結果

問題 No.2005 Sum of Power Sums
ユーザー akakimidoriakakimidori
提出日時 2022-12-22 15:53:25
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 82 ms / 2,000 ms
コード長 8,407 bytes
コンパイル時間 11,348 ms
コンパイル使用メモリ 386,140 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-18 03:21:50
合計ジャッジ時間 13,091 ms
ジャッジサーバーID
(参考情報)
judge5 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 18
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

// sum_i i^k * x^i
//
// k=0: 1/(1-x)
// x d/dx k
fn main() {
input! {
n: usize,
m: usize,
k: [usize; n],
}
let mut cnt = vec![M::zero(); *k.iter().max().unwrap() + 1];
for k in k {
cnt[k] += M::one();
}
let mut binom = vec![M::zero(); cnt.len() + 1];
binom[1] = M::binom(m + n, n);
for i in 2..binom.len() {
binom[i] = binom[i - 1] * M::from(m + n + i - 1) * M::from(n + i - 1).inv();
}
let mut ans = M::zero();
let mut dp = vec![M::zero(), M::one()];
for cnt in cnt[1..].iter() {
let mut next = vec![M::zero(); dp.len() + 1];
for (i, dp) in dp.iter().enumerate().filter(|p| !p.1.is_zero()) {
let k = M::from(i);
next[i] -= *dp * k;
next[i + 1] += *dp * k;
}
dp = next;
for (dp, binom) in dp.iter().zip(binom.iter()) {
ans += *cnt * *dp * *binom;
}
}
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>>;
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