結果

問題 No.1116 Cycles of Dense Graph
ユーザー akakimidoriakakimidori
提出日時 2020-07-17 22:11:14
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 72 ms / 2,000 ms
コード長 12,830 bytes
コンパイル時間 13,421 ms
コンパイル使用メモリ 377,640 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-11-30 00:25:17
合計ジャッジ時間 15,399 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 38
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 union_find ----------
#[allow(dead_code)]
mod union_find {
    use std;
    pub struct UF {
        parent: Vec<usize>,
        size: Vec<usize>,
        stack: Vec<Option<(usize, usize)>>,
    }
    impl UF {
        pub fn new(n: usize) -> UF {
            let mut u = UF {
                parent: vec![0; n],
                size: vec![1; n],
                stack: vec![],
            };
            u.init();
            u
        }
        pub fn init(&mut self) {
            for (i, p) in self.parent.iter_mut().enumerate() {
                *p = i;
            }
            self.size.clear();
            self.size.resize(self.parent.len(), 1);
            self.stack.clear();
        }
        pub fn root(&mut self, mut x: usize) -> usize {
            while self.parent[x] != x {
                x = self.parent[x];
            }
            x
        }
        pub fn same(&mut self, x: usize, y: usize) -> bool {
            self.root(x) == self.root(y)
        }
        pub fn unite(&mut self, mut x: usize, mut y: usize) -> Option<(usize, usize)> {
            x = self.root(x);
            y = self.root(y);
            if x == y {
                self.stack.push(None);
                return None;
            }
            if self.size[x] < self.size[y] {
                std::mem::swap(&mut x, &mut y);
            }
            self.size[x] += self.size[y];
            self.parent[y] = x;
            self.stack.push(Some((x, y)));
            Some((x, y))
        }
        pub fn undo(&mut self) -> Option<(usize, usize)> {
            self.stack
                .pop()
                .expect("union find undo error: stack is empty")
                .map(|(x, y)| {
                    self.size[x] -= self.size[y];
                    self.parent[y] = y;
                    (x, y)
                })
        }
        pub fn get_size(&mut self, x: usize) -> usize {
            let r = self.root(x);
            self.size[r]
        }
        pub fn parent(&self, x: usize) -> Option<usize> {
            if self.parent[x] == x {
                None
            } else {
                Some(self.parent[x])
            }
        }
    }
}
//---------- end union_find ----------
// ---------- begin ModInt ----------
mod modint {

    #[allow(dead_code)]
    pub struct Mod;
    impl ConstantModulo for Mod {
        const MOD: u32 = 998_244_353;
    }

    #[allow(dead_code)]
    pub struct StaticMod;
    static mut STATIC_MOD: u32 = 0;
    impl Modulo for StaticMod {
        fn modulo() -> u32 {
            unsafe { STATIC_MOD }
        }
    }

    #[allow(dead_code)]
    impl StaticMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                STATIC_MOD = p;
            }
        }
    }

    use std::marker::*;
    use std::ops::*;

    pub trait Modulo {
        fn modulo() -> u32;
    }

    pub trait ConstantModulo {
        const MOD: u32;
    }

    impl<T> Modulo for T
    where
        T: ConstantModulo,
    {
        fn modulo() -> u32 {
            T::MOD
        }
    }

    pub struct ModularInteger<T>(pub u32, PhantomData<T>);

    impl<T> Clone for ModularInteger<T> {
        fn clone(&self) -> Self {
            ModularInteger::new_unchecked(self.0)
        }
    }

    impl<T> Copy for ModularInteger<T> {}

    impl<T: Modulo> Add for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn add(self, rhs: Self) -> Self::Output {
            let mut d = self.0 + rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModularInteger::new_unchecked(d)
        }
    }

    impl<T: Modulo> AddAssign for ModularInteger<T> {
        fn add_assign(&mut self, rhs: Self) {
            *self = *self + rhs;
        }
    }

    impl<T: Modulo> Sub for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn sub(self, rhs: Self) -> Self::Output {
            let mut d = T::modulo() + self.0 - rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModularInteger::new_unchecked(d)
        }
    }

    impl<T: Modulo> SubAssign for ModularInteger<T> {
        fn sub_assign(&mut self, rhs: Self) {
            *self = *self - rhs;
        }
    }

    impl<T: Modulo> Mul for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn mul(self, rhs: Self) -> Self::Output {
            let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
            ModularInteger::new_unchecked(v as u32)
        }
    }

    impl<T: Modulo> MulAssign for ModularInteger<T> {
        fn mul_assign(&mut self, rhs: Self) {
            *self = *self * rhs;
        }
    }

    impl<T: Modulo> Neg for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn neg(self) -> Self::Output {
            if self.0 == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(T::modulo() - self.0)
            }
        }
    }

    impl<T> std::fmt::Display for ModularInteger<T> {
        fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

