#984213 (Rust) No.2990 Interval XOR

提出ソース

結果

問題	No.2990 Interval XOR
ユーザー	akakimidori
提出日時	2024-05-31 05:58:42
言語	Rust (1.77.0 + proconio)
結果	AC
実行時間	814 ms / 2,000 ms
コード長	16,211 bytes
コンパイル時間	15,817 ms
コンパイル使用メモリ	382,872 KB
実行使用メモリ	49,912 KB
最終ジャッジ日時	2024-12-14 23:31:03
合計ジャッジ時間	25,920 ms
ジャッジサーバーID （参考情報）	judge3 / judge5

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 6,816 KB
testcase_01	AC	1 ms 6,816 KB
testcase_02	AC	1 ms 6,816 KB
testcase_03	AC	2 ms 6,820 KB
testcase_04	AC	1 ms 6,816 KB
testcase_05	AC	1 ms 6,820 KB
testcase_06	AC	1 ms 6,820 KB
testcase_07	AC	1 ms 6,816 KB
testcase_08	AC	1 ms 6,820 KB
testcase_09	AC	1 ms 6,820 KB
testcase_10	AC	1 ms 6,820 KB
testcase_11	AC	1 ms 6,816 KB
testcase_12	AC	1 ms 6,816 KB
testcase_13	AC	2 ms 6,820 KB
testcase_14	AC	1 ms 6,820 KB
testcase_15	AC	2 ms 6,820 KB
testcase_16	AC	1 ms 6,820 KB
testcase_17	AC	1 ms 6,816 KB
testcase_18	AC	3 ms 6,816 KB
testcase_19	AC	2 ms 6,820 KB
testcase_20	AC	2 ms 6,820 KB
testcase_21	AC	1 ms 6,820 KB
testcase_22	AC	2 ms 6,820 KB
testcase_23	AC	2 ms 6,820 KB
testcase_24	AC	2 ms 6,820 KB
testcase_25	AC	50 ms 6,816 KB
testcase_26	AC	25 ms 6,816 KB
testcase_27	AC	16 ms 6,820 KB
testcase_28	AC	152 ms 12,672 KB
testcase_29	AC	49 ms 6,820 KB
testcase_30	AC	155 ms 12,672 KB
testcase_31	AC	156 ms 12,812 KB
testcase_32	AC	766 ms 49,664 KB
testcase_33	AC	774 ms 49,828 KB
testcase_34	AC	771 ms 49,880 KB
testcase_35	AC	814 ms 49,876 KB
testcase_36	AC	778 ms 49,788 KB
testcase_37	AC	770 ms 49,912 KB
testcase_38	AC	699 ms 49,824 KB
testcase_39	AC	69 ms 11,108 KB

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

raw source code

use std::io::Write;

fn main() {
    input! {
        n: usize,
        m: usize,
        p: [(usize, usize); m],
    }
    let p = p.into_iter().map(|p| (p.0, p.1 + 1)).collect::<Vec<_>>();
    let ans = fast(n, &p);
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    for a in ans.iter() {
        writeln!(out, "{}", *a).ok();
    }
}

