#723325 (Rust) No.1781 LCM

• 問題: No.1781 LCM
• ユーザー: akakimidori
• 提出日時: 2021-12-10 13:44:07
• 言語: Rust (1.83.0 + proconio)
• 結果: WA (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 10,927 bytes
• コンパイル時間: 12,020 ms
• コンパイル使用メモリ: 397,740 KB
• 実行使用メモリ: 36,236 KB
• 最終ジャッジ日時: 2024-07-18 07:37:41
• 合計ジャッジ時間: 39,061 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

ファイルパターン	結果
sample	AC * 2
other	AC * 30 WA * 1

コンパイルメッセージ

warning: unused variable: `sum_large`
   --> src/main.rs:331:13
    |
331 |     let mut sum_large: Vec<Option<(usize, usize, M)>> = vec![None; sqrt + 1];
    |             ^^^^^^^^^ help: if this is intentional, prefix it with an underscore: `_sum_large`
    |
    = note: `#[warn(unused_variables)]` on by default

warning: unused variable: `sum_small`
   --> src/main.rs:332:13
    |
332 |     let mut sum_small: Vec<Option<(usize, usize, M)>> = vec![None; sqrt + 1];
    |             ^^^^^^^^^ help: if this is intentional, prefix it with an underscore: `_sum_small`

warning: unused variable: `i`
   --> src/main.rs:336:10
    |
336 |     for (i, &p) in prime.iter().enumerate() {
    |          ^ help: if this is intentional, prefix it with an underscore: `_i`

warning: value assigned to `l` is never read
   --> src/main.rs:348:17
    |
348 |                 l = r + 1;
    |                 ^
    |
    = help: maybe it is overwritten before being read?
    = note: `#[warn(unused_assignments)]` on by default

warning: variable does not need to be mutable
   --> src/main.rs:331:9
    |
331 |     let mut sum_large: Vec<Option<(usize, usize, M)>> = vec![None; sqrt + 1];
    |         ----^^^^^^^^^
    |         |
    |         help: remove this `mut`
    |
    = note: `#[warn(unused_mut)]` on by default

warning: variable does not need to be mutable
   --> src/main.rs:332:9
    |
332 |     let mut sum_small: Vec<Option<(usize, usize, M)>> = vec![None; sqrt + 1];
    |         ----^^^^^^^^^
    |         |
    |         help: remove this `mut`

warning: type alias `Map` is never used
   --> src/main.rs:297:6
    |
297 | type Map<K, V> = HashMap<K, V>;
    |      ^^^
    |
    = note: `#[warn(dead_code)]` on by default

warning: function `naive` is never used
   --> src/main.rs:397:4
    |
397 | fn naive(n: usize, m: usize) {
    |    ^^^^^

ソースコード

// 初期化配列
// 初期値とサイズを与えて適当にやる系
// new(size, zero): zero埋めした長さsizeの配列を返す
// init(&mut self): 初期化
// index(mut) でアクセスしたときその履歴を溜め込む
// それ以外でアクセスすると死ぬので注意
//
// 考えるべきこと
// 1. deref で dataへアクセスできるようにしていいか
//    derefmut はダメ
// 2. 今のままだと二次元配列の初期化とかには対応できない
//    なんか方法を考えたい
// ---------- begin init array ----------
#[derive(Clone)]
pub struct InitArray<T> {
    data: Vec<T>,
    list: Vec<usize>,
    zero: T,
}

impl<T: Copy> InitArray<T> {
    pub fn new(zero: T, size: usize) -> Self {
        InitArray {
            data: vec![zero; size],
            list: vec![],
            zero: zero,
        }
    }
    pub fn init_with<F>(&mut self, mut f: F)
    where
        F: FnMut(usize, T),
    {
        for x in self.list.drain(..) {
            let v = std::mem::replace(&mut self.data[x], self.zero);
            f(x, v);
        }
    }
}

impl<T> std::ops::Index<usize> for InitArray<T> {
    type Output = T;
    fn index(&self, pos: usize) -> &Self::Output {
        &self.data[pos]
    }
}

