結果
問題 |
No.3187 Mingle
|
ユーザー |
![]() |
提出日時 | 2025-06-20 22:18:40 |
言語 | Rust (1.83.0 + proconio) |
結果 |
AC
|
実行時間 | 573 ms / 2,500 ms |
コード長 | 13,487 bytes |
コンパイル時間 | 13,157 ms |
コンパイル使用メモリ | 393,228 KB |
実行使用メモリ | 58,096 KB |
最終ジャッジ日時 | 2025-06-20 22:19:11 |
合計ジャッジ時間 | 24,519 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
コンパイルメッセージ
warning: unused import: `std::io::Write` --> src/main.rs:1:5 | 1 | use std::io::Write; | ^^^^^^^^^^^^^^ | = note: `#[warn(unused_imports)]` on by default warning: unused import: `modint::*` --> src/main.rs:377:5 | 377 | use modint::*; | ^^^^^^^^^ warning: type alias `Map` is never used --> src/main.rs:4:6 | 4 | type Map<K, V> = BTreeMap<K, V>; | ^^^ | = note: `#[warn(dead_code)]` on by default warning: type alias `Set` is never used --> src/main.rs:5:6 | 5 | type Set<T> = BTreeSet<T>; | ^^^ warning: type alias `Deque` is never used --> src/main.rs:6:6 | 6 | type Deque<T> = VecDeque<T>; | ^^^^^ warning: type alias `M` is never used --> src/main.rs:378:6 | 378 | type M = ModInt<StaticMod>; | ^ warning: method `join` is never used --> src/main.rs:98:12 | 97 | pub trait Join { | ---- method in this trait 98 | fn join(self, sep: &str) -> String; | ^^^^
ソースコード
use std::io::Write; use std::collections::*; type Map<K, V> = BTreeMap<K, V>; type Set<T> = BTreeSet<T>; type Deque<T> = VecDeque<T>; fn main() { input! { n: usize, p: u32, } type M = ModInt<StaticMod>; StaticMod::set_modulo(p); let mut divisor = vec![vec![]; n + 1]; for i in 1..=n { for j in 1..=(n / i) { divisor[i * j].push(i); } } let mut dp = vec![M::zero(); n + 1]; let mut imos = vec![M::zero(); n + 1]; for i in 3..=n { imos[i] = imos[i] + imos[i - 1]; dp[i] += imos[i]; dp[i] = (M::one() + dp[i] * M::from(i).inv()) * M::from(i - divisor[i].len()).inv() * M::from(i); let v = dp[i]; for &d in divisor[i].iter() { let q = i / d; imos[q * d] += v; let r = (q + 1) * d; if r <= n { imos[r] -= v; } } dp[i] = v; } println!("{}", dp[n]); } use modint::*; // ---------- 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 ---------- mod util { pub trait Join { fn join(self, sep: &str) -> String; } impl<T, I> Join for I where I: Iterator<Item = T>, T: std::fmt::Display, { fn join(self, sep: &str) -> String { let mut s = String::new(); use std::fmt::*; for (i, v) in self.enumerate() { if i > 0 { write!(&mut s, "{}", sep).ok(); } write!(&mut s, "{}", v).ok(); } s } } } mod modint { use std::marker::*; use std::ops::*; pub trait Modulo { fn modulo() -> u32; fn im() -> u64; fn reduce(z: u64) -> u32 { let x = (z as u128 * Self::im() as u128 >> 64) as u32; let mut v = z as u32 - x * Self::modulo(); if v >= Self::modulo() { v += Self::modulo(); } v } } pub struct StaticMod; static mut STATIC_MOD: u32 = 0; static mut STATIC_MOD_IM: u64 = 0; impl Modulo for StaticMod { fn modulo() -> u32 { unsafe { STATIC_MOD } } fn im() -> u64 { unsafe { STATIC_MOD_IM } } } #[allow(dead_code)] impl StaticMod { pub fn set_modulo(p: u32) { unsafe { STATIC_MOD = p; STATIC_MOD_IM = (!0u64 / p as u64) + 1; } } } pub struct ModInt<T>(u32, PhantomData<T>); impl<T> Clone for ModInt<T> { fn clone(&self) -> Self { ModInt::build(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 d = self.0 + rhs.0; if d >= T::modulo() { d -= T::modulo(); } Self::build(d) } } 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 d = self.0 - rhs.0; if self.0 < rhs.0 { d += T::modulo(); } Self::build(d) } } 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 { Self::build(T::reduce(self.0 as u64 * rhs.0 as u64)) } } 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.0 == 0 { Self::zero() } else { Self::build(T::modulo() - self.0) } } } impl<T: Modulo> std::fmt::Display for ModInt<T> { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.get()) } } impl<T: Modulo> std::fmt::Debug for ModInt<T> { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.get()) } } impl<T: Modulo> 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 m = T::modulo() as i64; ModInt::new((val % m + m) as u32) } } #[allow(dead_code)] impl<T> ModInt<T> { fn build(d: u32) -> Self { ModInt(d, PhantomData) } pub