結果
問題 | No.2127 Mod, Sum, Sum, Mod |
ユーザー |
![]() |
提出日時 | 2022-11-18 22:58:09 |
言語 | Rust (1.83.0 + proconio) |
結果 |
AC
|
実行時間 | 64 ms / 2,000 ms |
コード長 | 11,102 bytes |
コンパイル時間 | 12,151 ms |
コンパイル使用メモリ | 377,260 KB |
実行使用メモリ | 5,376 KB |
最終ジャッジ日時 | 2024-09-20 03:25:49 |
合計ジャッジ時間 | 13,532 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 27 |
コンパイルメッセージ
warning: unused import: `std::io::Write` --> src/main.rs:18:5 | 18 | use std::io::Write; | ^^^^^^^^^^^^^^ | = note: `#[warn(unused_imports)]` on by default warning: type alias `Map` is never used --> src/main.rs:21:6 | 21 | type Map<K, V> = BTreeMap<K, V>; | ^^^ | = note: `#[warn(dead_code)]` on by default warning: type alias `Set` is never used --> src/main.rs:22:6 | 22 | type Set<T> = BTreeSet<T>; | ^^^ warning: type alias `Deque` is never used --> src/main.rs:23:6 | 23 | type Deque<T> = VecDeque<T>; | ^^^^^
ソースコード
// 商を計算したい感// 1 <= i <= N, 1 <= j <= M// i/j >= q// なる数を計算したい?//// N について商列挙すると?// l, r, q// l <= d <= r で floor(n/d) = q//// sum_{l <= j <= r} sum_{1 <= i <= N} floor(i/j) * j// i < qj について// sum_j sum_{1 <= i < qj} ..// = sum_j (q-1)q/2 * j// qj <= i について// sum_j sum_i qj// sum_j (N - qj + 1) * q * juse 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: u64,m: u64,}let f = |n: u64| -> M {M::from(n) * M::from(n + 1) * M::new(2).inv()};let g = |n: u64| -> M {M::from(n) * M::from(n + 1) * M::from(2 * n + 1) * M::new(6).inv()};let mut ans = f(n) * M::from(m);quot_range_unorderd(n, |l, r, q| {if m < l {return;}let r = r.min(m);ans -= f(q - 1) * (g(r) - g(l - 1));ans -= M::from(n + 1) * M::from(q) * (f(r) - f(l - 1));ans += M::from(q) * M::from(q) * (g(r) - g(l - 1));});println!("{}", ans);}// ---------- 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 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 floor sum ----------// sum_{i = 0}^{n - 1} floor((ai + b) / m)pub fn floor_sum(n: u64, m: u64, mut a: u64, mut b: u64) -> u64 {assert!(n <= 10u64.pow(9));assert!(1 <= m && m <= 10u64.pow(9));let mut ans = 0;ans += a / m * n * (n - 1) / 2 + b / m * n;a %= m;b %= m;let p = a * n + b;if p >= m {ans += floor_sum(p / m, a, m, p % m);}ans}// ---------- end floor sum ----------// ---------- begin quot_range ----------// 商列挙// n を与えると [1, n] を (l, r, q) な組に分解する// (l, r, q): x \in [l, r] <=> floor(n / x) = q//// 実装が3通りある// quot_range_orderd// (l, r, q) を (1, 1, n), (2, 2, n / 2)... の順に返す// 除算 ceil(sqrt(n)) 回// メモリ O(sqrt(n))//// quot_range_unorderd// (l, r, q) を (1, 1, n), (ceil(n/2), n, 1), ...の順に返す// 除算 ceil(sqrt(n)) 回// メモリO(1)//// quot_range_nanka// (l, r, q) を (1, 1, n), (2, 2, n / 2)... の順に返す// 除算 2 * ceil(sqrt(n)) 回// メモリ O(1)//// どれがいいかはよくわからない// 順序不定でいいならunorderd// 除算が極めて重いならorderd// ML が気になるならnanka//// todo: u32 だけじゃなくu64 でも#[allow(dead_code)]pub fn quot_range_orderd<F>(n: u32, mut f: F)whereF: FnMut(u32, u32, u32),{let mut p = Vec::with_capacity((n as f64).sqrt().ceil() as usize + 1);for d in 1.. {let q = n / d;p.push((d, q));if q < d {break;}f(d, d, q);if q == d {break;}}for p in p.windows(2).rev() {let (l, r, q) = (p[1].1 + 1, p[0].1, p[0].0);f(l, r, q);}}#[allow(dead_code)]pub fn quot_range_unorderd<F>(n: u64, mut f: F)whereF: FnMut(u64, u64, u64){let mut pre = (0, 0);for d in 1.. {let q = n / d;if pre != (0, 0) {let (q, l, r) = (pre.0, q + 1, pre.1);f(l, r, q);}if q < d {break;}pre = (d, q);f(d, d, q);if q == d {break;}}}#[allow(dead_code)]pub fn quot_range_nanka<F>(n: u32, mut f: F)whereF: FnMut(u32, u32, u32){let mut l = 1;while l * l <= n {let q = n / l;f(l, l, q);l += 1;}let mut q = n / l;while q > 0 {let r = n / q;f(l, r, q);l = r + 1;q -= 1;}}// ---------- begin quot_range ----------