#618411 (Rust) No.1392 Don't be together

• 問題: No.1392 Don't be together
• ユーザー: ziita
• 提出日時: 2021-02-15 01:55:46
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 1,581 ms / 2,000 ms
• コード長: 8,411 bytes
• コンパイル時間: 14,583 ms
• コンパイル使用メモリ: 377,104 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-22 13:41:44
• 合計ジャッジ時間: 31,439 ms
• ジャッジサーバーID （参考情報）: judge2 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	2 ms; 5,248 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	649 ms; 5,376 KB
testcase_07	AC	1,235 ms; 5,376 KB
testcase_08	AC	1,094 ms; 5,376 KB
testcase_09	AC	1,581 ms; 5,376 KB
testcase_10	AC	737 ms; 5,376 KB
testcase_11	AC	1,160 ms; 5,376 KB
testcase_12	AC	684 ms; 5,376 KB
testcase_13	AC	968 ms; 5,376 KB
testcase_14	AC	1,083 ms; 5,376 KB
testcase_15	AC	724 ms; 5,376 KB
testcase_16	AC	1,176 ms; 5,376 KB
testcase_17	AC	784 ms; 5,376 KB
testcase_18	AC	1,066 ms; 5,376 KB
testcase_19	AC	948 ms; 5,376 KB
testcase_20	AC	374 ms; 5,376 KB
testcase_21	AC	112 ms; 5,376 KB
testcase_22	AC	625 ms; 5,376 KB
testcase_23	AC	413 ms; 5,376 KB
testcase_24	AC	229 ms; 5,376 KB
testcase_25	AC	454 ms; 5,376 KB
testcase_26	AC	94 ms; 5,376 KB
testcase_27	AC	162 ms; 5,376 KB
testcase_28	AC	493 ms; 5,376 KB
testcase_29	AC	227 ms; 5,376 KB

ソースコード

#![allow(unused_imports)]
#![allow(non_snake_case, unused)]

use std::cmp::*;
use std::collections::*;
use std::ops::*;

// https://atcoder.jp/contests/hokudai-hitachi2019-1/submissions/10518254 より

macro_rules! eprint {
    ($($t:tt)*) => {{
        use ::std::io::Write;
        let _ = write!(::std::io::stderr(), $($t)*);
    }};
}
macro_rules! eprintln {
    () => { eprintln!(""); };
    ($($t:tt)*) => {{
        use ::std::io::Write;
        let _ = writeln!(::std::io::stderr(), $($t)*);
    }};
}
macro_rules! dbg {
    ($v:expr) => {{
        let val = $v;
        eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val);
        val
    }}
}

macro_rules! mat {
    ($($e:expr),*) => { Vec::from(vec![$($e),*]) };
    ($($e:expr,)*) => { Vec::from(vec![$($e),*]) };
    ($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) };
    ($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) };
}

macro_rules! ok {
    ($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => {
        $a$([$i])*.$f($($t),*)
    };
    ($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { {
        let t = $e;
        ok!($a$([$i])*.$f($($es),*)$(@$t)*@t)
    } };
}

pub fn readln() -> String {
    let mut line = String::new();
    ::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e));
    line
}

macro_rules! read {
    ($($t:tt),*; $n:expr) => {{
        let stdin = ::std::io::stdin();
        let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
            let line = line.unwrap();
            let mut it = line.split_whitespace();
            _read!(it; $($t),*)
        }).collect::<Vec<_>>();
        ret
    }};
    ($($t:tt),*) => {{
        let line = readln();
        let mut it = line.split_whitespace();
        _read!(it; $($t),*)
    }};
}

macro_rules! _read {
    ($it:ident; [char]) => {
        _read!($it; String).chars().collect::<Vec<_>>()
    };
    ($it:ident; [u8]) => {
        Vec::from(_read!($it; String).into_bytes())
    };
    ($it:ident; usize1) => {
        $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1
    };
    ($it:ident; [usize1]) => {
        $it.map(|s| s.parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::<Vec<_>>()
    };
    ($it:ident; [$t:ty]) => {
        $it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
    };
    ($it:ident; $t:ty) => {
        $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
    };
    ($it:ident; $($t:tt),+) => {
        ($(_read!($it; $t)),*)
    };
}