impl<T: PartialEq> std::ops::IndexMut<usize> for InitArray<T> {
    fn index_mut(&mut self, pos: usize) -> &mut Self::Output {
        if self.data[pos] == self.zero {
            self.list.push(pos);
        }
        &mut self.data[pos]
    }
}
// ---------- end init array ----------
// ---------- begin prime count ----------
// 処理が終わった時
// large[i]: pi(floor(n / i))
// small[i]: pi(i)
// となっている
// O(N^(3/4)/log N)
pub fn prime_count(n: usize) -> (Vec<usize>, Vec<usize>) {
    if n <= 1 {
        return (vec![0, 0], vec![0, 0]);
    }
    let sqrt = (1..).find(|p| p * p > n).unwrap() - 1;
    let mut large = vec![0; sqrt + 1];
    let mut small = vec![0; sqrt + 1];
    for (i, (large, small)) in large.iter_mut().zip(&mut small).enumerate().skip(1) {
        *large = n / i - 1;
        *small = i - 1;
    }
    for p in 2..=sqrt {
        if small[p] == small[p - 1] {
            continue;
        }
        let pi = small[p] - 1;
        let q = p * p;
        for i in 1..=sqrt.min(n / q) {
            large[i] -= *large.get(i * p).unwrap_or_else(|| &small[n / (i * p)]) - pi;
        }
        for i in (q..=sqrt).rev() {
            small[i] -= small[i / p] - pi;
        }
    }
    (small, large)
}
// ---------- end prime count ----------
// ---------- begin enumerate prime ----------
fn enumerate_prime<F>(n: usize, mut f: F)
where
    F: FnMut(usize),
{
    assert!(1 <= n && n <= 5 * 10usize.pow(8));
    let batch = (n as f64).sqrt().ceil() as usize;
    let mut is_prime = vec![true; batch + 1];
    for i in (2..).take_while(|p| p * p <= batch) {
        if is_prime[i] {
            let mut j = i * i;
            while let Some(p) = is_prime.get_mut(j) {
                *p = false;
                j += i;
            }
        }
    }
    let mut prime = vec![];
    for (i, p) in is_prime.iter().enumerate().skip(2) {
        if *p && i <= n {
            f(i);
            prime.push(i);
        }
    }
    let mut l = batch + 1;
    while l <= n {
        let r = std::cmp::min(l + batch, n + 1);
        is_prime.clear();
        is_prime.resize(r - l, true);
        for &p in prime.iter() {
            let mut j = (l + p - 1) / p * p - l;
            while let Some(is_prime) = is_prime.get_mut(j) {
                *is_prime = false;
                j += p;
            }
        }
        for (i, _) in is_prime.iter().enumerate().filter(|p| *p.1) {
            f(i + l);
        }
        l += batch;
    }
}
// ---------- end enumerate prime ----------
use std::marker::*;
use std::ops::*;

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

pub struct ConstantModulo<const M: u32>;

impl<const M: u32> Modulo for ConstantModulo<{ M }> {
    fn modulo() -> u32 {
        M
    }
}

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

impl<T> PartialEq for ModInt<T> {
    fn eq(&self, rhs: &Self) -> bool {
        self.0 == rhs.0
    }
}

impl<T> Clone for ModInt<T> {
    fn clone(&self) -> Self {
        Self::new_unchecked(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 v = self.0 + rhs.0;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        Self::new_unchecked(v)
    }
}

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 v = self.0 - rhs.0;
        if self.0 < rhs.0 {
            v += T::modulo();
        }
        Self::new_unchecked(v)
    }
}

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 {
        let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
        Self::new_unchecked(v as u32)
    }
}

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.is_zero() {
            Self::zero()
        } else {
            Self::new_unchecked(T::modulo() - self.0)
        }
    }
}

