#509925 (Rust) No.1112 冥界の音楽

• 問題: No.1112 冥界の音楽
• ユーザー: cotton_fn_
• 提出日時: 2020-07-10 22:12:19
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 9 ms / 2,000 ms
• コード長: 8,541 bytes
• コンパイル時間: 13,951 ms
• コンパイル使用メモリ: 375,460 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-10-11 09:29:41
• 合計ジャッジ時間: 15,390 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

ファイルパターン	結果
sample	AC * 3
other	AC * 34

ソースコード

#![allow(unused_imports, unused_macros)]

use kyoproio::*;
use std::{
    collections::*,
    io::{self, prelude::*},
    iter,
    mem::{replace, swap},
};

fn main() -> io::Result<()> {
    std::thread::Builder::new()
        .stack_size(64 * 1024 * 1024)
        .spawn(|| {
            let stdin = io::stdin();
            let stdout = io::stdout();
            run(KInput::new(stdin.lock()), io::BufWriter::new(stdout.lock()))
        })?
        .join()
        .unwrap();
    Ok(())
}

fn run<I: Input, O: Write>(mut kin: I, mut out: O) {
    macro_rules! output { ($($args:expr),+) => { write!(&mut out, $($args),+).unwrap(); }; }
    macro_rules! outputln {
        ($($args:expr),+) => { output!($($args),+); outputln!(); };
        () => { output!("\n"); if cfg!(debug_assertions) { out.flush().unwrap(); } }
    }

    let (k, m, n): (usize, usize, i64) = kin.input();
    
    let mut a = SquareMatrix::zeros();
    for (p, q, r) in kin.iter::<(usize, usize, usize)>().take(m) {
        let (p, q, r) = (p - 1, q - 1, r - 1);
        a[k * p + q][k * q + r] = 1;
    }

    let a = a.pow(n - 2);

    /*
    for i in 0..k * k {
        for j in 0..k * k {
            eprint!("{} ", a[i][j]);
        }
        eprintln!();
    }
    */

    let mut ans = 0;
    for i in 0..k {
        for j in 0..k {
            ans += a[i][k * j];
        }
    }
    
    ans %= MOD;
    outputln!("{}", ans);
}

const MOD: i64 = 1e9 as i64 + 7;
pub const N: usize = 6 * 6;
#[derive(Clone)]
pub struct SquareMatrix(Box<[[i64; N]]>);
impl SquareMatrix {
    pub fn zeros() -> Self {
        Self(vec![[0; N]; N].into())
    }
    pub fn id() -> Self {
        let mut a = Self::zeros();
        for i in 0..N {
            a[i][i] = 1;
        }
        a
    }
    pub fn add(&self, rhs: &Self) -> Self {
        let mut a = Self::zeros();
        for i in 0..N {
            for j in 0..N {
                a[i][j] = (self[i][j] + rhs[i][j]) % MOD;
            }
        }
        a
    }
    pub fn mul(&self, rhs: &Self) -> Self {
        let mut a = Self::zeros();
        for i in 0..N {
            for k in 0..N {
                for j in 0..N {
                    a[i][j] = (a[i][j] + self[i][k] * rhs[k][j]) % MOD;
                }
            }
        }
        a
    }
    pub fn pow(&self, mut k: i64) -> Self {
        let mut a = self.clone();
        let mut b = Self::id();
        while k > 0 {
            if k & 1 == 1 {
                b = b.mul(&a);
            }
            a = a.mul(&a);
            k >>= 1;
        }
        b
    }
    // wip https://en.wikipedia.org/wiki/LU_decomposition
    pub fn lup(&mut self) -> Option<(Vec<usize>, i64)> {
        let mut p: Vec<_> = (0..N).collect();
        let mut swap_count = 0;
        let mut d_inv = vec![0; N];
        for k in 0..N {
            if self[k][k] == 0 {
                for i in k + 1..N {
                    if self[i][k] != 0 {
                        self.0.swap(i, k);
                        p.swap(i, k);
                        swap_count += 1;
                    }
                }
                if self[k][k] == 0 {
                    return None;
                }
            }
            d_inv[k] = mod_inv(self[k][k], MOD);
            for i in k + 1..N {
                self[i][k] = (self[i][k] * d_inv[k]).rem_euclid(MOD);
                for j in k + 1..N {
                    self[i][j] = (self[i][j] - self[i][k] * self[k][j]).rem_euclid(MOD);
                }
            }
        }
        Some((p, swap_count))
    }
    pub fn det(&mut self) -> i64 {
        if let Some((_, c)) = self.lup() {
            let mut det = if c & 1 == 0 { 1 } else { -1 };
            for i in 0..N {
                det = (det * self[i][i]).rem_euclid(MOD);
            }
            det
        } else {
            0
        }
    }
    pub fn inv(mut self) -> Option<Self> {
        self.lup().map(|(p, _)| {
            let mut inv = Self::zeros();
            for i in 0..N {
                inv[i][p[i]] = 1;
            }
            for k in 0..N {
                for i in k + 1..N {
                    for j in 0..N {
                        inv[i][j] = (inv[i][j] - self[i][k] * inv[k][j]).rem_euclid(MOD);
                    }
                }
            }
            for k in (0..N).rev() {
                let d = mod_inv(self[k][k], MOD);
                for i in 0..k {
                    let c = (d * self[i][k]).rem_euclid(MOD);
                    for j in 0..N {
                        inv[i][j] = (inv[i][j] - c * inv[k][j]).rem_euclid(MOD);
                    }
                }
                for j in 0..N {
                    inv[k][j] = (d * inv[k][j]).rem_euclid(MOD);
                }
            }
            inv
        })
    }
}
use std::ops::*;
impl<I: std::slice::SliceIndex<[[i64; N]]>> Index<I> for SquareMatrix {
    type Output = I::Output;
    fn index(&self, i: I) -> &Self::Output {
        &self.0[i]
    }
}
impl<I: std::slice::SliceIndex<[[i64; N]]>> IndexMut<I> for SquareMatrix {
    fn index_mut(&mut self, i: I) -> &mut Self::Output {
        &mut self.0[i]
    }
}

pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) {
    if b != 0 {
        let (g, y, x) = extgcd(b, a.rem_euclid(b));
        (g, x, y - a / b * x)
    } else {
        (a, 1, 0)
    }
}
pub fn mod_inv(x: i64, m: i64) -> i64 {
    extgcd(x, m).1
}

// -----------------------------------------------------------------------------
pub mod kyoproio {
    use std::io::prelude::*;
    pub trait Input {
        fn str(&mut self) -> &str;
        fn input<T: InputParse>(&mut self) -> T {
            T::input(self)
        }
        fn iter<T: InputParse>(&mut self) -> Iter<T, Self> {
            Iter(self, std::marker::PhantomData)
        }
        fn seq<T: InputParse, B: std::iter::FromIterator<T>>(&mut self, n: usize) -> B {
            self.iter().take(n).collect()
        }
    }
    pub struct KInput<R> {
        src: R,
        buf: String,
        pos: usize,
    }
    impl<R: BufRead> KInput<R> {
        pub fn new(src: R) -> Self {
            Self {
                src,
                buf: String::with_capacity(1024),
                pos: 0,
            }
        }
    }
    impl<R: BufRead> Input for KInput<R> {
        fn str(&mut self) -> &str {
            loop {
                if self.pos >= self.buf.len() {
                    self.pos = 0;
                    self.buf.clear();
                    if self.src.read_line(&mut self.buf).expect("io error") == 0 {
                        return &self.buf;
                    }
                }
                let range = self.pos
                    ..self.buf[self.pos..]
                        .find(|c: char| c.is_ascii_whitespace())
                        .map(|i| i + self.pos)
                        .unwrap_or_else(|| self.buf.len());
                self.pos = range.end + 1;
                if range.end > range.start {
                    return &self.buf[range];
                }
            }
        }
    }
    pub struct Iter<'a, T, I: ?Sized>(&'a mut I, std::marker::PhantomData<*const T>);
    impl<'a, T: InputParse, I: Input + ?Sized> Iterator for Iter<'a, T, I> {
        type Item = T;
        fn next(&mut self) -> Option<T> {
            Some(self.0.input())
        }
    }
    pub trait InputParse: Sized {
        fn input<I: Input + ?Sized>(src: &mut I) -> Self;
    }
    impl InputParse for Vec<u8> {
        fn input<I: Input + ?Sized>(src: &mut I) -> Self {
            src.str().as_bytes().to_owned()
        }
    }
    macro_rules! from_str_impl {
        { $($T:ty)* } => {
            $(impl InputParse for $T {
                fn input<I: Input + ?Sized>(src: &mut I) -> Self {
                    src.str().parse::<$T>().expect("parse error")
                }
            })*
        }
    }
    from_str_impl! {
        String char bool f32 f64 isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128
    }
    macro_rules! tuple_impl {
        ($H:ident $($T:ident)*) => {
            impl<$H: InputParse, $($T: InputParse),*> InputParse for ($H, $($T),*) {
                fn input<I: Input + ?Sized>(src: &mut I) -> Self {
                    ($H::input(src), $($T::input(src)),*)
                }
            }
            tuple_impl!($($T)*);
        };
        () => {}
    }
    tuple_impl!(A B C D E F G);
    #[macro_export]
    macro_rules! kdbg {
        ($($v:expr),*) => {
            if cfg!(debug_assertions) { dbg!($($v),*) } else { ($($v),*) }
        }
    }
}