結果
| 問題 |
No.2857 Div Array
|
| コンテスト | |
| ユーザー |
 urectanc
|
| 提出日時 | 2025-09-01 19:40:34 |
| 言語 | Rust (1.83.0 + proconio) |
| 結果 |
AC
|
| 実行時間 | 44 ms / 2,000 ms |
| コード長 | 8,767 bytes |
| コンパイル時間 | 14,627 ms |
| コンパイル使用メモリ | 400,376 KB |
| 実行使用メモリ | 7,716 KB |
| 最終ジャッジ日時 | 2025-09-01 19:40:51 |
| 合計ジャッジ時間 | 16,462 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 30 |
ソースコード
use std::collections::HashMap;
use modint::ModInt998244353;
use proconio::input;
type Mint = ModInt998244353;
type Mat = Vec<Vec<Mint>>;
fn main() {
input! {
n: usize, m: usize, k: usize
}
if n == 1 {
println!("{m}");
return;
}
let mut count = HashMap::new();
for i in 1..=m {
let div = m / i;
*count.entry(div).or_insert(0) += 1;
}
let s = count.len();
let (div, way): (Vec<_>, Vec<_>) = count.into_iter().unzip();
let mut a = vec![vec![Mint::new(0); s]; s];
for i in 0..s {
for j in 0..s {
if div[i].abs_diff(div[j]) <= k {
a[j][i] = way[j].into();
}
}
}
let trans = mat_pow(&a, n - 1);
let ans = trans
.iter()
.map(|row| row.iter().zip(&way).map(|(a, &x)| a * x).sum::<Mint>())
.sum::<Mint>();
println!("{ans}")
}
fn mat_mul(a: &Mat, b: &Mat) -> Mat {
let n = a.len();
let mut res = vec![vec![Mint::new(0); n]; n];
for i in 0..n {
for j in 0..n {
for k in 0..n {
res[i][j] += a[i][k] * b[k][j];
}
}
}
res
}
fn mat_pow(a: &Mat, mut k: usize) -> Mat {
assert!(k > 0);
k -= 1;
let mut res = a.clone();
let mut pow = a.clone();
while k > 0 {
if k & 1 == 1 {
res = mat_mul(&res, &pow);
}
pow = mat_mul(&pow, &pow);
k >>= 1;
}
res
}
#[allow(dead_code)]
mod modint {
use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign};
pub type ModInt998244353 = ModInt<998244353>;
pub type ModInt1000000007 = ModInt<1000000007>;
type ModIntInner = u64;
#[derive(Clone, Copy, PartialEq, Eq)]
pub struct ModInt<const M: ModIntInner> {
val: ModIntInner,
}
impl<const M: ModIntInner> ModInt<M> {
const IS_PRIME: bool = is_prime(M as u32);
pub const fn modulus() -> ModIntInner {
M
}
pub const fn new(val: ModIntInner) -> Self {
assert!(M < (1 << 31));
Self {
val: val.rem_euclid(M),
}
}
pub const fn new_unchecked(val: ModIntInner) -> Self {
Self { val }
}
pub const fn val(&self) -> ModIntInner {
self.val
}
pub fn pow(self, mut exp: u64) -> Self {
let mut result = Self::new(1);
let mut base = self;
while exp > 0 {
if exp & 1 == 1 {
result *= base;
}
base *= base;
exp >>= 1;
}
result
}
pub fn inv(self) -> Self {
assert!(Self::IS_PRIME);
self.pow(M as u64 - 2).into()
}
}
impl<const M: ModIntInner> std::fmt::Display for ModInt<M> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", self.val)
}
}
impl<const M: ModIntInner> std::fmt::Debug for ModInt<M> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(f, "{}", self.val)
}
}
impl<const M: ModIntInner> std::str::FromStr for ModInt<M> {
type Err = std::num::ParseIntError;
fn from_str(s: &str) -> Result<Self, Self::Err> {
let value = s.parse::<ModIntInner>()?;
Ok(ModInt::new(value))
}
}
impl<const M: ModIntInner> Neg for ModInt<M> {
type Output = Self;
fn neg(mut self) -> Self::Output {
if self.val > 0 {
self.val = M - self.val;
}
self
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
fn add_assign(&mut self, rhs: T) {
self.val += rhs.into().val;
if self.val >= M {
self.val -= M;
}
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