fn fast(n: usize, p: &[(usize, usize)]) -> Vec<M> {
    if p.iter().any(|p| *p == (0, 1 << n)) {
        let prod = p.iter().fold(M::one(), |s, a| s * M::from(a.1 - a.0));
        return vec![prod * M::new(1 << n).inv(); 1 << n];
    }
    let mut q = Vec::from(p);
    let mut ans = vec![M::zero(); 1 << n];
    for i in 0..n {
        let mut dp = vec![vec![M::one(); 4]; 1 << (n - i - 1)];
        let mut xor = 0;
        for (&(l, r), (ref mut s, ref mut t)) in p.iter().zip(q.iter_mut()) {
            xor ^= l & !((2 << i) - 1);
            let pos = if r == 1 << n { 0 } else { (l ^ r) >> (i + 1) };
            let mut ep = [M::zero(); 4];
            if l < *s {
                ep[l >> i & 1] += M::from(*s - l);
            }
            if *s < *t && *s >> i & 1 == 1 {
                ep[1] += M::new(1 << i);
                *s += 1 << i;
            }
            let up = if pos > 0 { 2 } else { 0 };
            if *t < r {
                ep[up + (r >> i & 1)] += M::from(r - *t);
            }
            if *s < *t && *t >> i & 1 == 1 {
                *t -= 1 << i;
                ep[up] += M::new(1 << i);
            }
            fwht(&mut ep);
            dp[pos].dot_assign(&ep);
        }
        dp[0].truncate(2);
        while dp.len() > 1 {
            dp = dp.chunks_exact_mut(2).enumerate().map(|(i, dp)| {
                let mut a = std::mem::take(&mut dp[0]);
                let mut b = std::mem::take(&mut dp[1]);
                if i == 0 {
                    let n = a.len();
                    a.resize(2 * n, M::zero());
                    for i in 0..n {
                        a[n + i] = a[i];
                    }
                } else {
                    let n = a.len() / 2;
                    a.resize(4 * n, M::zero());
                    a[n..].rotate_right(n);
                    b.resize(4 * n, M::zero());
                    b[n..].rotate_right(n);
                    for i in 0..n {
                        a[n + i] = a[i];
                        a[3 * n + i] = a[2 * n + i];
                        b[n + i] = b[i];
                        b[3 * n + i] = b[2 * n + i];
                    }
                    b[n..].rotate_left(n);
                }
                a.dot_assign(&b);
                a
            }).collect();
        }
        let mut dp = dp.pop().unwrap();
        fwht(&mut dp);
        let inv = M::from(dp.len()).inv();
        for dp in dp.iter_mut() {
            *dp *= inv;
        }
        let invi = M::new(1 << i).inv();
        for (j, &val) in dp.iter().enumerate() {
            let s = xor ^ (j << i);
            let t = s + (1 << i);
            let sum = ans[s..t].iter().fold(M::zero(), |s, a| s + *a);
            let add = (val - sum) * invi;
            for a in ans[s..t].iter_mut() {
                *a += add;
            }
        }
    }
    ans
}

fn fwht<T>(a: &mut [T])
where
    T: std::ops::Add<Output = T> + std::ops::Sub<Output = T> + Copy,
{
    bitwise_transform(a, |a, b| {
        let x = *a + *b;
        let y = *a - *b;
        *a = x;
        *b = y;
    });
}

pub fn xor_convolution<T>(a: &[T], b: &[T]) -> Vec<T>
where
    T: Field + Copy,
{
    let mut x = Vec::from(a);
    let mut y = Vec::from(b);
    fwht(&mut x);
    fwht(&mut y);
    for (x, y) in x.iter_mut().zip(y.iter()) {
        *x = *x * *y;
    }
    fwht(&mut x);
    let inv_2 = T::one() / (T::one() + T::one());
    let mut mul = T::one();
    let n = x.len().trailing_zeros();
    for _ in 0..n {
        mul = mul * inv_2;
    }
    for x in x.iter_mut() {
        *x = *x * mul;
    }
    x
}

type M = ModInt<998244353>;

// ---------- 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 ----------

use std::ops::*;

// ---------- begin trait ----------
pub trait Zero: Sized + Add<Self, Output = Self> {
    fn zero() -> Self;
    fn is_zero(&self) -> bool;
}

pub trait One: Sized + Mul<Self, Output = Self> {
    fn one() -> Self;
    fn is_one(&self) -> bool;
}

pub trait SemiRing: Zero + One {}

pub trait Ring: SemiRing + Sub<Output = Self> + Neg<Output = Self> {}

pub trait Field: Ring + Div<Output = Self> {}

impl<T> SemiRing for T where T: Zero + One {}

impl<T> Ring for T where T: SemiRing + Sub<Output = Self> + Neg<Output = Self> {}

impl<T> Field for T where T: Ring + Div<Output = Self> {}
// ---------- end trait ----------
// ---------- begin modint ----------
pub const fn pow_mod(mut r: u32, mut n: u32, m: u32) -> u32 {
    let mut t = 1;
    while n > 0 {
        if n & 1 == 1 {
            t = (t as u64 * r as u64 % m as u64) as u32;
        }
        r = (r as u64 * r as u64 % m as u64) as u32;
        n >>= 1;
    }
    t
}

pub const fn primitive_root(p: u32) -> u32 {
    let mut m = p - 1;
    let mut f = [1; 30];
    let mut k = 0;
    let mut d = 2;
    while d * d <= m {
        if m % d == 0 {
            f[k] = d;
            k += 1;
        }
        while m % d == 0 {
            m /= d;
        }
        d += 1;
    }
    if m > 1 {
        f[k] = m;
        k += 1;
    }
    let mut g = 1;
    while g < p {
        let mut ok = true;
        let mut i = 0;
        while i < k {
            ok &= pow_mod(g, (p - 1) / f[i], p) > 1;
            i += 1;
        }
        if ok {
            break;
        }
        g += 1;
    }
    g
}

pub const fn is_prime(n: u32) -> bool {
    if n <= 1 {
        return false;
    }
    let mut d = 2;
    while d * d <= n {
        if n % d == 0 {
            return false;
        }
        d += 1;
    }
    true
}

