結果
| 問題 | No.2116 Making Forest Hard |
| ユーザー |
 akakimidori
|
| 提出日時 | 2024-01-29 23:20:27 |
| 言語 | Rust (1.77.0) |
| 結果 |
AC
|
| 実行時間 | 1,974 ms / 8,000 ms |
| コード長 | 27,285 bytes |
| コンパイル時間 | 9,856 ms |
| コンパイル使用メモリ | 199,452 KB |
| 実行使用メモリ | 40,380 KB |
| 最終ジャッジ日時 | 2024-01-29 23:21:20 |
| 合計ジャッジ時間 | 51,958 ms |
|
ジャッジサーバーID （参考情報） |
judge11 / judge14 |
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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
6,676 KB |
| testcase_01 | AC | 1 ms
6,676 KB |
| testcase_02 | AC | 1,920 ms
40,376 KB |
| testcase_03 | AC | 1,963 ms
40,228 KB |
| testcase_04 | AC | 697 ms
30,508 KB |
| testcase_05 | AC | 709 ms
30,924 KB |
| testcase_06 | AC | 775 ms
30,492 KB |
| testcase_07 | AC | 797 ms
30,676 KB |
| testcase_08 | AC | 538 ms
23,160 KB |
| testcase_09 | AC | 677 ms
26,476 KB |
| testcase_10 | AC | 46 ms
6,676 KB |
| testcase_11 | AC | 514 ms
26,016 KB |
| testcase_12 | AC | 664 ms
28,304 KB |
| testcase_13 | AC | 683 ms
32,932 KB |
| testcase_14 | AC | 1,310 ms
31,760 KB |
| testcase_15 | AC | 12 ms
6,676 KB |
| testcase_16 | AC | 775 ms
30,008 KB |
| testcase_17 | AC | 898 ms
24,548 KB |
| testcase_18 | AC | 1,554 ms
35,224 KB |
| testcase_19 | AC | 291 ms
13,804 KB |
| testcase_20 | AC | 328 ms
15,084 KB |
| testcase_21 | AC | 479 ms
15,592 KB |
| testcase_22 | AC | 549 ms
28,612 KB |
| testcase_23 | AC | 84 ms
6,676 KB |
| testcase_24 | AC | 179 ms
6,676 KB |
| testcase_25 | AC | 412 ms
17,896 KB |
| testcase_26 | AC | 799 ms
30,008 KB |
| testcase_27 | AC | 163 ms
7,676 KB |
| testcase_28 | AC | 1,206 ms
27,088 KB |
| testcase_29 | AC | 568 ms
29,096 KB |
| testcase_30 | AC | 1,491 ms
33,368 KB |
| testcase_31 | AC | 187 ms
11,008 KB |
| testcase_32 | AC | 693 ms
32,976 KB |
| testcase_33 | AC | 27 ms
6,676 KB |
| testcase_34 | AC | 187 ms
9,472 KB |
| testcase_35 | AC | 704 ms
32,976 KB |
| testcase_36 | AC | 526 ms
23,584 KB |
| testcase_37 | AC | 30 ms
6,676 KB |
| testcase_38 | AC | 759 ms
30,084 KB |
| testcase_39 | AC | 673 ms
30,580 KB |
| testcase_40 | AC | 160 ms
10,076 KB |
| testcase_41 | AC | 452 ms
25,048 KB |
| testcase_42 | AC | 1,594 ms
35,640 KB |
| testcase_43 | AC | 1,972 ms
40,380 KB |
| testcase_44 | AC | 627 ms
29,388 KB |
| testcase_45 | AC | 312 ms
17,432 KB |
| testcase_46 | AC | 1,974 ms
40,380 KB |
| testcase_47 | AC | 185 ms
9,856 KB |
| testcase_48 | AC | 146 ms
9,184 KB |
| testcase_49 | AC | 1 ms
6,676 KB |
| testcase_50 | AC | 715 ms
32,928 KB |
| testcase_51 | AC | 665 ms
30,924 KB |
| testcase_52 | AC | 697 ms
30,872 KB |
| testcase_53 | AC | 657 ms
30,576 KB |
| testcase_54 | AC | 1,291 ms
31,816 KB |
ソースコード
// dp[v][a]: 部分木vでvを含みそれが最上位な連結成分について
// 連結成分のmaxがa であるようなものについての
// ... 何を管理するとdpできる？
// way: そうなるような切り方の個数
// sum: そうなる切り方についてのvを含む連結成分サイズの和
// というのを管理できてるとして