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

    impl<T: Modulo> From<usize> for ModularInteger<T> {
        fn from(val: usize) -> ModularInteger<T> {
            ModularInteger::new_unchecked((val % T::modulo() as usize) as u32)
        }
    }

    impl<T: Modulo> From<i64> for ModularInteger<T> {
        fn from(val: i64) -> ModularInteger<T> {
            let m = T::modulo() as i64;
            ModularInteger::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModularInteger<T> {
        fn new_unchecked(d: u32) -> Self {
            ModularInteger(d, PhantomData)
        }
        pub fn zero() -> Self {
            ModularInteger::new_unchecked(0)
        }
        pub fn one() -> Self {
            ModularInteger::new_unchecked(1)
        }
        pub fn is_zero(&self) -> bool {
            self.0 == 0
        }
    }

    #[allow(dead_code)]
    impl<T: Modulo> ModularInteger<T> {
        pub fn new(d: u32) -> Self {
            ModularInteger::new_unchecked(d % T::modulo())
        }
        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.0 != 0);
            self.pow(T::modulo() as u64 - 2)
        }
    }

    // ---------- begin Precalc ----------
    #[allow(dead_code)]
    pub struct Precalc<T> {
        inv: Vec<ModularInteger<T>>,
        fact: Vec<ModularInteger<T>>,
        ifact: Vec<ModularInteger<T>>,
    }

    #[allow(dead_code)]
    impl<T: Modulo> Precalc<T> {
        pub fn new(n: usize) -> Precalc<T> {
            let mut inv = vec![ModularInteger::one(); n + 1];
            let mut fact = vec![ModularInteger::one(); n + 1];
            let mut ifact = vec![ModularInteger::one(); n + 1];
            for i in 2..(n + 1) {
                fact[i] = fact[i - 1] * ModularInteger::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] * ModularInteger::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) -> ModularInteger<T> {
            assert!(n > 0);
            self.inv[n]
        }
        pub fn fact(&self, n: usize) -> ModularInteger<T> {
            self.fact[n]
        }
        pub fn ifact(&self, n: usize) -> ModularInteger<T> {
            self.ifact[n]
        }
        pub fn perm(&self, n: usize, k: usize) -> ModularInteger<T> {
            if k > n {
                return ModularInteger::zero();
            }
            self.fact[n] * self.ifact[n - k]
        }
        pub fn comb(&self, n: usize, k: usize) -> ModularInteger<T> {
            if k > n {
                return ModularInteger::zero();
            }
            self.fact[n] * self.ifact[k] * self.ifact[n - k]
        }
    }
    // ---------- end Precalc ----------
    #[allow(dead_code)]
    pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 {
        let mut t = 1 % m;
        let mut s = r % m;
        while n > 0 {
            if n & 1 == 1 {
                t = t * s % m;
            }
            s = s * s % m;
            n >>= 1;
        }
        t
    }
}
// ---------- end ModInt ----------
//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
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_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_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")
    };
}

//

use modint::*;
type ModInt = ModularInteger<Mod>;

fn run() {
    input! {
        n: usize,
        m: usize,
        e: [(usize1, usize1); m],
    }
    let pc = Precalc::new(n + 15);
    //ans += sign * pc.fact(v - 1) * ModInt::new(2).pow((v - 1) as u64) * pc.perm(n - used, k) * pc.comb(k + v - 1, v - 1);
    let a = 30;
    let b = 15;
    let mut memo = vec![vec![ModInt::zero(); a + 1]; b + 1];// v, used
    for i in 1..=b {
        for j in 1..=a {
            let mut sum = ModInt::zero();
            for k in 0.. {
                if k + j < 3 {
                    continue;
                }
                if j + k > n {
                    break;
                }
                sum += pc.perm(n - j, k) * pc.comb(k + i - 1, i - 1);
            }
            memo[i][j] = sum * pc.fact(i - 1) * ModInt::new(2).pow((i - 1) as u64);
        }
    }
    let mut u = union_find::UF::new(n);
    let mut ans = ModInt::zero();
    for i in 3..=n {
        ans += pc.comb(n, i) * pc.fact(i - 1) * ModInt::from(2usize).inv();
    }
    for i in 1..(1 << m) {
        let mut deg = std::collections::BTreeMap::new();
        let mut set = vec![];
        let mut sign = ModInt::one();
        let mut cycle = 0;
        for (j, &(a, b)) in e.iter().enumerate() {
            if (i >> j) & 1 == 1 {
                sign = -sign;
                set.push((a, b));
                *deg.entry(a).or_insert(0) += 1;
                *deg.entry(b).or_insert(0) += 1;
                if u.unite(a, b).is_none() {
                    cycle += 1;
                }
            }
        }
        for _ in 0..set.len() {
            u.undo();
        }
        if deg.iter().any(|p| *p.1 > 2) || cycle > 1 {
            continue;
        }
        if deg.iter().all(|p| *p.1 == 2) {
            ans += sign;
            continue;
        }
        if cycle > 0 {
            continue;
        }
        let v = deg.iter().filter(|p| *p.1 == 1).count() / 2;
        let used = deg.len();
        ans += sign * memo[v][used];
        /*
        for k in 0.. {
            if k + used < 3 {
                continue;
            }
            if used + k > n {
                break;
            }
            ans += sign * pc.fact(v - 1) * ModInt::new(2).pow((v - 1) as u64) * pc.perm(n - used, k) * pc.comb(k + v - 1, v - 1);
        }
        */
    }
    println!("{}", ans);
}

fn main() {
    run();
}
0