#898700 (Rust) No.2405 Minimal Matrix Decomposition

提出ソース

結果

問題	No.2405 Minimal Matrix Decomposition
ユーザー	akakimidori
提出日時	2023-08-04 22:45:56
言語	Rust (1.77.0 + proconio)
結果	AC
実行時間	231 ms / 2,000 ms
コード長	10,491 bytes
コンパイル時間	14,325 ms
コンパイル使用メモリ	381,224 KB
実行使用メモリ	5,760 KB
最終ジャッジ日時	2024-10-14 20:51:27
合計ジャッジ時間	19,254 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
（要ログイン）

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	1 ms 5,248 KB
testcase_02	AC	1 ms 5,248 KB
testcase_03	AC	1 ms 5,248 KB
testcase_04	AC	8 ms 5,248 KB
testcase_05	AC	231 ms 5,760 KB
testcase_06	AC	1 ms 5,248 KB
testcase_07	AC	1 ms 5,248 KB
testcase_08	AC	1 ms 5,248 KB
testcase_09	AC	1 ms 5,248 KB
testcase_10	AC	64 ms 5,248 KB
testcase_11	AC	81 ms 5,248 KB
testcase_12	AC	2 ms 5,248 KB
testcase_13	AC	14 ms 5,248 KB
testcase_14	AC	20 ms 5,248 KB
testcase_15	AC	6 ms 5,248 KB
testcase_16	AC	4 ms 5,248 KB
testcase_17	AC	32 ms 5,248 KB
testcase_18	AC	25 ms 5,248 KB
testcase_19	AC	23 ms 5,248 KB
testcase_20	AC	1 ms 5,248 KB
testcase_21	AC	5 ms 5,248 KB
testcase_22	AC	59 ms 5,248 KB
testcase_23	AC	2 ms 5,248 KB
testcase_24	AC	2 ms 5,248 KB
testcase_25	AC	3 ms 5,248 KB
testcase_26	AC	48 ms 5,248 KB
testcase_27	AC	13 ms 5,248 KB
testcase_28	AC	49 ms 5,248 KB
testcase_29	AC	10 ms 5,248 KB
testcase_30	AC	55 ms 5,248 KB
testcase_31	AC	19 ms 5,248 KB
testcase_32	AC	2 ms 5,248 KB
testcase_33	AC	41 ms 5,248 KB
testcase_34	AC	7 ms 5,248 KB
testcase_35	AC	1 ms 5,248 KB
testcase_36	AC	12 ms 5,248 KB
testcase_37	AC	22 ms 5,248 KB
testcase_38	AC	30 ms 5,248 KB
testcase_39	AC	58 ms 5,248 KB
testcase_40	AC	17 ms 5,248 KB
testcase_41	AC	3 ms 5,248 KB
testcase_42	AC	52 ms 5,248 KB
testcase_43	AC	10 ms 5,248 KB
testcase_44	AC	12 ms 5,248 KB
testcase_45	AC	4 ms 5,248 KB
testcase_46	AC	11 ms 5,248 KB
testcase_47	AC	15 ms 5,248 KB
testcase_48	AC	5 ms 5,248 KB
testcase_49	AC	2 ms 5,248 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

