#794375 (Rust) No.1781 LCM

提出ソース

結果

問題	No.1781 LCM
ユーザー	akakimidori
提出日時	2022-09-01 22:52:59
言語	Rust (1.77.0)
結果	AC
実行時間	1,981 ms / 5,000 ms
コード長	12,025 bytes
コンパイル時間	13,829 ms
コンパイル使用メモリ	391,768 KB
実行使用メモリ	8,384 KB
最終ジャッジ日時	2024-04-27 18:03:39
合計ジャッジ時間	24,788 ms
ジャッジサーバーID （参考情報）	judge5 / judge4

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 6,812 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	1 ms 6,812 KB
testcase_03	AC	1 ms 6,940 KB
testcase_04	AC	1 ms 6,940 KB
testcase_05	AC	1 ms 6,944 KB
testcase_06	AC	2 ms 6,940 KB
testcase_07	AC	0 ms 6,940 KB
testcase_08	AC	1 ms 6,944 KB
testcase_09	AC	1 ms 6,940 KB
testcase_10	AC	1 ms 6,940 KB
testcase_11	AC	1 ms 6,940 KB
testcase_12	AC	1 ms 6,944 KB
testcase_13	AC	1 ms 6,944 KB
testcase_14	AC	1 ms 6,944 KB
testcase_15	AC	1 ms 6,944 KB
testcase_16	AC	1 ms 6,940 KB
testcase_17	AC	1 ms 6,940 KB
testcase_18	AC	1 ms 6,940 KB
testcase_19	AC	1 ms 6,944 KB
testcase_20	AC	1 ms 6,940 KB
testcase_21	AC	1,771 ms 8,384 KB
testcase_22	AC	1,981 ms 8,276 KB
testcase_23	AC	1 ms 6,940 KB
testcase_24	AC	0 ms 6,940 KB
testcase_25	AC	1,745 ms 8,320 KB
testcase_26	AC	1,772 ms 8,280 KB
testcase_27	AC	1,770 ms 8,240 KB
testcase_28	AC	1,497 ms 7,680 KB
testcase_29	AC	402 ms 6,940 KB
testcase_30	AC	430 ms 6,940 KB
testcase_31	AC	1 ms 6,940 KB
testcase_32	AC	1 ms 6,940 KB

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ソースコード

raw source code

fn main() {
    input!(n: usize, m: usize);
    let mut pow = vec![M::zero(); 41];
    for i in 2..pow.len() {
        pow[i] = M::from(i).pow(n as u64);
    }
    let (s, l) = prime_count(m);
    let mut small = s
        .into_iter()
        .map(|s| M::from(s) * pow[2])
        .collect::<Vec<_>>();
    let mut large = l
        .into_iter()
        .map(|s| M::from(s) * pow[2])
        .collect::<Vec<_>>();
    sum_of_multicative_function(m, |_, c| pow[c + 1], &mut small, &mut large);
    println!("{}", large[1] + M::one());
}

// 素数のみの初期値を与えた時になんかうまいこと計算してくれるやつ、のはず
// 結果の列には1は含まれない
pub fn sum_of_multicative_function<F>(n: usize, f: F, small: &mut [M], large: &mut [M])
where
    F: Fn(usize, usize) -> M,
{
    let sqrt = (1..).find(|k| k * k > n).unwrap() - 1;
    assert!(small.len() == large.len() && small.len() == sqrt + 1);
    let mut prime = vec![];
    enumerate_prime(sqrt, |p| prime.push(p));
    for &p in prime.iter().rev() {
        let sub = small[p];
        for i in (1..=sqrt).take_while(|i| i * p * p <= n) {
            let mut pos = i * p;
            let mut c = 1;
            while pos <= sqrt {
                if c > 1 {
                    large[i] += f(p, c);
                }
                large[i] = large[i] + f(p, c) * (large[pos] - sub);
                pos *= p;
                c += 1;
            }
            pos = n / pos;
            while pos >= p {
                if c > 1 {
                    large[i] += f(p, c);
                }
                large[i] = large[i] + f(p, c) * (small[pos] - sub);
                pos /= p;
                c += 1;
            }
            large[i] += f(p, c);
        }
        for i in ((p * p)..=sqrt).rev() {
            let mut pos = i / p;
            let mut c = 1;
            while pos >= p {
                if c > 1 {
                    small[i] += f(p, c);
                }
                small[i] = small[i] + f(p, c) * (small[pos] - sub);
                pos /= p;
                c += 1;
            }
            small[i] += f(p, c);
        }
    }
}

// ---------- 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 ----------
// ---------- begin prime count ----------
// pi(i): i以下の素数の数
// small[i]: pi(i)
// large[i]: pi(floor(n / i))
// として、 (small, large) を返す
// O(N^(3/4))
pub fn prime_count(n: usize) -> (Vec<usize>, Vec<usize>) {
    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;
    }
    fn mydiv(a: usize, b: u32) -> u32 {
        (a as f64 / b as f64) as u32
    }
    for p in 2..=sqrt {
        if small[p] == small[p - 1] {
            continue;
        }
        let pi = small[p] - 1;
        let q = p * p;
        let d = sqrt / p;
        for i in 1..=d {
            large[i] -= large[i * p] - pi;
        }
        let m = n / p;
        let r = sqrt.min(n / q);
        for i in (d + 1)..=r {
            large[i] -= small[mydiv(m, i as u32) as usize] - pi;
        }
        for i in (p..=d).rev() {
            let sub = small[i] - pi;
            small[(i * p)..].iter_mut().take(p).for_each(|p| *p -= sub);
        }
    }
    (small, large)
}
// ---------- end prime count ----------
// ---------- begin modint ----------
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> 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: Modulo> From<i64> for ModInt<T> {
    fn from(val: i64) -> ModInt<T> {
        let mut v = ((val % T::modulo() as i64) + T::modulo() as i64) as u32;
        if v >= T::modulo() {
            v -= T::modulo();
        }
        ModInt::new_unchecked(v)
    }
}

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
    }
    pub fn inv(&self) -> Self {
        assert!(!self.is_zero());
        self.pow(T::modulo() as u64 - 2)
    }
    pub fn fact(n: usize) -> Self {
        (1..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn perm(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        ((n - k + 1)..=n).fold(Self::one(), |s, a| s * Self::from(a))
    }
    pub fn binom(n: usize, k: usize) -> Self {
        if k > n {
            return Self::zero();
        }
        let k = k.min(n - k);
        let mut nu = Self::one();
        let mut de = Self::one();
        for i in 0..k {
            nu *= Self::from(n - i);
            de *= Self::from(i + 1);
        }
        nu * de.inv()
    }
}
// ---------- end modint ----------
// ---------- begin precalc ----------
pub struct Precalc<T> {
    fact: Vec<ModInt<T>>,
    ifact: Vec<ModInt<T>>,
    inv: Vec<ModInt<T>>,
}

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 {
            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 { fact, ifact, inv }
    }
    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 ----------

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

// ---------- begin enumerate prime ----------
pub 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 ----------

yukicoder

結果

テストケース

ソースコード