#663364 (Rust) No.1529 Constant Lcm

• 問題: No.1529 Constant Lcm
• ユーザー: Moss_Local
• 提出日時: 2021-06-04 20:38:19
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 1,103 ms / 3,000 ms
• コード長: 15,648 bytes
• コンパイル時間: 4,307 ms
• コンパイル使用メモリ: 163,088 KB
• 実行使用メモリ: 8,644 KB
• 最終ジャッジ日時: 2023-08-12 09:52:04
• 合計ジャッジ時間: 16,393 ms
• ジャッジサーバーID （参考情報）: judge13 / judge14

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 4,380 KB
testcase_01	AC	2 ms; 4,384 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; 4,380 KB
testcase_08	AC	1 ms; 4,380 KB
testcase_09	AC	1 ms; 4,376 KB
testcase_10	AC	976 ms; 8,100 KB
testcase_11	AC	307 ms; 4,428 KB
testcase_12	AC	10 ms; 4,380 KB
testcase_13	AC	806 ms; 7,228 KB
testcase_14	AC	450 ms; 5,476 KB
testcase_15	AC	500 ms; 5,456 KB
testcase_16	AC	365 ms; 4,608 KB
testcase_17	AC	174 ms; 4,376 KB
testcase_18	AC	192 ms; 4,376 KB
testcase_19	AC	466 ms; 5,492 KB
testcase_20	AC	1,093 ms; 8,644 KB
testcase_21	AC	1,087 ms; 8,620 KB
testcase_22	AC	1,086 ms; 8,576 KB
testcase_23	AC	1,103 ms; 8,620 KB
testcase_24	AC	1,080 ms; 8,644 KB
testcase_25	AC	1,086 ms; 8,572 KB

コンパイルメッセージ

warning: unnecessary parentheses around type
  --> Main.rs:66:15
   |
66 | fn readi() -> (i64) {
   |               ^   ^
   |
   = note: `#[warn(unused_parens)]` on by default
help: remove these parentheses
   |
66 - fn readi() -> (i64) {
66 + fn readi() -> i64 {
   |

warning: unnecessary parentheses around method argument
   --> Main.rs:630:18
    |
630 |         vec.push((n - i));
    |                  ^     ^
    |
help: remove these parentheses
    |
630 -         vec.push((n - i));
630 +         vec.push(n - i);
    |

warning: unused variable: `a2`
   --> Main.rs:450:14
    |
450 |         let (a2, e2) = mod_fact(k, p, fact);
    |              ^^ help: if this is intentional, prefix it with an underscore: `_a2`
    |
    = note: `#[warn(unused_variables)]` on by default

warning: unused variable: `a2`
   --> Main.rs:498:18
    |
498 |             let (a2, e2) = mod_fact(k, p, &self.f_table);
    |                  ^^ help: if this is intentional, prefix it with an underscore: `_a2`

warning: unused variable: `res`
   --> Main.rs:593:13
    |
593 |     let mut res = 1;
    |             ^^^ help: if this is intentional, prefix it with an underscore: `_res`

warning: variable does not need to be mutable
   --> Main.rs:593:9
    |
593 |     let mut res = 1;
    |         ----^^^
    |         |
    |         help: remove this `mut`
    |
    = note: `#[warn(unused_mut)]` on by default

warning: 6 warnings emitted

ソースコード

// -*- coding:utf-8-unix -*-
// #![feature(map_first_last)]
#![allow(dead_code)]
#![allow(unused_imports)]
#![allow(unused_macros)]
use std::collections::*;
use std::convert::*;
use std::convert::{From, Into};
use std::fmt::Debug;
use std::fs::File;
use std::io::prelude::*;
use std::io::*;
use std::marker::Copy;
use std::mem::*;
use std::ops::Bound::*;
use std::ops::{Add, Mul, Neg, Sub};
use std::str;
use std::vec;
use std::{cmp, process::Output};
use std::{cmp::Ordering, env::consts::DLL_PREFIX};
use std::{cmp::Ordering::*, f32::consts::PI};

const INF: i64 = 1223372036854775807;
const UINF: usize = INF as usize;
const FINF: f64 = 122337203685.0;
const INF128: i128 = 1223372036854775807000000000000;
const LINF: i64 = 2147483647;
// const MOD: i64 = 1000000007;
const MOD: i64 = 998244353;
// const MOD: i64 = INF;

const UMOD: usize = MOD as usize;
use std::cmp::*;
use std::collections::*;
use std::io::stdin;
use std::io::stdout;
use std::io::Write;

macro_rules! p {
    ($x:expr) => {
        println!("{}", $x);
    };
}
macro_rules! d {
    ($x:expr) => {
        println!("{:?}", $x);
    };
}
macro_rules! dd {
    (x:expr) => {
        dbg!(x);
    };
}

// use str::Chars;