#[derive(Clone, Copy, PartialEq, Eq)]
pub struct ModInt<const M: u32>(u32);

impl<const M: u32> ModInt<{ M }> {
    const REM: u32 = {
        let mut t = 1u32;
        let mut s = !M + 1;
        let mut n = !0u32 >> 2;
        while n > 0 {
            if n & 1 == 1 {
                t = t.wrapping_mul(s);
            }
            s = s.wrapping_mul(s);
            n >>= 1;
        }
        t
    };
    const INI: u64 = ((1u128 << 64) % M as u128) as u64;
    const IS_PRIME: () = assert!(is_prime(M));
    const fn reduce(x: u64) -> u32 {
        let _ = Self::IS_PRIME;
        let b = (x as u32 * Self::REM) as u64;
        let t = x + b * M as u64;
        let mut c = (t >> 32) as u32;
        if c >= M {
            c -= M;
        }
        c as u32
    }
    const fn multiply(a: u32, b: u32) -> u32 {
        Self::reduce(a as u64 * b as u64)
    }
    pub const fn new(v: u32) -> Self {
        assert!(v < M);
        Self(Self::reduce(v as u64 * Self::INI))
    }
    pub const fn const_mul(&self, rhs: Self) -> Self {
        Self(Self::multiply(self.0, rhs.0))
    }
    pub const fn pow(&self, mut n: u64) -> Self {
        let mut t = Self::new(1);
        let mut r = *self;
        while n > 0 {
            if n & 1 == 1 {
                t = t.const_mul(r);
            }
            r = r.const_mul(r);
            n >>= 1;
        }
        t
    }
    pub const fn inv(&self) -> Self {
        assert!(self.0 != 0);
        self.pow(M as u64 - 2)
    }
    pub const fn get(&self) -> u32 {
        Self::reduce(self.0 as u64)
    }
    pub const fn zero() -> Self {
        Self::new(0)
    }
    pub const fn one() -> Self {
        Self::new(1)
    }
}

impl<const M: u32> Add for ModInt<{ M }> {
    type Output = Self;
    fn add(self, rhs: Self) -> Self::Output {
        let mut v = self.0 + rhs.0;
        if v >= M {
            v -= M;
        }
        Self(v)
    }
}

impl<const M: u32> Sub for ModInt<{ M }> {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self::Output {
        let mut v = self.0 - rhs.0;
        if self.0 < rhs.0 {
            v += M;
        }
        Self(v)
    }
}

impl<const M: u32> Mul for ModInt<{ M }> {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self::Output {
        self.const_mul(rhs)
    }
}

impl<const M: u32> Div for ModInt<{ M }> {
    type Output = Self;
    fn div(self, rhs: Self) -> Self::Output {
        self * rhs.inv()
    }
}

impl<const M: u32> AddAssign for ModInt<{ M }> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl<const M: u32> SubAssign for ModInt<{ M }> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl<const M: u32> MulAssign for ModInt<{ M }> {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl<const M: u32> DivAssign for ModInt<{ M }> {
    fn div_assign(&mut self, rhs: Self) {
        *self = *self / rhs;
    }
}

impl<const M: u32> Neg for ModInt<{ M }> {
    type Output = Self;
    fn neg(self) -> Self::Output {
        if self.0 == 0 {
            self
        } else {
            Self(M - self.0)
        }
    }
}

impl<const M: u32> std::fmt::Display for ModInt<{ M }> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.get())
    }
}

impl<const M: u32> std::fmt::Debug for ModInt<{ M }> {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.get())
    }
}