fn main() {
    input! {
        p: u32,
        h: usize,
        w: usize,
        a: [[u32; w]; h],
    }
    StaticMod::set_modulo(p);
    let mat = a
        .into_iter()
        .map(|a| a.into_iter().map(|a| M::new(a)).collect())
        .collect::<Vec<Vec<_>>>();
    let mut ans = vec![mat.clone()];
    let mut a = mat.clone();
    let mut s = 0;
    for j in 0..w {
        if let Some(x) = (s..h).find(|&x| !a[x][j].is_zero()) {
            a.swap(s, x);
            let mut src = std::mem::take(&mut a[s]);
            let inv = src[j].inv();
            for a in src.iter_mut() {
                *a *= inv;
            }
            for i in 0..h {
                if i != s {
                    let mul = a[i][j];
                    for (a, s) in a[i].iter_mut().zip(src.iter()) {
                        *a -= mul * *s;
                    }
                }
            }
            a[s] = src;
            s += 1;
        }
    }
    a.truncate(s);
    let mut b = vec![vec![M::zero(); a.len()]; h];
    if a.len() == 0 {
        a = vec![vec![M::zero(); w]];
        b = vec![vec![M::zero()]; h];
    } else {
        for (b, mat) in b.iter_mut().zip(mat.iter()) {
            for (b, a) in b.iter_mut().zip(a.iter()) {
                let x = a.iter().position(|a| !a.is_zero()).unwrap();
                *b = mat[x];
            }
        }
    }
    if h * w > (h + w) * a.len() {
        ans = vec![b, a];
    }
    use util::*;
    println!("{}", ans.len());
    for a in ans {
        println!("{} {}", a.len(), a[0].len());
        for a in a {
            println!("{}", a.iter().join(" "));
        }
    }
}

// ---------- 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 ----------
mod modint {

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

    pub trait Modulo {
        fn modulo() -> u32;
        fn im() -> u64;
        fn reduce(z: u64) -> u32 {
            let x = (z as u128 * Self::im() as u128 >> 64) as u32;
            let mut v = z as u32 - x * Self::modulo();
            if v >= Self::modulo() {
                v += Self::modulo();
            }
            v
        }
    }

    pub struct StaticMod;
    static mut STATIC_MOD: u32 = 0;
    static mut STATIC_MOD_IM: u64 = 0;
    impl Modulo for StaticMod {
        fn modulo() -> u32 {
            unsafe { STATIC_MOD }
        }
        fn im() -> u64 {
            unsafe { STATIC_MOD_IM }
        }
    }

    #[allow(dead_code)]
    impl StaticMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                STATIC_MOD = p;
                STATIC_MOD_IM = (!0u64 / p as u64) + 1;
            }
        }
    }

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

    impl<T> Clone for ModInt<T> {
        fn clone(&self) -> Self {
            ModInt::build(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();
            }
            Self::build(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 = self.0 - rhs.0;
            if self.0 < rhs.0 {
                d += T::modulo();
            }
            Self::build(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 {
            Self::build(T::reduce(self.0 as u64 * rhs.0 as u64))
        }
    }

    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::build(T::modulo() - self.0)
            }
        }
    }

    impl<T: Modulo> std::fmt::Display for ModInt<T> {
        fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
            write!(f, "{}", self.get())
        }
    }

    impl<T: Modulo> std::fmt::Debug for ModInt<T> {
        fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
            write!(f, "{}", self.get())
        }
    }

    impl<T: Modulo> 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 m = T::modulo() as i64;
            ModInt::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModInt<T> {
        fn build(d: u32) -> Self {
            ModInt(d, PhantomData)
        }
        pub fn zero() -> Self {
            Self::build(0)
        }
        pub fn is_zero(&self) -> bool {
            self.0 == 0
        }
    }

    #[allow(dead_code)]
    impl<T: Modulo> ModInt<T> {
        pub fn new_unchecked(d: u32) -> Self {
            Self::build(d)
        }
        pub fn new(d: u32) -> Self {
            Self::new_unchecked(d % T::modulo())
        }
        pub fn one() -> Self {
            Self::new_unchecked(1)
        }
        pub fn get(&self) -> u32 {
            self.0
        }
        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() - 2) as u64)
        }
    }
}
// ---------- 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<StaticMod>;

mod util {
    pub trait Join {
        fn join(self, sep: &str) -> String;
    }

    impl<T, I> Join for I
    where
        I: Iterator<Item = T>,
        T: std::fmt::Display,
    {
        fn join(self, sep: &str) -> String {
            let mut s = String::new();
            use std::fmt::*;
            for (i, v) in self.enumerate() {
                if i > 0 {
                    write!(&mut s, "{}", sep).ok();
                }
                write!(&mut s, "{}", v).ok();
            }
            s
        }
    }
}

yukicoder

結果

テストケース

ソースコード