fn sub_assign(&mut self, rhs: T) {
self.val = self.val.wrapping_sub(rhs.into().val);
if self.val > M {
self.val = self.val.wrapping_add(M);
}
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
fn mul_assign(&mut self, rhs: T) {
self.val = self.val * rhs.into().val % M;
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> DivAssign<T> for ModInt<M> {
fn div_assign(&mut self, rhs: T) {
*self *= rhs.into().inv();
}
}
macro_rules! impl_binnary_operators {
($({ $op: ident, $op_assign: ident, $fn: ident, $fn_assign: ident}),*) => {$(
impl<const M: ModIntInner, T: Into<ModInt<M>>> $op<T> for ModInt<M> {
type Output = ModInt<M>;
fn $fn(mut self, rhs: T) -> ModInt<M> {
self.$fn_assign(rhs.into());
self
}
}
impl<const M: ModIntInner> $op<&ModInt<M>> for ModInt<M> {
type Output = ModInt<M>;
fn $fn(self, rhs: &ModInt<M>) -> ModInt<M> {
self.$fn(*rhs)
}
}
impl<const M: ModIntInner, T: Into<ModInt<M>>> $op<T> for &ModInt<M> {
type Output = ModInt<M>;
fn $fn(self, rhs: T) -> ModInt<M> {
(*self).$fn(rhs.into())
}
}
impl<const M: ModIntInner> $op<&ModInt<M>> for &ModInt<M> {
type Output = ModInt<M>;
fn $fn(self, rhs: &ModInt<M>) -> ModInt<M> {
(*self).$fn(*rhs)
}
}
impl<const M: ModIntInner> $op_assign<&ModInt<M>> for ModInt<M> {
fn $fn_assign(&mut self, rhs: &ModInt<M>) {
*self = self.$fn(*rhs);
}
}
)*};
}
impl_binnary_operators!(
{Add, AddAssign, add, add_assign},
{Sub, SubAssign, sub, sub_assign},
{Mul, MulAssign, mul, mul_assign},
{Div, DivAssign, div, div_assign}
);
impl<const M: ModIntInner> std::iter::Sum for ModInt<M> {
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::new(0), Add::add)
}
}
impl<'a, const M: ModIntInner> std::iter::Sum<&'a Self> for ModInt<M> {
fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(Self::new(0), Add::add)
}
}
impl<const M: ModIntInner> std::iter::Product for ModInt<M> {
fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(Self::new(1), Mul::mul)
}
}
impl<'a, const M: ModIntInner> std::iter::Product<&'a Self> for ModInt<M> {
fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(Self::new(1), Mul::mul)
}
}
macro_rules! impl_rem_euclid_signed {
($($ty:tt),*) => {
$(
impl<const M: ModIntInner> From<$ty> for ModInt<M> {
fn from(value: $ty) -> ModInt<M> {
Self::new_unchecked((value as i64).rem_euclid(M as i64) as ModIntInner)
}
}
)*
};
}
impl_rem_euclid_signed!(i8, i16, i32, i64, isize);
macro_rules! impl_rem_euclid_unsigned {
($($ty:tt),*) => {
$(
impl<const M: ModIntInner> From<$ty> for ModInt<M> {
fn from(value: $ty) -> ModInt<M> {
Self::new_unchecked((value as u64).rem_euclid(M as u64) as ModIntInner)
}
}
)*
};
}
impl_rem_euclid_unsigned!(u8, u16, u32, u64, usize);
const fn is_prime(n: u32) -> bool {
const fn miller_rabin(n: u32, witness: u32) -> bool {
let (n, witness) = (n as u64, witness as u64);
let mut d = n >> (n - 1).trailing_zeros();
let mut y = {
let (mut res, mut pow, mut e) = (1, witness, d);
while e > 0 {
if e & 1 == 1 {
res = res * pow % n;
}
pow = pow * pow % n;
e >>= 1;
}
res
};
while d != n - 1 && y != 1 && y != n - 1 {
y = y * y % n;
d <<= 1;
}
y == n - 1 || d & 1 == 1
}
const WITNESS: [u32; 3] = [2, 7, 61];
if n == 1 || n % 2 == 0 {
return n == 2;
}
let mut i = 0;
while i < WITNESS.len() {
if !miller_rabin(n, WITNESS[i]) {
return false;
}
i += 1;
}
true
}
}