結果

問題 No.621 3 x N グリッド上のドミノの置き方の数
ユーザー koba-e964koba-e964
提出日時 2021-10-16 16:50:54
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 124 ms / 3,000 ms
コード長 5,204 bytes
コンパイル時間 12,675 ms
コンパイル使用メモリ 385,620 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-09-17 19:28:32
合計ジャッジ時間 19,395 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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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 4 ms
6,816 KB
testcase_01 AC 8 ms
6,940 KB
testcase_02 AC 3 ms
6,944 KB
testcase_03 AC 4 ms
6,940 KB
testcase_04 AC 5 ms
6,940 KB
testcase_05 AC 5 ms
6,940 KB
testcase_06 AC 6 ms
6,940 KB
testcase_07 AC 6 ms
6,940 KB
testcase_08 AC 7 ms
6,940 KB
testcase_09 AC 6 ms
6,940 KB
testcase_10 AC 7 ms
6,940 KB
testcase_11 AC 8 ms
6,944 KB
testcase_12 AC 12 ms
6,944 KB
testcase_13 AC 14 ms
6,940 KB
testcase_14 AC 21 ms
6,944 KB
testcase_15 AC 29 ms
6,944 KB
testcase_16 AC 33 ms
6,940 KB
testcase_17 AC 34 ms
6,944 KB
testcase_18 AC 45 ms
6,940 KB
testcase_19 AC 46 ms
6,944 KB
testcase_20 AC 52 ms
6,940 KB
testcase_21 AC 54 ms
6,940 KB
testcase_22 AC 63 ms
6,940 KB
testcase_23 AC 66 ms
6,940 KB
testcase_24 AC 71 ms
6,944 KB
testcase_25 AC 82 ms
6,940 KB
testcase_26 AC 80 ms
6,940 KB
testcase_27 AC 91 ms
6,944 KB
testcase_28 AC 91 ms
6,940 KB
testcase_29 AC 99 ms
6,940 KB
testcase_30 AC 93 ms
6,944 KB
testcase_31 AC 91 ms
6,940 KB
testcase_32 AC 85 ms
6,944 KB
testcase_33 AC 98 ms
6,944 KB
testcase_34 AC 93 ms
6,944 KB
testcase_35 AC 88 ms
6,944 KB
testcase_36 AC 92 ms
6,940 KB
testcase_37 AC 100 ms
6,944 KB
testcase_38 AC 103 ms
6,940 KB
testcase_39 AC 104 ms
6,944 KB
testcase_40 AC 104 ms
6,944 KB
testcase_41 AC 104 ms
6,940 KB
testcase_42 AC 102 ms
6,940 KB
testcase_43 AC 103 ms
6,940 KB
testcase_44 AC 103 ms
6,940 KB
testcase_45 AC 104 ms
6,940 KB
testcase_46 AC 103 ms
6,944 KB
testcase_47 AC 104 ms
6,940 KB
testcase_48 AC 105 ms
6,940 KB
testcase_49 AC 105 ms
6,940 KB
testcase_50 AC 103 ms
6,940 KB
testcase_51 AC 104 ms
6,944 KB
testcase_52 AC 104 ms
6,944 KB
testcase_53 AC 105 ms
6,944 KB
testcase_54 AC 105 ms
6,940 KB
testcase_55 AC 105 ms
6,940 KB
testcase_56 AC 105 ms
6,940 KB
testcase_57 AC 106 ms
6,940 KB
testcase_58 AC 88 ms
6,944 KB
testcase_59 AC 121 ms
6,940 KB
testcase_60 AC 122 ms
6,940 KB
testcase_61 AC 122 ms
6,944 KB
testcase_62 AC 124 ms
6,940 KB
testcase_63 AC 65 ms
6,944 KB
testcase_64 AC 65 ms
6,940 KB
testcase_65 AC 66 ms
6,940 KB
testcase_66 AC 66 ms
6,944 KB
testcase_67 AC 66 ms
6,944 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

diff # 

use std::io::Read;

fn get_word() -> String {
    let stdin = std::io::stdin();
    let mut stdin=stdin.lock();
    let mut u8b: [u8; 1] = [0];
    loop {
        let mut buf: Vec<u8> = Vec::with_capacity(16);
        loop {
            let res = stdin.read(&mut u8b);
            if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
                break;
            } else {
                buf.push(u8b[0]);
            }
        }
        if buf.len() >= 1 {
            let ret = String::from_utf8(buf).unwrap();
            return ret;
        }
    }
}