// use str::Chars;
#[allow(dead_code)]
fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

#[allow(dead_code)]
fn readi() -> (i64) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    iter.next().unwrap().parse::<i64>().unwrap()
}

#[allow(dead_code)]
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}
#[allow(dead_code)]
fn read_vec2<T: std::str::FromStr>(n: u32) -> Vec<Vec<T>> {
    (0..n).map(|_| read_vec()).collect()
}

#[allow(dead_code)]
fn readii() -> (i64, i64) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
    )
}

fn readff() -> (f64, f64) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<f64>().unwrap(),
        iter.next().unwrap().parse::<f64>().unwrap(),
    )
}

#[allow(dead_code)]
fn readiii() -> (i64, i64, i64) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
    )
}
#[allow(dead_code)]
fn readuu() -> (usize, usize) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
    )
}

fn readcc() -> (char, char) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<char>().unwrap(),
        iter.next().unwrap().parse::<char>().unwrap(),
    )
}

#[allow(dead_code)]
fn readuuu() -> (usize, usize, usize) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
    )
}

#[allow(dead_code)]
fn readuuuu() -> (usize, usize, usize, usize) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
        iter.next().unwrap().parse::<usize>().unwrap(),
    )
}

fn readiiii() -> (i64, i64, i64, i64) {
    let mut str = String::new();
    let _ = stdin().read_line(&mut str).unwrap();
    let mut iter = str.split_whitespace();
    (
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
        iter.next().unwrap().parse::<i64>().unwrap(),
    )
}

macro_rules! M {
    (a :expr ) => {
        M::new({ a })
    };
}
#[derive(Copy, Clone)]
pub struct M(i64);
impl M {
    fn new(x: i64) -> Self {
        M(x.rem_euclid(MOD))
    }
    fn pow(self, n: usize) -> Self {
        match n {
            0 => M::new(1),
            _ => {
                let mut a = self.pow(n >> 1);
                a *= a;
                if n & 1 == 1 {
                    a *= self;
                }
                a
            }
        }
    }
    fn inv(self) -> Self {
        self.pow((MOD - 2) as usize)
    }
}
impl std::ops::Neg for M {
    type Output = M;
    fn neg(self) -> Self::Output {
        Self::new(-self.0)
    }
}
impl std::ops::AddAssign<M> for M {
    fn add_assign(&mut self, rhs: Self) {
        self.0 += rhs.0;
        self.0 %= MOD;
    }
}
impl std::ops::AddAssign<i64> for M {
    fn add_assign(&mut self, rhs: i64) {
        *self += M::new(rhs);
    }
}
impl std::ops::AddAssign<usize> for M {
    fn add_assign(&mut self, rhs: usize) {
        *self += M::new(rhs as i64);
    }
}
impl<T> std::ops::Add<T> for M
where
    M: std::ops::AddAssign<T>,
{
    type Output = Self;
    fn add(self, other: T) -> Self {
        let mut res = self;
        res += other;
        res
    }
}
impl std::ops::SubAssign<M> for M {
    fn sub_assign(&mut self, rhs: Self) {
        self.0 -= rhs.0;
        if self.0 < 0 {
            self.0 += MOD;
        }
    }
}
impl std::ops::SubAssign<i64> for M {
    fn sub_assign(&mut self, rhs: i64) {
        *self -= M::new(rhs);
        if (*self).0 < 0 {
            self.0 += MOD;
        }
    }
}
impl std::ops::SubAssign<usize> for M {
    fn sub_assign(&mut self, rhs: usize) {
        *self -= M::new(rhs as i64);
        if (*self).0 < 0 {
            self.0 += MOD;
        }
    }
}
impl<T> std::ops::Sub<T> for M
where
    M: std::ops::SubAssign<T>,
{
    type Output = Self;
    fn sub(self, other: T) -> Self {
        let mut res = self;
        res -= other;
        res
    }
}
impl std::ops::MulAssign<M> for M {
    fn mul_assign(&mut self, rhs: Self) {
        self.0 *= rhs.0;
        self.0 %= MOD;
    }
}
impl std::ops::MulAssign<i64> for M {
    fn mul_assign(&mut self, rhs: i64) {
        *self *= M::new(rhs);
    }
}
impl std::ops::MulAssign<usize> for M {
    fn mul_assign(&mut self, rhs: usize) {
        *self *= M::new(rhs as i64);
    }
}
impl<T> std::ops::Mul<T> for M
where
    M: std::ops::MulAssign<T>,
{
    type Output = Self;
    fn mul(self, other: T) -> Self {
        let mut res = self;
        res *= other;
        res
    }
}
impl std::ops::DivAssign<M> for M {
    fn div_assign(&mut self, rhs: Self) {
        *self *= rhs.inv();
    }
}
impl std::ops::DivAssign<i64> for M {
    fn div_assign(&mut self, rhs: i64) {
        *self /= M::new(rhs);
    }
}
impl std::ops::DivAssign<usize> for M {
    fn div_assign(&mut self, rhs: usize) {
        *self /= M::new(rhs as i64);
    }
}
impl<T> std::ops::Div<T> for M
where
    M: std::ops::DivAssign<T>,
{
    type Output = Self;
    fn div(self, other: T) -> Self {
        let mut res = self;
        res /= other;
        res
    }
}
impl std::fmt::Display for M {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
impl std::ops::Deref for M {
    type Target = i64;
    fn deref(&self) -> &Self::Target {
        &self.0
    }
}
impl std::ops::DerefMut for M {
    fn deref_mut(&mut self) -> &mut Self::Target {
        &mut self.0
    }
}

