ: 378,616 KB
• 実行使用メモリ: 24,384 KB
• 最終ジャッジ日時: 2024-12-28 17:17:08
• 合計ジャッジ時間: 26,127 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 18

コンパイルメッセージ

warning: unused import: `std::io::Write`
 --> src/main.rs:2:5
  |
2 | use std::io::Write;
  |     ^^^^^^^^^^^^^^
  |
  = note: `#[warn(unused_imports)]` on by default

warning: type alias `Map` is never used
 --> src/main.rs:4:6
  |
4 | type Map<K, V> = BTreeMap<K, V>;
  |      ^^^
  |
  = note: `#[warn(dead_code)]` on by default

warning: type alias `Set` is never used
 --> src/main.rs:5:6
  |
5 | type Set<T> = BTreeSet<T>;
  |      ^^^

warning: type alias `Deque` is never used
 --> src/main.rs:6:6
  |
6 | type Deque<T> = VecDeque<T>;
  |      ^^^^^

ソースコード

use std::collections::*;
use std::io::Write;

type Map<K, V> = BTreeMap<K, V>;
type Set<T> = BTreeSet<T>;
type Deque<T> = VecDeque<T>;

fn main() {
    input! {
        n: usize,
        p: [(usize1, usize); n],
    }
    let mut z = p.iter().flat_map(|p| [p.0, p.1]).collect::<Vec<_>>();
    z.sort();
    z.dedup();
    let mut seg = LazySegmentTree::build(
        z.windows(2).map(|z| (M::zero(), M::from(z[1] - z[0]))),
        z.len() - 1,
        R,
    );
    let mut cnt = M::zero();
    let mut all = M::one();
    for &(l, r) in p.iter() {
        all *= M::from(r - l);
        let s = z.binary_search(&l).unwrap();
        let t = z.binary_search(&r).unwrap();
        cnt += seg.find(s, t).0 * M::from(r - l).inv();
        seg.update(s, t, M::from(r - l).inv());
    }
    let ans = (M::from(n * (n - 1) / 2) - cnt) * M::new(2).inv() * M::fact(n);
    println!("{}", ans);
}

struct R;
impl TE for R {
    type T = (M, M);
    type E = M;
    fn fold(&self, l: &Self::T, r: &Self::T) -> Self::T {
        (l.0 + r.0, l.1 + r.1)
    }
    fn eval(&self, x: &Self::T, f: &Self::E) -> Self::T {
        (x.0 + x.1 * *f, x.1)
    }
    fn merge(&self, g: &Self::E, h: &Self::E) -> Self::E {
        *g + *h
    }
    fn e(&self) -> Self::T {
        (M::zero(), M::zero())
    }
    fn id(&self) -> Self::E {
        M::zero()
    }
}

// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[macro_export]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

#[macro_export]
macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

#[macro_export]
macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}
// ---------- end input macro ----------
// ---------- begin modint ----------
use std::marker::*;
use std::ops::*;

pub trait Modulo {
    fn modulo() -> u32;
}

pub struct ConstantModulo<const M: u32>;

impl<const M: u32> Modulo for ConstantModulo<{ M }> {
    fn modulo() -> u32 {
        M
    }
}

pub struct ModInt<T>(u32, PhantomData<T>);

impl<T> Clone for ModInt<T> {
    fn clone(&self) -> Self {
        Self::new_unchecked(self.0)
    }
}

impl<T> Copy for ModInt<T> {}

impl<T: Modulo> Add for ModInt<T> {
    type Output = ModInt<T>;
    fn add(self, rhs: Self) -> Self::Output {
        let mut v = self.0 + rhs.0;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        Self::new_unchecked(v)
    }
}

impl<T: Modulo> AddAssign for ModInt<T> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl<T: Modulo> Sub for ModInt<T> {
    type Output = ModInt<T>;
    fn sub(self, rhs: Self) -> Self::Output {
        let mut v = self.0 - rhs.0;
        if self.0 < rhs.0 {
            v += T::modulo();
        }
        Self::new_unchecked(v)
    }
}