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

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

impl<T> 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> ModInt<T> {
    pub fn new_unchecked(n: u32) -> Self {
        ModInt(n, PhantomData)
    }
    pub fn zero() -> Self {
        ModInt::new_unchecked(0)
    }
    pub fn one() -> Self {
        ModInt::new_unchecked(1)
    }
    pub fn is_zero(&self) -> bool {
        self.0 == 0
    }
}

impl<T: Modulo> ModInt<T> {
    pub fn new(d: u32) -> Self {
        ModInt::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
    }
}

type M = ModInt<ConstantModulo<998_244_353>>;

use std::collections::*;

type Map<K, V> = HashMap<K, V>;

fn read() -> (usize, usize) {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    let a = s
        .trim()
        .split_whitespace()
        .flat_map(|s| s.parse())
        .collect::<Vec<_>>();
    (a[0], a[1])
}

fn solve(n: usize, m: usize) {
    let mut pow = vec![M::zero(); 40 + 1];
    for i in 1..=40 {
        pow[i] = M::from(i).pow(n as u64);
    }
    let pow = pow.windows(2).map(|p| p[1] - p[0]).collect::<Vec<_>>();
    let sqrt = (2..).find(|p| p * p > m).unwrap() - 1;
    let pi = prime_count(m);
    let pi = |x: usize| -> usize {
        if x <= sqrt {
            return pi.0[x];
        }
        let q = m / x;
        pi.1[q]
    };
    let mut prime = vec![];
    enumerate_prime(sqrt + 1000, |p| prime.push(p));
    let mut large = InitArray::new(M::zero(), sqrt + 1);
    let mut small = InitArray::new(M::zero(), sqrt + 1);
    let mut next_large = InitArray::new(M::zero(), sqrt + 1);
    let mut next_small = InitArray::new(M::zero(), sqrt + 1);
    let mut sum_large: Vec<Option<(usize, usize, M)>> = vec![None; sqrt + 1];
    let mut sum_small: Vec<Option<(usize, usize, M)>> = vec![None; sqrt + 1];
    large[1] = M::one();
    let mut ans = M::zero();
    let mut last = M::zero();
    for (i, &p) in prime.iter().enumerate() {
        let mut calc = |m: usize, v: M| {
            ans += M::from(m) * v;
            let mut l = p;
            let mut q = m / l;
            let mut add = 0usize;
            let mut pl = pi(l - 1);
            while q > 0 {
                let r = m / q;
                let pr = pi(r);
                add += q * (pr - pl);
                pl = pr;
                l = r + 1;
                q -= 1;
            }
            last += M::from(add) * v;
        };
        large.init_with(|d, v| {
            let m = m / d;
            if p * p > m {
                calc(m, v);
            } else {
                let mut pp = 1;
                let mut k = 0;
                while d * pp <= sqrt {
                    let v = v * pow[k];
                    let d = d * pp;
                    next_large[d] += v;
                    k += 1;
                    pp *= p;
                }
                let mut m = m / pp;
                while m > 0 {
                    let v = v * pow[k];
                    next_small[m] += v;
                    m /= p;
                    k += 1;
                }
            }
        });
        small.init_with(|m, v| {
            if p * p > m {
                calc(m, v);
            } else {
                let mut m = m;
                let mut k = 0;
                while m > 0 {
                    let v = v * pow[k];
                    next_small[m] += v;
                    m /= p;
                    k += 1;
                }
            }
        });
        std::mem::swap(&mut small, &mut next_small);
        std::mem::swap(&mut large, &mut next_large);
    }
    ans += pow[1] * last;
    println!("{}", ans);
}

fn naive(n: usize, m: usize) {
    let mut dp = vec![M::one(); m + 1];
    enumerate_prime(m, |p| {
        for i in 1..=(m / p) {
            dp[p * i] = dp[p * i] + dp[i];
        }
    });
    for dp in dp.iter_mut() {
        *dp = dp.pow(n as u64);
    }
    enumerate_prime(m, |p| {
        for i in (1..=(m / p)).rev() {
            dp[p * i] = dp[p * i] - dp[i];
        }
    });
    let mut ans = M::zero();
    for i in 1..=m {
        ans += M::from(m / i) * dp[i];
    }
    println!("{}", ans);
}

fn main() {
    let (n, m) = read();
    solve(n, m);
}