#[allow(dead_code)]
pub fn gcd(a: usize, b: usize) -> usize {
    if b == 0 {
        a
    } else {
        gcd(b, a % b)
    }
}
#[allow(dead_code)]
pub fn lcm(a: usize, b: usize) -> usize {
    a / gcd(a, b) * b
}
#[allow(dead_code)]
/// (gcd, x, y)
pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) {
    if b == 0 {
        (a, 1, 0)
    } else {
        let (gcd, x, y) = extgcd(b, a % b);
        (gcd, y, x - (a / b) * y)
    }
}
#[allow(dead_code)]
/// x ^ n % m
pub fn mod_pow(x: usize, n: usize, m: usize) -> usize {
    let mut res = 1;
    let mut x = x % m;
    let mut n = n;
    while n > 0 {
        if n & 1 == 1 {
            res = (res * x) % m;
        }
        x = (x * x) % m;
        n >>= 1;
    }
    res
}
#[allow(dead_code)]
pub fn mod_inverse(a: usize, m: usize) -> usize {
    let (_, x, _) = extgcd(a as i64, m as i64);
    ((m as i64 + x) as usize % m) % m
}
#[allow(dead_code)]
pub fn fact_table(len: usize, m: usize) -> Vec<usize> {
    let mut res = vec![1; len + 1];
    for i in 1..len + 1 {
        res[i] = (i as usize * res[i - 1]) % m;
    }
    res
}
#[allow(dead_code)]
/// Factorial and Inverse factorial table
pub fn fact_inv_table(size: usize, m: usize) -> (Vec<usize>, Vec<usize>) {
    let mut fact = vec![1; size];
    let mut fact_inv = vec![1; size];
    for i in 2..size {
        fact[i] = fact[i - 1] * i as usize % m;
        fact_inv[i] = m - ((m / i as usize) * fact_inv[(m % i as usize) as usize] % m);
    }
    for i in 1..size {
        fact_inv[i] = fact_inv[i - 1] * fact_inv[i] % m;
    }
    (fact, fact_inv)
}
#[allow(dead_code)]
/// (a mod p, e when n! = a p\^e)
pub fn mod_fact(n: usize, p: usize, fact: &[usize]) -> (usize, usize) {
    if n == 0 {
        (1, 0)
    } else {
        let (a, b) = mod_fact(n / p, p, fact);
        let pow = b + n / p;
        if n / p % 2 != 0 {
            (a * (p - fact[(n % p) as usize]) % p, pow)
        } else {
            (a * fact[(n % p) as usize] % p, pow)
        }
    }
}
#[allow(dead_code)]
/// C(n, k) % p
pub fn mcom(n: usize, k: usize, fact: &[usize]) -> usize {
    let p = MOD as usize;
    if k == 0 {
        return 1;
    }
    if n < k {
        0
    } else {
        let (a1, e1) = mod_fact(n, p, fact);
        let (a2, e2) = mod_fact(k, p, fact);
        let (a3, e3) = mod_fact(n - k, p, fact);
        if e1 > e2 + e3 {
            0
        } else {
            a1 * mod_inverse(a2 * a3 % p, p) % p
        }
    }
}

pub fn mperm(n: usize, k: usize, fact: &[usize]) -> usize {
    let p = MOD as usize;
    if k == 0 {
        return 1;
    }
    if n < k {
        0
    } else {
        let (a1, e1) = mod_fact(n, p, fact);
        let (a2, e2) = mod_fact(k, p, fact);
        let (a3, e3) = mod_fact(n - k, p, fact);
        if e1 > e2 + e3 {
            0
        } else {
            a1 * mod_inverse(a3 % p, p) % p
        }
    }
}

pub fn hcom(n: usize, k: usize, fact: &[usize]) -> usize {
    return mcom(n + k - 1, k, fact);
}

