結果

問題 No.907 Continuous Kadomatu
ユーザー akakimidoriakakimidori
提出日時 2021-05-11 03:56:41
言語 Rust
(1.77.0)
結果
AC  
実行時間 177 ms / 2,000 ms
コード長 13,882 bytes
コンパイル時間 4,248 ms
コンパイル使用メモリ 177,584 KB
実行使用メモリ 4,348 KB
最終ジャッジ日時 2023-10-21 08:56:17
合計ジャッジ時間 4,477 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge9
このコードへのチャレンジ（β）

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
4,348 KB
testcase_01 AC 2 ms
4,348 KB
testcase_02 AC 1 ms
4,348 KB
testcase_03 AC 1 ms
4,348 KB
testcase_04 AC 1 ms
4,348 KB
testcase_05 AC 4 ms
4,348 KB
testcase_06 AC 1 ms
4,348 KB
testcase_07 AC 2 ms
4,348 KB
testcase_08 AC 3 ms
4,348 KB
testcase_09 AC 2 ms
4,348 KB
testcase_10 AC 6 ms
4,348 KB
testcase_11 AC 7 ms
4,348 KB
testcase_12 AC 12 ms
4,348 KB
testcase_13 AC 13 ms
4,348 KB
testcase_14 AC 13 ms
4,348 KB
testcase_15 AC 14 ms
4,348 KB
testcase_16 AC 14 ms
4,348 KB
testcase_17 AC 14 ms
4,348 KB
testcase_18 AC 13 ms
4,348 KB
testcase_19 AC 15 ms
4,348 KB
testcase_20 AC 3 ms
4,348 KB
testcase_21 AC 1 ms
4,348 KB
testcase_22 AC 1 ms
4,348 KB
testcase_23 AC 177 ms
4,348 KB
testcase_24 AC 177 ms
4,348 KB
testcase_25 AC 1 ms
4,348 KB
testcase_26 AC 1 ms
4,348 KB
testcase_27 AC 1 ms
4,348 KB
testcase_28 AC 1 ms
4,348 KB
testcase_29 AC 1 ms
4,348 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
warning: associated function `one` is never used
   --> Main.rs:452:8
    |
440 | impl Poly {
    | --------- associated function in this implementation
...
452 |     fn one() -> Self {
    |        ^^^
    |
    = note: `#[warn(dead_code)]` on by default

warning: 1 warning emitted

ソースコード

diff # 

// ---------- begin ModInt ----------
mod modint {

    #[allow(dead_code)]
    pub struct Mod;
    impl ConstantModulo for Mod {
        const MOD: u32 = 1_000_000_007;
    }

    #[allow(dead_code)]
    pub struct StaticMod;
    static mut STATIC_MOD: u32 = 0;
    impl Modulo for StaticMod {
        fn modulo() -> u32 {
            unsafe { STATIC_MOD }
        }
    }

    #[allow(dead_code)]
    impl StaticMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                STATIC_MOD = p;
            }
        }
    }

    use std::marker::*;
    use std::ops::*;

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

    pub trait ConstantModulo {
        const MOD: u32;
    }

    impl<T> Modulo for T
    where
        T: ConstantModulo,
    {
        fn modulo() -> u32 {
            T::MOD
        }
    }

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

    impl<T> Clone for ModInt<T> {
        fn clone(&self) -> Self {
            ModInt::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 d = self.0 + rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    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 d = T::modulo() + self.0 - rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    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;
            ModInt::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.0 == 0 {
                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: 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 m = T::modulo() as i64;
            ModInt::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModInt<T> {
        pub fn new_unchecked(d: u32) -> Self {
            ModInt(d, 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
        }
    }

    #[allow(dead_code)]
    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.0 != 0);
            self.pow(T::modulo() as u64 - 2)
        }
    }
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
mod precalc {
    use super::modint::*;
    #[allow(dead_code)]
    pub struct Precalc<T> {
        inv: Vec<ModInt<T>>,
        fact: Vec<ModInt<T>>,
        ifact: Vec<ModInt<T>>,
    }
    #[allow(dead_code)]
    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 + 1) {
                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 {
                inv: inv,
                fact: fact,
                ifact: ifact,
            }
        }
        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 comb(&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 ----------

use modint::*;
type M = ModInt<Mod>;
// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
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_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_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 ----------

// 適当に座標圧縮
// dp[区間] = (確率密度関数)
// として頑張る

#[derive(Clone)]
pub struct Poly(Vec<M>);

use std::ops::*;

impl Add for Poly {
    type Output = Self;
    fn add(self, rhs: Self) -> Self::Output {
        &self + &rhs
    }
}

impl Add<&Poly> for Poly {
    type Output = Self;
    fn add(self, rhs: &Self) -> Self::Output {
        &self + rhs
    }
}

impl Add<Poly> for &Poly {
    type Output = Poly;
    fn add(self, rhs: Poly) -> Self::Output {
        self + &rhs
    }
}

impl Add for &Poly {
    type Output = Poly;
    fn add(self, rhs: Self) -> Self::Output {
        let mut c = vec![M::zero(); self.0.len().max(rhs.0.len())];
        c.iter_mut().zip(&self.0).for_each(|p| *p.0 += *p.1);
        c.iter_mut().zip(&rhs.0).for_each(|p| *p.0 += *p.1);
        Poly::new(c)
    }
}

impl AddAssign<&Poly> for Poly {
    fn add_assign(&mut self, rhs: &Self) {
        if self.0.len() < rhs.0.len() {
            self.0.resize(rhs.0.len(), M::zero());
        }
        self.0.iter_mut().zip(rhs.0.iter()).for_each(|p| *p.0 += *p.1);
        self.fix();
    }
}