impl<T: Modulo> SubAssign for ModInt<T> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl<T: Modulo> Mul for ModInt<T> {
    type Output = ModInt<T>;
    fn mul(self, rhs: Self) -> Self::Output {
        let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
        Self::new_unchecked(v as u32)
    }
}

impl<T: Modulo> MulAssign for ModInt<T> {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl<T: Modulo> Neg for ModInt<T> {
    type Output = ModInt<T>;
    fn neg(self) -> Self::Output {
        if self.is_zero() {
            Self::zero()
        } else {
            Self::new_unchecked(T::modulo() - self.0)
        }
    }
}

impl<T> std::fmt::Display for ModInt<T> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<T> std::fmt::Debug for ModInt<T> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl<T> Default for ModInt<T> {
    fn default() -> Self {
        Self::zero()
    }
}

impl<T: Modulo> std::str::FromStr for ModInt<T> {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<u32>()?;
        Ok(ModInt::new(val))
    }
}

impl<T: Modulo> From<usize> for ModInt<T> {
    fn from(val: usize) -> ModInt<T> {
        ModInt::new_unchecked((val % T::modulo() as usize) as u32)
    }
}

impl<T: Modulo> From<u64> for ModInt<T> {
    fn from(val: u64) -> ModInt<T> {
        ModInt::new_unchecked((val % T::modulo() as u64) as u32)
    }
}

impl<T: Modulo> From<i64> for ModInt<T> {
    fn from(val: i64) -> ModInt<T> {
        let mut v = ((val % T::modulo() as i64) + T::modulo() as i64) as u32;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        ModInt::new_unchecked(v)
    }
}

impl<T> ModInt<T> {
    pub fn new_unchecked(n: u32) -> Self {
        ModInt(n, PhantomData)
    }
    pub fn zero() -> Self {
        ModInt::new_unchecked(0)
    }
    pub fn one() -> Self {
        ModInt::new_unchecked(1)
    }
    pub fn is_zero(&self) -> bool {
        self.0 == 0
    }
}

impl<T: Modulo> ModInt<T> {
    pub fn new(d: u32) -> Self {
        ModInt::new_unchecked(d % T::modulo())
    }
    pub fn pow(&self, mut n: u64) -> Self {
        let mut t = Self::one();
        let mut s = *self;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        t
    }
    pub fn inv(&self) -> Self {
        assert!(!self.is_zero());
        self.pow(T::modulo() as u64 - 2)
    }
    pub fn fact(n: usize) -> Self {
        (1..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn perm(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        ((n - k + 1)..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn binom(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        let k = k.min(n - k);
        let mut nu = Self::one();
        let mut de = Self::one();
        for i in 0..k {
            nu *= Self::from(n - i);
            de *= Self::from(i + 1);
        }
        nu * de.inv()
    }
}
// ---------- end modint ----------
// ---------- begin precalc ----------
pub struct Precalc<T> {
    fact: Vec<ModInt<T>>,
    ifact: Vec<ModInt<T>>,
    inv: Vec<ModInt<T>>,
}

impl<T: Modulo> Precalc<T> {
    pub fn new(n: usize) -> Precalc<T> {
        let mut inv = vec![ModInt::one(); n + 1];
        let mut fact = vec![ModInt::one(); n + 1];
        let mut ifact = vec![ModInt::one(); n + 1];
        for i in 2..=n {
            fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
        }
        ifact[n] = fact[n].inv();
        if n > 0 {
            inv[n] = ifact[n] * fact[n - 1];
        }
        for i in (1..n).rev() {
            ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
            inv[i] = ifact[i] * fact[i - 1];
        }
        Precalc { fact, ifact, inv }
    }
    pub fn inv(&self, n: usize) -> ModInt<T> {
        assert!(n > 0);
        self.inv[n]
    }
    pub fn fact(&self, n: usize) -> ModInt<T> {
        self.fact[n]
    }
    pub fn ifact(&self, n: usize) -> ModInt<T> {
        self.ifact[n]
    }
    pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[n - k]
    }
    pub fn binom(&self, n: usize, k: usize) -> ModInt<T> {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[k] * self.ifact[n - k]
    }
}
// ---------- end precalc ----------

type M = ModInt<ConstantModulo<998_244_353>>;