pub fn main() {
    let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join();
}

const MOD: usize = 998244353;
// const MOD: usize = 1_000_000_007;
const INF: i64 = std::i64::MAX/100;

pub struct UnionFind {
    data: Vec<i32>,
}

impl UnionFind {
    pub fn new(n: usize) -> Self{
        UnionFind {
            data: vec![-1;n]
        }
    }
    pub fn root(&mut self, x: usize) -> usize{
        if self.data[x]<0 {
            x
        }
        else {
            let p = self.data[x] as usize;
            self.data[x] = self.root(p) as i32;
            self.data[x] as usize
        }
    }
    pub fn unite(&mut self, x: usize, y: usize){
        let rx = self.root(x);
        let ry = self.root(y);
        if rx!=ry {
            let (rx,ry) = if self.data[rx]<=self.data[ry] {
                (rx,ry)
            }
            else{
                (ry,rx)
            };
            self.data[rx] += self.data[ry];
            self.data[ry] = rx as i32;
        }
    }
    pub fn same(&mut self, x: usize, y: usize) ->  bool{
        self.root(x) == self.root(y)
    }
    pub fn size(&mut self, x: usize) -> i32 {
        let r = self.root(x);
        - self.data[r]
    }
}

#[derive(Clone, Copy)]
struct ModInt(usize);
 
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 usize)
    }
}
 
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(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
*/
 
#[allow(dead_code)]
impl ModInt {
    pub fn new(n: usize) -> ModInt {
        ModInt(n % MOD)
    }
    pub fn zero() -> ModInt {
        ModInt(0)
    }
    pub fn one() -> ModInt {
        ModInt(1)
    }
    pub fn pow(self, mut n: usize) -> 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 {
        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) {
            inv[i] = -inv[MOD as usize % i] * ModInt(MOD / i as usize);
            fact[i] = fact[i - 1] * ModInt(i as usize);
            ifact[i] = ifact[i - 1] * inv[i];
        }
        Precalc {
            inv: inv,
            fact: fact,
            ifact: ifact,
        }
    }
    pub fn inv(&self, n: usize) -> ModInt {
        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 ----------

fn solve() {
    let (n,m) = read!(usize,usize);
    let p = read!([usize]);
    let mut uf = UnionFind::new(n);
    for i in 0..n {
        uf.unite(i,p[i]-1);
    }
    let mut v = vec![vec![];n];
    for i in 0..n {
        v[uf.root(i)].push(i);
    }
    let mut sum = ModInt(0);
    let mut f = Precalc::new(m);
    for x in 0..m {
        let mut a = ModInt(1);
        let mut cum = vec![ModInt(0);n+1];
        for i in 0..n {
            if (i+1)%2==0 {
                cum[i+1] =  cum[i] + ModInt(m-1-x).pow(i+1);
            }
            else {
                cum[i+1] =  cum[i] - ModInt(m-1-x).pow(i+1);
            }
        }
        for i in 0..n {
            let s = v[i].len();
            if s==0 {
                continue;
            }
            if s>=2 && m<=1 {
                a = ModInt(0);
                break;
            }
            if s%2==0 {
                a *= ModInt(m-x)*(ModInt(m-1-x).pow(s-1)-cum[s-2]);
            }
            else {
                a *= ModInt(m-x)*(ModInt(m-1-x).pow(s-1)+cum[s-2]);
            }
        }
        if x%2==0 {
            sum += a * f.comb(m,x);
        }
        else {
            sum -= a * f.comb(m,x);
        }
    }
    println!("{}",(sum*f.fact(m).inv()).0);
}

fn run() {
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    solve();
}