#707860 (Rust) No.621 3 x N グリッド上のドミノの置き方の数

提出ソース

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-e964
提出日時	2021-10-16 16:49:42
言語	Rust (1.77.0 + proconio)
結果	AC
実行時間	124 ms / 3,000 ms
コード長	6,269 bytes
コンパイル時間	13,156 ms
コンパイル使用メモリ	383,028 KB
実行使用メモリ	6,948 KB
最終ジャッジ日時	2024-09-17 19:28:12
合計ジャッジ時間	20,226 ms
ジャッジサーバーID （参考情報）	judge1 / judge2

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	4 ms 6,816 KB
testcase_01	AC	9 ms 6,812 KB
testcase_02	AC	3 ms 6,816 KB
testcase_03	AC	5 ms 6,944 KB
testcase_04	AC	6 ms 6,940 KB
testcase_05	AC	5 ms 6,940 KB
testcase_06	AC	7 ms 6,944 KB
testcase_07	AC	6 ms 6,940 KB
testcase_08	AC	7 ms 6,940 KB
testcase_09	AC	7 ms 6,944 KB
testcase_10	AC	8 ms 6,940 KB
testcase_11	AC	7 ms 6,944 KB
testcase_12	AC	12 ms 6,940 KB
testcase_13	AC	15 ms 6,944 KB
testcase_14	AC	22 ms 6,940 KB
testcase_15	AC	29 ms 6,940 KB
testcase_16	AC	34 ms 6,944 KB
testcase_17	AC	35 ms 6,940 KB
testcase_18	AC	45 ms 6,944 KB
testcase_19	AC	46 ms 6,940 KB
testcase_20	AC	52 ms 6,940 KB
testcase_21	AC	54 ms 6,940 KB
testcase_22	AC	64 ms 6,940 KB
testcase_23	AC	66 ms 6,944 KB
testcase_24	AC	71 ms 6,940 KB
testcase_25	AC	82 ms 6,940 KB
testcase_26	AC	80 ms 6,940 KB
testcase_27	AC	92 ms 6,940 KB
testcase_28	AC	91 ms 6,944 KB
testcase_29	AC	99 ms 6,940 KB
testcase_30	AC	94 ms 6,940 KB
testcase_31	AC	91 ms 6,940 KB
testcase_32	AC	85 ms 6,940 KB
testcase_33	AC	98 ms 6,948 KB
testcase_34	AC	93 ms 6,940 KB
testcase_35	AC	88 ms 6,940 KB
testcase_36	AC	92 ms 6,940 KB
testcase_37	AC	101 ms 6,940 KB
testcase_38	AC	103 ms 6,944 KB
testcase_39	AC	104 ms 6,944 KB
testcase_40	AC	104 ms 6,944 KB
testcase_41	AC	105 ms 6,944 KB
testcase_42	AC	101 ms 6,944 KB
testcase_43	AC	104 ms 6,940 KB
testcase_44	AC	104 ms 6,940 KB
testcase_45	AC	104 ms 6,944 KB
testcase_46	AC	103 ms 6,944 KB
testcase_47	AC	104 ms 6,944 KB
testcase_48	AC	105 ms 6,944 KB
testcase_49	AC	105 ms 6,940 KB
testcase_50	AC	103 ms 6,944 KB
testcase_51	AC	104 ms 6,940 KB
testcase_52	AC	104 ms 6,940 KB
testcase_53	AC	105 ms 6,940 KB
testcase_54	AC	104 ms 6,944 KB
testcase_55	AC	105 ms 6,940 KB
testcase_56	AC	104 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 6,944 KB
testcase_63	AC	64 ms 6,940 KB
testcase_64	AC	65 ms 6,944 KB
testcase_65	AC	66 ms 6,940 KB
testcase_66	AC	66 ms 6,940 KB
testcase_67	AC	65 ms 6,944 KB

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ソースコード

raw source code

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::Read;

#[allow(dead_code)]
fn getline() -> String {
    let mut ret = String::new();
    std::io::stdin().read_line(&mut ret).ok().unwrap();
    ret
}

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> ::std::fmt::Debug for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            let (mut a, mut b, _) = red(self.x, M::m());
            if b < 0 {
                a = -a;
                b = -b;
            }
            write!(f, "{}/{}", a, b)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
    // Finds the simplest fraction x/y congruent to r mod p.
    // The return value (x, y, z) satisfies x = y * r + z * p.
    fn red(r: i64, p: i64) -> (i64, i64, i64) {
        if r.abs() <= 10000 {
            return (r, 1, 0);
        }
        let mut nxt_r = p % r;
        let mut q = p / r;
        if 2 * nxt_r >= r {
            nxt_r -= r;
            q += 1;
        }
        if 2 * nxt_r <= -r {
            nxt_r += r;
            q -= 1;
        }
        let (x, z, y) = red(nxt_r, r);
        (x, y - q * z, z)
    }
} // 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
}

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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結果

テストケース

ソースコード