#1032560 (Rust) No.2996 Floor Sum

提出ソース

結果

問題	No.2996 Floor Sum
ユーザー	akakimidori
提出日時	2024-12-21 19:03:46
言語	Rust (1.77.0 + proconio)
結果	AC
実行時間	239 ms / 5,000 ms
コード長	17,488 bytes
コンパイル時間	18,630 ms
コンパイル使用メモリ	379,176 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-12-21 19:04:07
合計ジャッジ時間	15,392 ms
ジャッジサーバーID （参考情報）	judge2 / judge3

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	3 ms 5,248 KB
testcase_02	AC	1 ms 5,248 KB
testcase_03	AC	239 ms 5,248 KB
testcase_04	AC	100 ms 5,248 KB
testcase_05	AC	4 ms 5,248 KB
testcase_06	AC	11 ms 5,248 KB
testcase_07	AC	5 ms 5,248 KB
testcase_08	AC	4 ms 5,248 KB
testcase_09	AC	5 ms 5,248 KB
testcase_10	AC	5 ms 5,248 KB
testcase_11	AC	1 ms 5,248 KB
testcase_12	AC	2 ms 5,248 KB
testcase_13	AC	237 ms 5,248 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 constants `PRIMITIVE_ROOT` and `ORDER` are never used
   --> src/main.rs:487:11
    |
471 | impl<const M: u32> ModInt<{ M }> {
    | -------------------------------- associated constants in this implementation
...
487 |     const PRIMITIVE_ROOT: u32 = primitive_root(M);
    |           ^^^^^^^^^^^^^^
488 |     const ORDER: usize = 1 << (M - 1).trailing_zeros();
    |           ^^^^^
    |
    = note: `#[warn(dead_code)]` on by default

ソースコード

raw source code

fn main() {
    input! {
        t: usize,
        ask: [(usize, usize, i64, i64, i64, i64); t],
    }
    if t <= 5 {
        solve::<21, 11>(ask);
    } else {
        solve::<5, 3>(ask);
    }
}

fn solve<const A: usize, const B: usize>(ask: Vec<(usize, usize, i64, i64, i64, i64)>) {
    let pc = Precalc::new(100);
    for (p, q, n, m, a, b) in ask {
        let c = a.div_euclid(m);
        let a = a - c * m;
        let d = b.div_euclid(m);
        let b = b - d * m;
        let res = under_fold(
            n as usize + 1,
            m as usize,
            a as usize,
            b as usize,
            FloorSum::<M, A, B>::dx(),
            FloorSum::<M, A, B>::dy(),
        )
        .flush();
        let c = M::from(c);
        let d = M::from(d);
        let mut ans = M::zero();
        for i in 0..=q {
            for j in 0..=(q - i) {
                let k = q - i - j;
                let mut v = res[p + j][i];
                v *= c.pow(j as u64) * d.pow(k as u64);
                v *= pc.fact(q) * pc.ifact(i) * pc.ifact(j) * pc.ifact(k);
                ans += v;
            }
        }
        println!("{}", ans);
    }
}

type M = ModInt<998_244_353>;

#[derive(Clone)]
pub struct FloorSum<T, const A: usize, const B: usize> {
    x: [T; A],
    y: [T; B],
    sum: [[T; B]; A],
    id: bool,
}

impl<T, const A: usize, const B: usize> FloorSum<T, A, B>
where
    T: Ring + Copy,
{
    fn dx() -> Self {
        let mut res = Self::id();
        let u = A.min(2);
        res.x[..u].fill(T::one());
        res.y[0] = T::one();
        res.sum[0][0] = T::one();
        res.id = false;
        res
    }
    fn dy() -> Self {
        let mut res = Self::id();
        let u = B.min(2);
        res.y[..u].fill(T::one());
        res.x[0] = T::one();
        res.id = false;
        res
    }
    fn flush(&self) -> [[T; B]; A] {
        let coef = FloorPow::<T, B>::precalc();
        let mut sum = self.sum;
        for s in sum.iter_mut() {
            let mut t = [T::zero(); B];
            for (t, c) in t.iter_mut().zip(coef.iter()) {
                for (s, c) in s.iter().zip(c.iter()) {
                    *t = *t + *c * *s;
                }
            }
            *s = t;
        }
        let mut sum = transpose(sum);
        let coef = FloorPow::<T, A>::precalc();
        for s in sum.iter_mut() {
            let mut t = [T::zero(); A];
            for (t, c) in t.iter_mut().zip(coef.iter()) {
                for (s, c) in s.iter().zip(c.iter()) {
                    *t = *t + *c * *s;
                }
            }
            *s = t;
        }
        transpose(sum)
    }
}

impl<T, const A: usize, const B: usize> Monoid for FloorSum<T, A, B>
where
    T: Ring + Copy,
{
    fn id() -> Self {
        Self {
            x: [T::zero(); A],
            y: [T::zero(); B],
            sum: [[T::zero(); B]; A],
            id: true,
        }
    }
    fn merge(&self, rhs: &Self) -> Self {
        if self.id {
            return rhs.clone();
        }
        if rhs.id {
            return self.clone();
        }
        let mut res = Self::id();
        res.id = false;
        for (i, a) in self.x.iter().enumerate() {
            for (x, b) in res.x[i..].iter_mut().zip(rhs.x.iter()) {
                *x = *x + *a * *b;
            }
        }
        for (i, a) in self.y.iter().enumerate() {
            for (x, b) in res.y[i..].iter_mut().zip(rhs.y.iter()) {
                *x = *x + *a * *b;
            }
        }
        for (i, a) in self.x.iter().enumerate() {
            for (res, b) in res.sum[i..].iter_mut().zip(rhs.sum.iter()) {
                for (res, b) in res.iter_mut().zip(b.iter()) {
                    *res = *res + *a * *b;
                }
            }
        }
        for res in res.sum.iter_mut() {
            let mut next = [T::zero(); B];
            for (j, b) in self.y.iter().enumerate() {
                for (next, res) in next[j..].iter_mut().zip(res.iter()) {
                    *next = *next + *res * *b;
                }
            }
            *res = next;
        }
        for (res, a) in res.sum.iter_mut().zip(self.sum.iter()) {
            for (res, a) in res.iter_mut().zip(a.iter()) {
                *res = *res + *a;
            }
        }
        res
    }
}

