結果

問題 No.1073 無限すごろく
ユーザー akakimidoriakakimidori
提出日時 2020-06-05 21:39:25
言語 Rust
(1.77.0)
結果
AC  
実行時間 1 ms / 2,000 ms
コード長 7,299 bytes
コンパイル時間 1,588 ms
コンパイル使用メモリ 156,804 KB
実行使用メモリ 4,380 KB
最終ジャッジ日時 2023-08-22 14:41:34
合計ジャッジ時間 2,737 ms
ジャッジサーバーID
（参考情報） 		judge15 / judge12
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 1 ms
4,376 KB
testcase_01 AC 1 ms
4,376 KB
testcase_02 AC 1 ms
4,380 KB
testcase_03 AC 1 ms
4,376 KB
testcase_04 AC 1 ms
4,380 KB
testcase_05 AC 1 ms
4,380 KB
testcase_06 AC 1 ms
4,376 KB
testcase_07 AC 1 ms
4,376 KB
testcase_08 AC 1 ms
4,376 KB
testcase_09 AC 1 ms
4,376 KB
testcase_10 AC 1 ms
4,376 KB
testcase_11 AC 1 ms
4,376 KB
testcase_12 AC 1 ms
4,376 KB
testcase_13 AC 1 ms
4,376 KB
testcase_14 AC 1 ms
4,380 KB
testcase_15 AC 1 ms
4,380 KB
testcase_16 AC 1 ms
4,380 KB
testcase_17 AC 1 ms
4,376 KB
testcase_18 AC 1 ms
4,380 KB
testcase_19 AC 1 ms
4,376 KB
testcase_20 AC 1 ms
4,380 KB
testcase_21 AC 1 ms
4,376 KB
testcase_22 AC 1 ms
4,380 KB
testcase_23 AC 1 ms
4,376 KB
testcase_24 AC 1 ms
4,376 KB
testcase_25 AC 1 ms
4,380 KB
testcase_26 AC 1 ms
4,380 KB
testcase_27 AC 1 ms
4,376 KB
testcase_28 AC 1 ms
4,380 KB
testcase_29 AC 1 ms
4,380 KB
testcase_30 AC 1 ms
4,376 KB
testcase_31 AC 1 ms
4,376 KB
testcase_32 AC 1 ms
4,376 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 # 

// ---------- begin ModInt ----------
const MOD: u32 = 1_000_000_007;

#[derive(Clone, Copy)]
struct ModInt(u32);

impl std::ops::Add for ModInt {
    type Output = ModInt;
    fn add(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + rhs.0;
        if d >= MOD {
            d -= MOD;
        }
        ModInt(d)
    }
}

impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: ModInt) {
        *self = *self + rhs;
    }
}

impl std::ops::Sub for ModInt {
    type Output = ModInt;
    fn sub(self, rhs: ModInt) -> Self::Output {
        let mut d = self.0 + MOD - rhs.0;
        if d >= MOD {
            d -= MOD;
        }
        ModInt(d)
    }
}

impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: ModInt) {
        *self = *self - rhs;
    }
}

impl std::ops::Mul for ModInt {
    type Output = ModInt;
    fn mul(self, rhs: ModInt) -> Self::Output {
        ModInt((self.0 as u64 * rhs.0 as u64 % MOD as u64) as u32)
    }
}

impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: ModInt) {
        *self = *self * rhs;
    }
}

impl std::ops::Neg for ModInt {
    type Output = ModInt;
    fn neg(self) -> Self::Output {
        ModInt(if self.0 == 0 {0} else {MOD - self.0})
    }
}

impl std::fmt::Display for ModInt {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}

impl std::str::FromStr for ModInt {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<u32>()?;
        Ok(ModInt::new(val))
    }
}

impl From<usize> for ModInt {
    fn from(val: usize) -> ModInt {
        ModInt((val % MOD as usize) as u32)
    }
}

#[allow(dead_code)]
impl ModInt {
    pub fn new(n: u32) -> ModInt {
        ModInt(n % MOD)
    }
    pub fn zero() -> ModInt {
        ModInt(0)
    }
    pub fn one() -> ModInt {
        ModInt(1)
    }
    pub fn pow(self, mut n: u32) -> ModInt {
        let mut t = ModInt::one();
        let mut s = self;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        t
    }
    pub fn inv(self) -> ModInt {
        assert!(self.0 > 0);
        self.pow(MOD - 2)
    }
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
#[allow(dead_code)]
struct Precalc {
    inv: Vec<ModInt>,
    fact: Vec<ModInt>,
    ifact: Vec<ModInt>,
}