fn zero() -> Self { Self::build(0) } pub fn is_zero(&self) -> bool { self.0 == 0 } } #[allow(dead_code)] impl<T: Modulo> ModInt<T> { pub fn new_unchecked(d: u32) -> Self { Self::build(d) } pub fn new(d: u32) -> Self { Self::new_unchecked(d % T::modulo()) } pub fn one() -> Self { Self::new_unchecked(1) } pub fn get(&self) -> u32 { self.0 } 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() - 2) as u64) } } } // ---------- end ModInt ---------- // ---------- begin Precalc ---------- mod precalc { use super::modint::*; #[allow(dead_code)] pub struct Precalc<T> { inv: Vec<ModInt<T>>, fact: Vec<ModInt<T>>, ifact: Vec<ModInt<T>>, } #[allow(dead_code)] 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 + 1) { 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 { inv: inv, fact: fact, ifact: ifact, } } 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 comb(&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 ---------- use modint::*; type M = ModInt<StaticMod>; use std::ops::*; pub trait Zero: Sized + Add<Output = Self> { fn zero() -> Self; } pub fn zero<T: Zero>() -> T { T::zero() } impl<T: Modulo> Zero for ModInt<T> { fn zero() -> Self { Self::zero() } } impl Zero for usize { fn zero() -> Self { 0 } } pub trait ArrayAdd { type Item; fn add(&self, rhs: &[Self::Item]) -> Vec<Self::Item>; } impl<T> ArrayAdd for [T] where T: Zero + Copy, { type Item = T; fn add(&self, rhs: &[Self::Item]) -> Vec<Self::Item> { let mut c = vec![T::zero(); self.len().max(rhs.len())]; c[..self.len()].copy_from_slice(self); c.add_assign(rhs); c } } pub trait ArrayAddAssign { type Item; fn add_assign(&mut self, rhs: &[Self::Item]); } impl<T> ArrayAddAssign for [T] where T: Add<Output = T> + Copy, { type Item = T; fn add_assign(&mut self, rhs: &[Self::Item]) { assert!(self.len() >= rhs.len()); self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x + *a); } } impl<T> ArrayAddAssign for Vec<T> where T: Zero + Add<Output = T> + Copy, { type Item = T; fn add_assign(&mut self, rhs: &[Self::Item]) { if self.len() < rhs.len() { self.resize(rhs.len(), T::zero()); } self.as_mut_slice().add_assign(rhs); } } pub trait ArraySub { type Item; fn sub(&self, rhs: &[Self::Item]) -> Vec<Self::Item>; } impl<T> ArraySub for [T] where T: Zero + Sub<Output = T> + Copy, { type Item = T; fn sub(&self, rhs: &[Self::Item]) -> Vec<Self::Item> { let mut c = vec![T::zero(); self.len().max(rhs.len())]; c[..self.len()].copy_from_slice(self); c.sub_assign(rhs); c } } pub trait ArraySubAssign { type Item; fn sub_assign(&mut self, rhs: &[Self::Item]); } impl<T> ArraySubAssign for [T] where T: Sub<Output = T> + Copy, { type Item = T; fn sub_assign(&mut self, rhs: &[Self::Item]) { assert!(self.len() >= rhs.len()); self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x - *a); } } impl<T> ArraySubAssign for Vec<T> where T: Zero + Sub<Output = T> + Copy, { type Item = T; fn sub_assign(&mut self, rhs: &[Self::Item]) { if self.len() < rhs.len() { self.resize(rhs.len(), T::zero()); } self.as_mut_slice().sub_assign(rhs); } } pub trait ArrayDot { type Item; fn dot(&self, rhs: &[Self::Item]) -> Vec<Self::Item>; } impl<T> ArrayDot for [T] where T: Mul<Output = T> + Copy, { type Item = T; fn dot(&self, rhs: &[Self::Item]) -> Vec<Self::Item> { assert!(self.len() == rhs.len()); self.iter().zip(rhs).map(|p| *p.0 * *p.1).collect() } } pub trait ArrayDotAssign { type Item; fn dot_assign(&mut self, rhs: &[Self::Item]); } impl<T> ArrayDotAssign for [T] where T: MulAssign + Copy, { type Item = T; fn dot_assign(&mut self, rhs: &[Self::Item]) { assert!(self.len() == rhs.len()); self.iter_mut().zip(rhs).for_each(|(x, a)| *x *= *a); } } pub trait ArrayMul { type Item; fn mul(&self, rhs: &[Self::Item]) -> Vec<Self::Item>; } impl<T> ArrayMul for [T] where T: Zero + Mul<Output = T> + Copy, { type Item = T; fn mul(&self, rhs: &[Self::Item]) -> Vec<Self::Item> { if self.is_empty() || rhs.is_empty() { return vec![]; } let mut res = vec![zero(); self.len() + rhs.len() - 1]; for (i, a) in self.iter().enumerate() { for (c, b) in res[i..].iter_mut().zip(rhs) { *c = *c + *a * *b; } } res } }