結果

問題 No.2917 二重木
ユーザー akakimidoriakakimidori
提出日時 2024-10-05 09:51:21
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 2,774 ms / 3,000 ms
コード長 9,498 bytes
コンパイル時間 14,619 ms
コンパイル使用メモリ 397,428 KB
実行使用メモリ 13,824 KB
最終ジャッジ日時 2024-10-05 09:52:01
合計ジャッジ時間 37,775 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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
6,820 KB
testcase_01 AC 0 ms
6,816 KB
testcase_02 AC 1 ms
6,816 KB
testcase_03 AC 1 ms
6,816 KB
testcase_04 AC 0 ms
6,816 KB
testcase_05 AC 1 ms
6,820 KB
testcase_06 AC 1 ms
6,816 KB
testcase_07 AC 1 ms
6,824 KB
testcase_08 AC 1 ms
6,816 KB
testcase_09 AC 1 ms
6,816 KB
testcase_10 AC 0 ms
6,820 KB
testcase_11 AC 1 ms
6,816 KB
testcase_12 AC 1 ms
6,820 KB
testcase_13 AC 1 ms
6,816 KB
testcase_14 AC 1 ms
6,820 KB
testcase_15 AC 1 ms
6,820 KB
testcase_16 AC 1 ms
6,820 KB
testcase_17 AC 0 ms
6,816 KB
testcase_18 AC 1 ms
6,816 KB
testcase_19 AC 1 ms
6,820 KB
testcase_20 AC 2 ms
6,816 KB
testcase_21 AC 18 ms
6,820 KB
testcase_22 AC 79 ms
6,820 KB
testcase_23 AC 172 ms
6,820 KB
testcase_24 AC 254 ms
6,820 KB
testcase_25 AC 349 ms
6,820 KB
testcase_26 AC 488 ms
7,808 KB
testcase_27 AC 1,017 ms
10,240 KB
testcase_28 AC 1,524 ms
11,520 KB
testcase_29 AC 2,641 ms
13,568 KB
testcase_30 AC 2,651 ms
13,568 KB
testcase_31 AC 2,664 ms
13,568 KB
testcase_32 AC 2,672 ms
13,696 KB
testcase_33 AC 2,752 ms
13,824 KB
testcase_34 AC 2,774 ms
13,824 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 # 

fn main() {
    input!(n: usize, p: u32);
    StaticMod::set_modulo(p);
    let mut dp = vec![vec![M::zero(); n]; n];
    let mut pow = vec![vec![M::zero(); n]; n];
    let mut binom = vec![vec![M::zero(); n + 1]; n + 1];
    for i in 1..n {
        dp[i][i] = M::one();
    }
    for i in 1..n {
        for j in 1..n {
            pow[i][j] = M::from(i).pow(j as u64);
        }
    }
    binom[0][0] = M::one();
    for i in 1..=n {
        binom[i][0] = M::one();
        for j in 1..=i {
            binom[i][j] = binom[i - 1][j - 1] + binom[i - 1][j];
        }
    }
    for all in 1..n {
        for now in 1..(all + 1) {
            let v = dp[all][now];
            for j in (all + 1)..n {
                dp[j][j - all] += pow[j - all][now] * binom[j][all] * v;
            }
        }
    }
    let mut ans = M::from(n).pow(n.saturating_sub(2) as u64);
    for i in (1..n).rev() {
        let mut way = binom[n][i];
        way *= M::from(i).pow(i.saturating_sub(2) as u64);
        let mut sum = M::zero();
        for j in 1..(n - i + 1) {
            sum += pow[i][j] * dp[n - i][j];
        }
        way *= sum;
        ans += way;
    }
    println!("{}", ans);
}

// ---------- 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 binom(&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>;
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