impl Sub for Poly {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self::Output {
        &self - &rhs
    }
}

impl Sub<&Poly> for Poly {
    type Output = Self;
    fn sub(self, rhs: &Self) -> Self::Output {
        &self - rhs
    }
}

impl Sub<Poly> for &Poly {
    type Output = Poly;
    fn sub(self, rhs: Poly) -> Self::Output {
        self - &rhs
    }
}

impl Sub for &Poly {
    type Output = Poly;
    fn sub(self, rhs: Self) -> Self::Output {
        let mut c = vec![M::zero(); self.0.len().max(rhs.0.len())];
        c.iter_mut().zip(&self.0).for_each(|p| *p.0 += *p.1);
        c.iter_mut().zip(&rhs.0).for_each(|p| *p.0 -= *p.1);
        Poly::new(c)
    }
}

impl SubAssign<&Poly> for Poly {
    fn sub_assign(&mut self, rhs: &Self) {
        if self.0.len() < rhs.0.len() {
            self.0.resize(rhs.0.len(), M::zero());
        }
        self.0.iter_mut().zip(rhs.0.iter()).for_each(|p| *p.0 -= *p.1);
        self.fix();
    }
}

impl Mul for Poly {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self::Output {
        &self * &rhs
    }
}

impl Mul<&Poly> for Poly {
    type Output = Self;
    fn mul(self, rhs: &Self) -> Self::Output {
        &self * rhs
    }
}

impl Mul<Poly> for &Poly {
    type Output = Poly;
    fn mul(self, rhs: Poly) -> Self::Output {
        self * &rhs
    }
}

impl Mul for &Poly {
    type Output = Poly;
    fn mul(self, rhs: Self) -> Self::Output {
        if self.is_zero() || rhs.is_zero() {
            return Poly::zero();
        }
        let mut c = vec![M::zero(); self.0.len() + rhs.0.len() - 1];
        for (i, a) in self.0.iter().enumerate() {
            for (c, b) in c[i..].iter_mut().zip(rhs.0.iter()) {
                *c += *a * *b;
            }
        }
        Poly::new(c)
    }
}

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

impl Poly {
    fn from(a: &[M]) -> Self {
        Poly::new(Vec::from(a))
    }
    fn new(a: Vec<M>) -> Self {
        let mut res = Poly(a);
        res.fix();
        res
    }
    fn zero() -> Self {
        Poly::new(vec![])
    }
    fn one() -> Self {
        Poly::new(vec![M::one()])
    }
    fn fix(&mut self) {
        while self.0.last().map_or(false, |a| a.is_zero()) {
            self.0.pop();
        }
    }
    fn is_zero(&self) -> bool {
        self.0.is_empty()
    }
    fn integral(&self) -> Self {
        if self.is_zero() {
            return Poly::zero();
        }
        let mut inv = vec![M::one(); self.0.len() + 1];
        for i in 1..inv.len() {
            inv[i] = M::from(i) * inv[i - 1];
        }
        let mut ifact = inv[self.0.len()].inv();
        for i in (1..inv.len()).rev() {
            inv[i] = inv[i - 1] * ifact;
            ifact *= M::from(i);
        }
        let mut c = vec![M::zero(); self.0.len() + 1];
        for (i, a) in self.0.iter().enumerate() {
            c[i + 1] = inv[i + 1] * *a;
        }
        Poly::new(c)
    }
    fn eval(&self, x: M) -> M {
        self.0.iter().rfold(M::zero(), |s, a| s * x + *a)
    }
}

fn run() {
    input! {
        n: usize,
        p: [(usize, usize); n],
    }
    let mut z = vec![];
    z.extend(p.iter().map(|p| p.0));
    z.extend(p.iter().map(|p| p.1));
    z.sort();
    z.dedup();
    let mut dp = vec![Poly::zero(); z.len() - 1];
    let ini = Poly::from(&[M::from(p[0].1 - p[0].0).inv()]);
    for (i, z) in z.windows(2).enumerate() {
        if p[0].0 <= z[0] && z[1] <= p[0].1 {
            dp[i] = ini.clone();
        }
    }
    for (p, &(l, r)) in p[1..].iter().enumerate() {
        let inv = M::from(r - l).inv();
        let l = z.binary_search(&l).unwrap();
        let r = z.binary_search(&r).unwrap();
        let mut all = M::zero();
        for (z, dp) in z.windows(2).zip(&dp) {
            let f = dp.integral();
            all += f.eval(M::from(z[1])) - f.eval(M::from(z[0]));
        }
        let all = all;
        let mut sum = M::zero();
        for i in 0..dp.len() {
            let f = dp[i].integral();
            dp[i] = Poly::zero();
            if l <= i && i < r {
                let mut g = f.clone();
                g -= &Poly::from(&[f.eval(M::from(z[i]))]);
                g += &Poly::from(&[sum]);
                if p % 2 == 1 {
                    g = Poly::from(&[all]) - g;
                }
                g *= &Poly::from(&[inv]);
                dp[i] = g;
            }
            sum += f.eval(M::from(z[i + 1])) - f.eval(M::from(z[i]));
        }
    }
    let mut ans = M::zero();
    for (i, z) in z.windows(2).enumerate() {
        let f = dp[i].integral();
        ans += f.eval(M::from(z[1])) - f.eval(M::from(z[0]));
    }
    println!("{}", ans);
}

fn main() {
    run();
}
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