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

impl<const M: u32> From<usize> for ModInt<{ M }> {
    fn from(val: usize) -> ModInt<{ M }> {
        ModInt::new((val % M as usize) as u32)
    }
}
// ---------- end modint ----------
// ---------- begin precalc ----------
pub struct Precalc<const MOD: u32> {
    fact: Vec<ModInt<MOD>>,
    ifact: Vec<ModInt<MOD>>,
    inv: Vec<ModInt<MOD>>,
}

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

impl<const M: u32> Zero for ModInt<{ M }> {
    fn zero() -> Self {
        Self::zero()
    }
    fn is_zero(&self) -> bool {
        self.0 == 0
    }
}

impl<const M: u32> One for ModInt<{ M }> {
    fn one() -> Self {
        Self::one()
    }
    fn is_one(&self) -> bool {
        self.get() == 1
    }
}

// ---------- begin array op ----------

pub trait ArrayAdd {
    type Item;
    fn add(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}

impl<T> ArrayAdd for [T]
where
    T: Zero + Copy,
{
    type Item = T;
    fn add(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
        let mut c = vec![T::zero(); self.len().max(rhs.len())];
        c[..self.len()].copy_from_slice(self);
        c.add_assign(rhs);
        c
    }
}

pub trait ArrayAddAssign {
    type Item;
    fn add_assign(&mut self, rhs: &[Self::Item]);
}

impl<T> ArrayAddAssign for [T]
where
    T: Add<Output = T> + Copy,
{
    type Item = T;
    fn add_assign(&mut self, rhs: &[Self::Item]) {
        assert!(self.len() >= rhs.len());
        self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x + *a);
    }
}

impl<T> ArrayAddAssign for Vec<T>
where
    T: Zero + Add<Output = T> + Copy,
{
    type Item = T;
    fn add_assign(&mut self, rhs: &[Self::Item]) {
        if self.len() < rhs.len() {
            self.resize(rhs.len(), T::zero());
        }
        self.as_mut_slice().add_assign(rhs);
    }
}

pub trait ArraySub {
    type Item;
    fn sub(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}

impl<T> ArraySub for [T]
where
    T: Zero + Sub<Output = T> + Copy,
{
    type Item = T;
    fn sub(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
        let mut c = vec![T::zero(); self.len().max(rhs.len())];
        c[..self.len()].copy_from_slice(self);
        c.sub_assign(rhs);
        c
    }
}

pub trait ArraySubAssign {
    type Item;
    fn sub_assign(&mut self, rhs: &[Self::Item]);
}

impl<T> ArraySubAssign for [T]
where
    T: Sub<Output = T> + Copy,
{
    type Item = T;
    fn sub_assign(&mut self, rhs: &[Self::Item]) {
        assert!(self.len() >= rhs.len());
        self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x - *a);
    }
}

impl<T> ArraySubAssign for Vec<T>
where
    T: Zero + Sub<Output = T> + Copy,
{
    type Item = T;
    fn sub_assign(&mut self, rhs: &[Self::Item]) {
        if self.len() < rhs.len() {
            self.resize(rhs.len(), T::zero());
        }
        self.as_mut_slice().sub_assign(rhs);
    }
}

pub trait ArrayDot {
    type Item;
    fn dot(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}

impl<T> ArrayDot for [T]
where
    T: Mul<Output = T> + Copy,
{
    type Item = T;
    fn dot(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
        assert!(self.len() == rhs.len());
        self.iter().zip(rhs).map(|p| *p.0 * *p.1).collect()
    }
}

pub trait ArrayDotAssign {
    type Item;
    fn dot_assign(&mut self, rhs: &[Self::Item]);
}

impl<T> ArrayDotAssign for [T]
where
    T: MulAssign + Copy,
{
    type Item = T;
    fn dot_assign(&mut self, rhs: &[Self::Item]) {
        assert!(self.len() == rhs.len());
        self.iter_mut().zip(rhs).for_each(|(x, a)| *x *= *a);
    }
}

// ---------- end array op ----------
pub fn bitwise_transform<T, F>(a: &mut [T], f: F)
where
    F: Fn(&mut T, &mut T),
{
    let size = a.len();
    assert!(size > 0 && size.next_power_of_two() == size);
    let n = size.trailing_zeros();
    for i in 0..n {
        let w = 1 << i;
        for a in a.chunks_exact_mut(2 * w) {
            let (l, r) = a.split_at_mut(w);
            for (l, r) in l.iter_mut().zip(r.iter_mut()) {
                f(l, r);
            }
        }
    }
}

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結果

テストケース

ソースコード