結果

問題 No.2362 Inversion Number of Mod of Linear
ユーザー akakimidoriakakimidori
提出日時 2023-06-24 00:49:22
言語 Rust
(1.77.0)
結果
AC  
実行時間 1,532 ms / 2,000 ms
コード長 13,477 bytes
コンパイル時間 6,015 ms
コンパイル使用メモリ 170,428 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-09-13 20:00:32
合計ジャッジ時間 10,595 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge14
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
4,376 KB
testcase_01 AC 1 ms
4,380 KB
testcase_02 AC 1 ms
4,376 KB
testcase_03 AC 640 ms
4,376 KB
testcase_04 AC 189 ms
4,376 KB
testcase_05 AC 46 ms
4,380 KB
testcase_06 AC 1,532 ms
4,380 KB
testcase_07 AC 394 ms
4,376 KB
testcase_08 AC 417 ms
4,380 KB
testcase_09 AC 429 ms
4,380 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 `find` is never used
   --> Main.rs:157:12
    |
157 |     pub fn find(&self, n: i64, m: i64, a: i64, b: i64, c: usize, d: usize) -> ModInt<Mod> {
    |            ^^^^
    |
    = note: `#[warn(dead_code)]` on by default

warning: 1 warning emitted

ソースコード

diff # 

// sum_{0 <= i < j < N} ceil((A_i - A_j) / M)
// = sum_{i < j} ceil((Xi + Y - M(
//
// V = x (mod A)
// V = y (mod B)
// V = x * B * B^(-1) (mod A)

use std::io::Write;

const MOD1: u32 = 1_000_000_007;
const MOD2: u32 = 1_000_000_009;

fn main() {
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    input! {
        t: usize,
        ask: [(i64, i64, i64, i64); t],
    }
    for (n, m, a, b) in ask {
        let x = {
            type Mod = ConstantModulo<MOD1>;
            type M = ModInt<Mod>;
            let x = Solver::<Mod>::new(2);
            let v = x.find_all(n, m, a, b);
            let u = x.find_all(n, m, a, 0);
            let mut ans = M::zero();
            ans += M::new(2) * v[1][1];
            ans -= M::from(n - 1) * v[0][1];
            ans += u[1][1];
            ans -= M::from(n) * u[0][1];
            ans
        };
        let y = {
            type Mod = ConstantModulo<MOD2>;
            type M = ModInt<Mod>;
            let x = Solver::<Mod>::new(2);
            let v = x.find_all(n, m, a, b);
            let u = x.find_all(n, m, a, 0);
            let mut ans = M::zero();
            ans += M::new(2) * v[1][1];
            ans -= M::from(n - 1) * v[0][1];
            ans += u[1][1];
            ans -= M::from(n) * u[0][1];
            ans
        };
        let (a, b) = (x.0, y.0);
        let mut ans = 0;
        ans += a as u128 * pow(MOD2, MOD1 - 2, MOD1) as u128 * MOD2 as u128;
        ans += b as u128 * pow(MOD1, MOD2 - 2, MOD2) as u128 * MOD1 as u128;
        ans %= MOD1 as u128 * MOD2 as u128;
        writeln!(out, "{}", ans).ok();
    }
}

fn pow(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
}

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

struct Solver<Mod> {
    p: Vec<Vec<ModInt<Mod>>>,
    pc: Precalc<Mod>,
    size: usize,
}

impl<Mod> Solver<Mod>
where
    Mod: Modulo,
{
    pub fn new(size: usize) -> Self {
        let mut p = vec![vec![]; 1];
        let pc = Precalc::new(size + 1);
        p[0] = vec![ModInt::zero(), ModInt::one()];
        for i in 1..=size {
            let mut a = vec![ModInt::zero(); i + 2];
            a[i + 1] = ModInt::one();
            for j in 0..i {
                let m = pc.binom(i + 1, j);
                for (a, p) in a.iter_mut().zip(p[j].iter()) {
                    *a -= m * *p;
                }
            }
            let inv = pc.inv(i + 1);
            a.iter_mut().for_each(|a| *a *= inv);
            p.push(a);
        }
        Self {
            p: p,
            pc: pc,
            size: size,
        }
    }
    pub fn find_all(&self, n: i64, m: i64, a: i64, b: i64) -> Vec<Vec<ModInt<Mod>>> {
        self.find_rec(n, m, a, b, self.size)
    }
    pub fn find(&self, n: i64, m: i64, a: i64, b: i64, c: usize, d: usize) -> ModInt<Mod> {
        assert!(c + d <= self.size);
        let t = self.find_rec(n, m, a, b, c + d);
        t[c][d]
    }
    fn find_rec(&self, n: i64, m: i64, a: i64, b: i64, s: usize) -> Vec<Vec<ModInt<Mod>>> {
        if a >= m {
            let x = a.div_euclid(m);
            let pre = self.find_rec(n, m, a - x * m, b, s);
            let mut res = (0..=s)
                .map(|c| vec![ModInt::zero(); s - c + 1])
                .collect::<Vec<_>>();
            for c in 0..=s {
                for d in 0..=(s - c) {
                    let mut sum = ModInt::zero();
                    for q in (0..=d).rev() {
                        let p = d - q;
                        sum = ModInt::from(x) * sum + self.pc.binom(d, q) * pre[q + c][p];
                    }
                    res[c][d] = sum;
                }
            }
            return res;
        }
        if b >= m {
            let y = b.div_euclid(m);
            let pre = self.find_rec(n, m, a, b - y * m, s);
            let mut res = (0..=s)
                .map(|c| vec![ModInt::zero(); s - c + 1])
                .collect::<Vec<_>>();
            for c in 0..=s {
                for d in 0..=(s - c) {
                    let mut sum = ModInt::zero();
                    for r in (0..=d).rev() {
                        let p = d - r;
                        sum = ModInt::from(y) * sum + self.pc.binom(d, r) * pre[c][p];
                    }
                    res[c][d] = sum;
                }
            }
            return res;
        }
        if a * (n - 1) + b < m {
            let mut res = (0..=s)
                .map(|c| vec![ModInt::zero(); s - c + 1])
                .collect::<Vec<_>>();
            for i in 0..=s {
                res[i][0] = self.p[i]
                    .iter()
                    .rfold(ModInt::zero(), |s, a| s * ModInt::from(n) + *a);
            }
            return res;
        }
        let pc = &self.pc;
        let mut res = (0..=s)
            .map(|c| vec![ModInt::zero(); s - c + 1])
            .collect::<Vec<_>>();
        for i in 0..=s {
            res[i][0] = self.p[i]
                .iter()
                .rfold(ModInt::zero(), |s, a| s * ModInt::from(n) + *a);
        }
        let y = (a * (n - 1) + b) / m;
        let pre = self.find_rec(y, a, m, m - b + a - 1, s);
        let mut sum = (0..=s)
            .map(|c| vec![ModInt::zero(); s - c + 2])
            .collect::<Vec<_>>();
        for c in 0..=s {
            for d in 0..=(s - c + 1) {
                let mut s = ModInt::zero();
                for i in 0..d {
                    s += pc.binom(d, i) * pre[i][c];
                }
                sum[c][d] = s;
            }
        }
        for c in 0..=s {
            for d in 1..=(s - c) {
                let mut p = self.p[c].clone();
                p.iter_mut().for_each(|p| *p = -*p);
                p[0] += self.p[c]
                    .iter()
                    .rfold(ModInt::zero(), |s, a| s * ModInt::from(n) + *a);
                for (i, p) in p.iter().enumerate() {
                    res[c][d] += *p * sum[i][d];
                }
            }
        }
        res
    }
}

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