#[allow(dead_code)]
impl Precalc {
    pub fn new(n: usize) -> Precalc {
        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(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((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 {
        assert!(n > 0);
        self.inv[n]
    }
    pub fn fact(&self, n: usize) -> ModInt {
        self.fact[n]
    }
    pub fn ifact(&self, n: usize) -> ModInt {
        self.ifact[n]
    }
    pub fn comb(&self, n: usize, k: usize) -> ModInt {
        if k > n {
            return ModInt::zero();
        }
        self.fact[n] * self.ifact[k] * self.ifact[n - k]
    }
}
// ---------- end Precalc ----------
// ---------- begin Matrix ----------
mod matrix {
    use std::ops::*;
    pub trait SemiRing: Add<Output = Self> + Mul<Output = Self> + Copy {
        fn zero() -> Self;
        fn one() -> Self;
    }
    #[derive(Clone)]
    pub struct SquareMatrix<R> {
        size: usize,
        buf: Box<[R]>,
    }
    #[allow(dead_code)]
    impl<R: SemiRing> SquareMatrix<R> {
        pub fn zero(size: usize) -> Self {
            SquareMatrix {
                size: size,
                buf: vec![R::zero(); size * size].into_boxed_slice(),
            }
        }
        pub fn identity(size: usize) -> Self {
            let mut e = Self::zero(size);
            for i in 0..size {
                e.buf[i * size + i] = R::one();
            }
            e
        }
        pub fn set_at(&mut self, x: usize, y: usize, val: R) {
            assert!(x < self.size && y < self.size);
            self.buf[x * self.size + y] = val;
        }
        pub fn get_at(&self, x: usize, y: usize) -> R {
            assert!(x < self.size && y < self.size);
            self.buf[x * self.size + y]
        }
        pub fn matadd(&self, rhs: &Self) -> Self {
            assert!(self.size == rhs.size);
            let buf: Vec<R> = self
                .buf
                .iter()
                .zip(rhs.buf.iter())
                .map(|p| *p.0 + *p.1)
                .collect();
            SquareMatrix {
                size: self.size,
                buf: buf.into_boxed_slice(),
            }
        }
        pub fn matmul(&self, rhs: &Self) -> Self {
            let size = self.size;
            assert!(size == rhs.size);
            let mut res = Self::zero(size);
            for (x, a) in res.buf.chunks_mut(size).zip(self.buf.chunks(size)) {
                for (a, b) in a.iter().zip(rhs.buf.chunks(size)) {
                    for (x, b) in x.iter_mut().zip(b.iter()) {
                        *x = *x + *a * *b;
                    }
                }
            }
            res
        }
        pub fn mat_pow(&self, mut n: usize) -> Self {
            let size = self.size;
            let mut t = Self::identity(size);
            let mut s = self.clone();
            while n > 0 {
                if n & 1 == 1 {
                    t = t.matmul(&s);
                }
                s = s.matmul(&s);
                n >>= 1;
            }
            t
        }
    }
    #[allow(dead_code)]
    impl<R: SemiRing + Sub<Output = R>> SquareMatrix<R> {
        pub fn matsub(&self, rhs: &Self) -> Self {
            assert!(self.size == rhs.size);
            let buf: Vec<R> = self
                .buf
                .iter()
                .zip(rhs.buf.iter())
                .map(|p| *p.0 - *p.1)
                .collect();
            SquareMatrix {
                size: self.size,
                buf: buf.into_boxed_slice(),
            }
        }
    }
}
// ---------- end Matrix ----------

use matrix::*;

impl SemiRing for ModInt {
    fn zero() -> Self {
        ModInt::zero()
    }
    fn one() -> Self {
        ModInt::one()
    }
}

type M = SquareMatrix<ModInt>;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let mut n: u64 = s.trim().parse().unwrap();
    let mut t = M::identity(6);
    let mut s = M::zero(6);
    for i in 1..6 {
        s.set_at(i, i - 1, ModInt::one());
    }
    for i in 0..6 {
        s.set_at(i, 5, ModInt(6).inv());
    }
    while n > 0 {
        if n & 1 == 1 {
            t = t.matmul(&s);
        }
        s = s.matmul(&s);
        n >>= 1;
    }
    let ans = t.get_at(5, 5);
    println!("{}", ans);
}

fn main() {
    run();
}
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