pub trait Monoid: Clone {
    fn id() -> Self;
    fn merge(&self, rhs: &Self) -> Self;
    fn pow(&self, mut n: usize) -> Self {
        let mut t = Self::id();
        let mut r = self.clone();
        while n > 0 {
            if n & 1 == 1 {
                t = t.merge(&r);
            }
            r = r.merge(&r);
            n >>= 1;
        }
        t
    }
}

pub fn under_fold<T>(
    mut n: usize,
    mut m: usize,
    mut a: usize,
    mut b: usize,
    mut x: T,
    mut y: T,
) -> T
where
    T: Monoid,
{
    let mut front = T::id();
    let mut tail = T::id();
    let mut c = (a * n + b) / m;
    loop {
        if a >= m {
            let q = a / m;
            a %= m;
            x = x.merge(&y.pow(q));
            c -= q * n;
        }
        if b >= m {
            let q = b / m;
            b %= m;
            front = front.merge(&y.pow(q));
            c -= q;
        }
        if c == 0 {
            break;
        }
        let need = (m * c - b + a - 1) / a;
        tail = y.merge(&x.pow(n - need)).merge(&tail);
        n = c - 1;
        c = need;
        b = m - b + a - 1;
        std::mem::swap(&mut a, &mut m);
        std::mem::swap(&mut x, &mut y);
    }
    front.merge(&x.pow(n)).merge(&tail)
}

#[derive(Clone)]
pub struct FloorPow<T, const N: usize> {
    y: [T; N],
    s: [T; N],
}

impl<T, const N: usize> Monoid for FloorPow<T, N>
where
    T: Ring + Copy,
{
    fn id() -> Self {
        let mut y = [T::zero(); N];
        y[0] = T::one();
        Self {
            y,
            s: [T::zero(); N],
        }
    }
    fn merge(&self, rhs: &Self) -> Self {
        let mut y = [T::zero(); N];
        for (i, a) in self.y.iter().enumerate() {
            for (y, b) in y[i..].iter_mut().zip(rhs.y.iter()) {
                *y = *y + *a * *b;
            }
        }
        let mut s = self.s;
        for (i, a) in self.y.iter().enumerate() {
            for (s, b) in s[i..].iter_mut().zip(rhs.s.iter()) {
                *s = *s + *a * *b;
            }
        }
        Self { y, s }
    }
}

impl<T, const N: usize> FloorPow<T, N>
where
    T: Ring + Copy,
{
    pub fn dx() -> Self {
        let mut res = Self::id();
        res.s[0] = T::one();
        res
    }
    pub fn dy() -> Self {
        assert!(N >= 2);
        let mut res = Self::id();
        res.y[1] = T::one();
        res
    }
    pub fn flush(&self) -> [T; N] {
        let coef = Self::precalc();
        let mut res = [T::zero(); N];
        for (res, coef) in res.iter_mut().zip(coef.iter()) {
            for (s, c) in self.s.iter().zip(coef.iter()) {
                *res = *res + *c * *s;
            }
        }
        res
    }
    fn precalc() -> [[T; N]; N] {
        let mut binom = [[T::zero(); N]; N];
        binom[0][0] = T::one();
        for i in 1..N {
            binom[i][0] = T::one();
            for j in 1..(i + 1) {
                binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j];
            }
        }
        let mut pow = [[T::zero(); N]; N];
        let mut r = T::zero();
        for i in 1..N {
            r = r + T::one();
            pow[i][0] = T::one();
            for j in 1..N {
                pow[i][j] = pow[i][j - 1] * r;
            }
        }
        let mut coef = [[T::zero(); N]; N];
        for k in 1..N {
            for i in 1..(k + 1) {
                let mut c = T::zero();
                for j in 1..(i + 1) {
                    let v = binom[i][j] * pow[j][k];
                    if (i - j) % 2 == 0 {
                        c = c + v;
                    } else {
                        c = c - v;
                    }
                }
                coef[k][i] = c;
            }
        }
        coef[0][0] = T::one();
        coef
    }
}

pub fn transpose<T, const A: usize, const B: usize>(a: [[T; B]; A]) -> [[T; A]; B]
where
    T: Copy,
{
    let mut res = [[a[0][0]; A]; B];
    for (i, a) in a.iter().enumerate() {
        for (res, a) in res.iter_mut().zip(a.iter()) {
            res[i] = *a;
        }
    }
    res
}

// ---------- 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 PRIMITIVE_ROOT: u32 = primitive_root(M);
    const ORDER: usize = 1 << (M - 1).trailing_zeros();
    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)
    }
}

impl<const M: u32> From<i64> for ModInt<{ M }> {
    fn from(val: i64) -> ModInt<{ M }> {
        ModInt::new((val % M as i64 + M as i64) as u32 % M)
    }
}
// ---------- 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
    }
}

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結果

テストケース

コンパイルメッセージ

ソースコード