pub struct Combination {
    m: usize,
    f_table: Vec<usize>,
}

impl Combination {
    // 0 <= size <= 10^8 is constrained.
    pub fn new(mod_num: usize, table_size: usize) -> Self {
        Self {
            m: mod_num,
            f_table: vec![0; table_size],
        }
    }
    pub fn build(&mut self) {
        let size = self.f_table.len();
        self.f_table = fact_table(size, self.m);
    }
    fn fact_table(len: usize, m: usize) -> Vec<usize> {
        let mut res = vec![1; len + 1];
        for i in 1..len + 1 {
            res[i] = (i as usize * res[i - 1]) % m;
        }
        res
    }

    pub fn p(&mut self, n: usize, k: usize) -> usize {
        let p = MOD as usize;
        if k == 0 {
            return 1;
        }
        if n < k {
            0
        } else {
            let (a1, e1) = mod_fact(n, p, &self.f_table);
            let (a2, e2) = mod_fact(k, p, &self.f_table);
            let (a3, e3) = mod_fact(n - k, p, &self.f_table);
            if e1 > e2 + e3 {
                0
            } else {
                a1 * mod_inverse(a3 % p, p) % p
            }
        }
    }
    pub fn c(&mut self, n: usize, k: usize) -> usize {
        let p = MOD as usize;
        if n == 0 {
            return 0;
        }
        if k == 0 {
            return 1;
        }
        if n < k {
            0
        } else {
            let (a1, e1) = mod_fact(n, p, &self.f_table);
            let (a2, e2) = mod_fact(k, p, &self.f_table);
            let (a3, e3) = mod_fact(n - k, p, &self.f_table);
            if e1 > e2 + e3 {
                0
            } else {
                a1 * mod_inverse(a2 * a3 % p, p) % p
            }
        }
    }
    pub fn h(&mut self, n: usize, k: usize) -> usize {
        return mcom(n + k - 1, k, &self.f_table);
    }

    pub fn factorial(&mut self, n: usize) -> usize {
        return self.p(n, n);
    }

    fn extgcd(a: i64, b: i64) -> (i64, i64, i64) {
        if b == 0 {
            (a, 1, 0)
        } else {
            let (gcd, x, y) = extgcd(b, a % b);
            (gcd, y, x - (a / b) * y)
        }
    }
    pub fn mod_inverse(a: usize, m: usize) -> usize {
        let (_, x, _) = extgcd(a as i64, m as i64);
        ((m as i64 + x) as usize % m) % m
    }
    fn mod_fact(&mut self, n: usize, p: usize, fact: &[usize]) -> (usize, usize) {
        if n == 0 {
            (1, 0)
        } else {
            let (a, b) = mod_fact(n / p, p, fact);
            let pow = b + n / p;
            if n / p % 2 != 0 {
                (a * (p - fact[(n % p) as usize]) % p, pow)
            } else {
                (a * fact[(n % p) as usize] % p, pow)
            }
        }
    }
}
fn prime_factorization(x: usize) -> BTreeMap<usize, usize> {
    let mut res: BTreeMap<usize, usize> = BTreeMap::new();
    let mut xx = x;
    let mut p: usize = 2;
    while p * p <= xx {
        while xx % p == 0 {
            // println!("{:?}", p);
            let t = res.get_mut(&p);
            if t.is_none() {
                res.insert(p, 1);
            } else {
                *t.unwrap() += 1;
            }
            xx /= p;
        }
        // println!("{:?} {:?}", p, res);
        p += 1;
    }

    if xx != 1 {
        let t = res.get_mut(&xx);
        if t.is_none() {
            res.insert(xx, 1);
        } else {
            *t.unwrap() += 1;
        }
    }
    res
}

pub fn vector_lcm(vec: &Vec<usize>, n: usize) -> usize {
    let mut res = 1;

    let mut alcm: BTreeMap<usize, usize> = BTreeMap::new();
    for i in 0..vec.len() {
        let mut pf = prime_factorization(vec[i]);
        let pf2 = prime_factorization(n - vec[i]);
        // println!("{:?}", vec[i]);
        // println!("{:?}", pf);
        for j in pf2 {
            *pf.entry(j.0).or_insert(0) += j.1;
        }
        for i in pf {
            let t = alcm.get_mut(&i.0);
            if t.is_none() {
                alcm.insert(i.0, i.1);
            } else {
                let val = *t.unwrap();
                *alcm.get_mut(&i.0).unwrap() = max(val, i.1);
            }
        }
    }
    let mut r = M(1);
    for i in alcm {
        // for j in 0..i.1 {
        //     // res *= i.0;
        // }
        r *= M(i.0 as i64).pow(i.1);
        // println!("{:?}", i);
    }

    r.0 as usize
}

fn solve() {
    let n: usize = read();
    let mut vec = vec![];
    for i in 1..=n / 2 {
        vec.push((n - i));
    }
    // println!("{:?}", vec);
    println!("{:?}", vector_lcm(&vec, n));
    return;
}

fn main() {
    solve();
}