#832301 (Rust) No.1907 DETERMINATION

提出ソース
結果

問題	No.1907 DETERMINATION
コンテスト
ユーザー	akakimidori
提出日時	2023-01-13 19:17:00
言語	Rust (1.83.0 + proconio)
結果	AC
実行時間	294 ms / 4,000 ms
コード長	11,252 bytes
コンパイル時間	13,440 ms
コンパイル使用メモリ	379,136 KB
実行使用メモリ	6,656 KB
最終ジャッジ日時	2024-12-24 14:05:40
合計ジャッジ時間	30,011 ms
ジャッジサーバーID （参考情報）	judge4 / judge2
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 4
other	AC * 63
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ソースコード

raw source code
fn main() {
    input! {
        n: usize,
        a: [[M; n]; n],
        b: [[M; n]; n],
    }
    let t = det_a_xb(a, b);
    for i in 0..=n {
        println!("{}", t[i]);
    }
}

// det(A + xB)
// 乱数でやるやつ、N/P の確率で失敗するので注意
pub fn det_a_xb(mut a: Vec<Vec<M>>, mut b: Vec<Vec<M>>) -> Vec<M> {
    let n = a.len();
    assert!(b.len() == n && a.iter().chain(b.iter()).all(|p| p.len() == n));
    let c = M::from(rand());
    for (a, b) in a.iter_mut().zip(b.iter()) {
        for (a, b) in a.iter_mut().zip(b.iter()) {
            *a += c * *b;
        }
    }
    std::mem::swap(&mut a, &mut b);
    let mut det = M::one();
    for i in 0..n {
        if let Some(x) = (i..n).find(|&x| !b[x][i].is_zero()) {
            if x != i {
                det = -det;
                a.swap(i, x);
                b.swap(i, x);
            }
        } else {
            return vec![M::zero(); n + 1];
        }
        let v = b[i][i];
        det *= v;
        let inv = v.inv();
        for (a, b) in a[i].iter_mut().zip(b[i].iter_mut()) {
            *a *= inv;
            *b *= inv;
        }
        let sa = std::mem::take(&mut a[i]);
        let sb = std::mem::take(&mut b[i]);
        for (a, b) in a.iter_mut().zip(b.iter_mut()).filter(|p| !p.0.is_empty()) {
            let v = b[i];
            for (a, sa) in a.iter_mut().zip(&sa) {
                *a -= *sa * v;
            }
            for (b, sb) in b[i..].iter_mut().zip(&sb[i..]) {
                *b -= *sb * v;
            }
        }
        a[i] = sa;
        b[i] = sb;
    }
    for a in a.iter_mut().flatten() {
        *a = -*a;
    }
    let mut p = characteristic_polynomial(a);
    p.iter_mut().for_each(|p| *p *= det);
    let mut res = vec![];
    for (i, p) in p.iter().enumerate() {
        let mut next = vec![M::zero(); i + 1];
        for (j, res) in res.iter().enumerate() {
            next[j + 1] += *res;
            next[j] -= c * *res;
        }
        next[0] += *p;
        res = next;
    }
    res
}

pub fn characteristic_polynomial(mut a: Vec<Vec<M>>) -> Vec<M> {
    let n = a.len();
    if n == 0 {
        return vec![M::one()];
    }
    assert!(a.iter().all(|a| a.len() == n));
    for j in 0..(n - 1) {
        if let Some(x) = ((j + 1)..n).find(|&x| !a[x][j].is_zero()) {
            a.swap(j + 1, x);
            a.iter_mut().for_each(|a| a.swap(j + 1, x));
            let inv = a[j + 1][j].inv();
            let mut v = vec![];
            let src = std::mem::take(&mut a[j + 1]);
            for a in a[(j + 2)..].iter_mut() {
                let mul = a[j] * inv;
                v.push(mul);
                for (a, src) in a[j..].iter_mut().zip(src[j..].iter()) {
                    *a -= mul * *src;
                }
            }
            a[j + 1] = src;
            for a in a.iter_mut() {
                let v = a[(j + 2)..].iter().zip(v.iter()).fold(M::zero(), |s, a| s + *a.0 * *a.1);
                a[j + 1] += v;
            }
        }
    }
    let mut dp = vec![vec![M::one()]];
    for i in 0..n {
        let mut next = vec![M::zero(); i + 2];
        for (j, dp) in dp[i].iter().enumerate() {
            next[j] -= *dp * a[i][i];
            next[j + 1] += *dp;
        }
        let mut mul = M::one();
        for j in (0..i).rev() {
            mul *= a[j + 1][j];
            let c = -mul * a[j][i];
            for (next, dp) in next.iter_mut().zip(dp[j].iter()) {
                *next += c * *dp;
            }
        }
        dp.push(next);
    }
    dp.pop().unwrap()
}

// ---------- 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>>;

fn rand_memory() -> usize {
    Box::into_raw(Box::new("I hope this is a random number")) as usize
}

fn rand() -> usize {
    static mut X: usize = 0;
    unsafe {
        if X == 0 {
            X = rand_memory();
        }
        X ^= X << 13;
        X ^= X >> 17;
        X ^= X << 5;
        X
    }
}
yukicoder

結果

ソースコード