#[allow(dead_code)]
fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }

/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
mod mod_int {
    use std::ops::*;
    pub trait Mod: Copy { fn m() -> i64; }
    #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
    pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
    impl<M: Mod> ModInt<M> {
        // x >= 0
        pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) }
        fn new_internal(x: i64) -> Self {
            ModInt { x: x, phantom: ::std::marker::PhantomData }
        }
        pub fn pow(self, mut e: i64) -> Self {
            debug_assert!(e >= 0);
            let mut sum = ModInt::new_internal(1);
            let mut cur = self;
            while e > 0 {
                if e % 2 != 0 { sum *= cur; }
                cur *= cur;
                e /= 2;
            }
            sum
        }
        #[allow(dead_code)]
        pub fn inv(self) -> Self { self.pow(M::m() - 2) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
        type Output = Self;
        fn add(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x + other.x;
            if sum >= M::m() { sum -= M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
        type Output = Self;
        fn sub(self, other: T) -> Self {
            let other = other.into();
            let mut sum = self.x - other.x;
            if sum < 0 { sum += M::m(); }
            ModInt::new_internal(sum)
        }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
        type Output = Self;
        fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
        fn add_assign(&mut self, other: T) { *self = *self + other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
        fn sub_assign(&mut self, other: T) { *self = *self - other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
        fn mul_assign(&mut self, other: T) { *self = *self * other; }
    }
    impl<M: Mod> Neg for ModInt<M> {
        type Output = Self;
        fn neg(self) -> Self { ModInt::new(0) - self }
    }
    impl<M> ::std::fmt::Display for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
} // mod mod_int

macro_rules! define_mod {
    ($struct_name: ident, $modulo: expr) => {
        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
        struct $struct_name {}
        impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
    }
}
const MOD: i64 = 1_000_000_007;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;

// Depends on MInt.rs
// Verified by: https://atcoder.jp/contests/abc199/submissions/22259436
fn squmul(a: &[Vec<MInt>], b: &[Vec<MInt>]) -> Vec<Vec<MInt>> {
    let n = a.len();
    let mut ret = vec![vec![MInt::new(0); n]; n];
    for i in 0..n {
        for j in 0..n {
            for k in 0..n {
                ret[i][k] += a[i][j] * b[j][k];
            }
        }
    }
    ret
}

fn squpow(a: &[Vec<MInt>], mut e: i64) -> Vec<Vec<MInt>> {
    let n = a.len();
    let mut sum = vec![vec![MInt::new(0); n]; n];
    for i in 0..n { sum[i][i] = 1.into(); }
    let mut cur = a.to_vec();
    while e > 0 {
        if e % 2 == 1 {
            sum = squmul(&sum, &cur);
        }
        cur = squmul(&cur, &cur);
        e /= 2;
    }
    sum
}

// Tags: matrix-multiplication
fn main() {
    let n: i64 = get();
    let mut mat = vec![vec![MInt::new(0); 64]; 64];
    for pre in 0..8 {
        for i in 0..8 {
            for j in 0..8 {
                if (i & j) != j { continue; }
                let diff = i ^ j;
                if (diff & 3) == 3 || (diff & 6) == 6 { continue; }
                let x = 7 ^ j;
                for &k in &[0, 3, 6] {
                    if (x & k) == k && (diff & pre) == 0 {
                        mat[8 * i + pre][(7 - j - k) * 8 + (i ^ j)] += 1;
                    }
                }
            }
        }
    }
    let ans = squpow(&mat, n);
    let mut tot = MInt::new(0);
    for &i in &[0, 1, 2, 4, 5] {
        for &j in &[0, 1, 2, 4, 5] {
            if (i & j) == 0 {
                tot += ans[0][i * 8 + j];
            }
        }
    }
    println!("{}", tot);
}
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