// ---------- begin Lazy Segment Tree ----------
pub trait TE {
    type T: Clone;
    type E: Clone;
    fn fold(&self, l: &Self::T, r: &Self::T) -> Self::T;
    fn eval(&self, x: &Self::T, f: &Self::E) -> Self::T;
    fn merge(&self, g: &Self::E, h: &Self::E) -> Self::E;
    fn e(&self) -> Self::T;
    fn id(&self) -> Self::E;
}

pub struct LazySegmentTree<R: TE> {
    n: usize,
    size: usize,
    bit: u32,
    op: R,
    data: Vec<(R::T, R::E)>,
}

impl<R: TE> LazySegmentTree<R> {
    pub fn new(n: usize, op: R) -> Self {
        assert!(n > 0);
        let size = n.next_power_of_two();
        let bit = size.trailing_zeros();
        let data = vec![(op.e(), op.id()); 2 * size];
        Self {
            n,
            size,
            bit,
            op,
            data,
        }
    }
    pub fn build<I>(init: I, n: usize, op: R) -> Self
    where
        I: Iterator<Item = R::T>,
    {
        let mut seg = Self::new(n, op);
        for (data, ini) in seg.data[seg.size..].iter_mut().zip(init) {
            data.0 = ini;
        }
        for i in (1..seg.size).rev() {
            seg.pull(i);
        }
        seg
    }
    pub fn update(&mut self, l: usize, r: usize, f: R::E) {
        assert!(l <= r && r <= self.n);
        if l == r {
            return;
        }
        self.push_range(l, r);
        let mut s = l + self.size;
        let mut t = r + self.size;
        while s < t {
            if s & 1 == 1 {
                self.apply(s, &f);
                s += 1;
            }
            if t & 1 == 1 {
                t -= 1;
                self.apply(t, &f);
            }
            s >>= 1;
            t >>= 1;
        }
        let l = l + self.size;
        let r = r + self.size;
        for k in 1..=self.bit {
            if (l >> k) << k != l {
                self.pull(l >> k);
            }
            if (r >> k) << k != r {
                self.pull((r - 1) >> k);
            }
        }
    }
    pub fn find(&mut self, l: usize, r: usize) -> R::T {
        assert!(l <= r && r <= self.n);
        if l == r {
            return self.op.e();
        }
        self.push_range(l, r);
        let mut l = l + self.size;
        let mut r = r + self.size;
        let mut p = self.op.e();
        let mut q = self.op.e();
        while l < r {
            if l & 1 == 1 {
                p = self.op.fold(&p, &self.data[l].0);
                l += 1;
            }
            if r & 1 == 1 {
                r -= 1;
                q = self.op.fold(&self.data[r].0, &q);
            }
            l >>= 1;
            r >>= 1;
        }
        self.op.fold(&p, &q)
    }
    pub fn set_at(&mut self, x: usize, v: R::T) {
        assert!(x < self.n);
        let x = x + self.size;
        for k in (1..=self.bit).rev() {
            self.push(x >> k);
        }
        self.data[x].0 = v;
        for k in 1..=self.bit {
            self.pull(x >> k);
        }
    }
    fn push_range(&mut self, l: usize, r: usize) {
        let l = l + self.size;
        let r = r + self.size;
        for k in (1..=self.bit).rev() {
            if (l >> k) << k != l {
                self.push(l >> k);
            }
            if (r >> k) << k != r {
                self.push((r - 1) >> k);
            }
        }
    }
    fn apply(&mut self, x: usize, f: &R::E) {
        self.data[x].0 = self.op.eval(&self.data[x].0, f);
        self.data[x].1 = self.op.merge(&self.data[x].1, f);
    }
    fn push(&mut self, x: usize) {
        let f = std::mem::replace(&mut self.data[x].1, self.op.id());
        self.apply(2 * x, &f);
        self.apply(2 * x + 1, &f);
    }
    fn pull(&mut self, x: usize) {
        self.data[x].0 = self.op.fold(&self.data[2 * x].0, &self.data[2 * x + 1].0);
    }
}
// ---------- end Lazy Segment Tree ----------