// 根vに親pが生成される時
// dp[p][A_p].0 = dp[v][*].0 + dp[v][A <= A_p].0
// dp[p][A_p].1 = 2 * dp[v][*].0 + dp[v][A <= A_p].1
//
// dp[p][x] = (0, 0) (x < A_p)
// dp[p][x].0 = dp[v][x].0
// dp[p][x].1 = dp[v][x].0 + dp[v][x].1 (x > A_p)
//
// 子にuが生えた時
type M = ModInt<998244353>;
fn run() {
input! {
n: usize,
a: [u32; n],
e: [(usize1, usize1); n - 1],
}
let a = a
.into_iter()
.enumerate()
.map(|p| (p.1, p.0))
.collect::<Vec<_>>();
let mut g = vec![vec![]; n];
for &(a, b) in e.iter() {
g[a].push(b);
g[b].push(a);
}
let root = 0;
let mut topo = vec![root];
let mut parent = vec![n; n];
for i in 0..n {
let v = topo[i];
for u in g[v].clone() {
g[u].retain(|p| *p != v);
topo.push(u);
parent[u] = v;
}
}
let mut size = vec![1usize; n];
for &v in topo.iter().rev() {
g[v].sort_by_key(|u| !size[*u]);
for &u in g[v].iter() {
size[v] += size[u];
}
}
let mut memo: Vec<Vec<((u32, usize), Dual<M>)>> = vec![vec![]; n];
let mut ans = M::zero();
for &v in topo.iter().rev() {
if v != root && g[parent[v]][0] == v {
continue;
}
let mut z = vec![];
let mut pos = v;
let mut path = vec![];
loop {
z.push(a[pos]);
path.push(pos);
for &u in g[pos].iter().skip(1) {
z.extend(memo[u].iter().map(|p| p.0));
}
if g[pos].is_empty() {
break;
}
pos = g[pos][0];
}
z.sort();
let mut seg = LazySegmentTree::new(z.len(), R);
for &v in path.iter().rev() {
let x = z.binary_search(&a[v]).unwrap();
let Dual(w, s) = seg.find(0, x).0;
let Dual(all, _) = seg.find(0, z.len()).0;
seg.update(0, x, Dual::zero());
seg.update(x + 1, z.len(), Dual::new(M::one(), M::one()));
let mut p = Dual::new(all + w, all + s + w);
if v == *path.last().unwrap() {
p = Dual::new(M::one(), M::one());
}
seg.set_at(x, (p, p * Dual::new(M::new(a[v].0), M::zero())));
for &u in g[v].iter().skip(1) {
let c = std::mem::take(&mut memo[u]);
let mut memo = vec![Dual::zero(); c.len()];
let mut pos = vec![0; c.len()];
for (i, &(key, _)) in c.iter().enumerate() {
let x = z.binary_search(&key).unwrap();
memo[i] = seg.find(0, x).0;
pos[i] = x;
}
pos.insert(0, 0);
pos.push(z.len());
let way = c.iter().fold(M::zero(), |s, &(_, a)| s + a.0);
let mut pre = Dual::new(way, M::zero());
for (i, x) in pos.windows(2).enumerate() {
let (l, r) = (x[0], x[1]);
seg.update(l, r, pre);
if i < c.len() {
let c = c[i].1;
pre = pre + c;
}
}
for i in 0..c.len() {
let a = M::new(c[i].0 .0);
let c = c[i].1;
let memo = memo[i];
let pos = pos[i + 1];
seg.set_at(pos, (c * memo, c * memo * Dual::new(a, M::zero())));
}
}
if v == root {
ans += seg.find(0, z.len()).1 .1;
} else {
ans += seg.find(0, z.len()).1 .1 * M::new(2).pow((n - 1 - size[v]) as u64);
}
}
memo[v] = (0..z.len()).map(|x| (z[x], seg.find(x, x + 1).0)).collect();
}
println!("{}", ans);
}
struct R;
impl TE for R {
type T = (Dual<M>, Dual<M>);
type E = Dual<M>;
fn fold(&self, l: &Self::T, r: &Self::T) -> Self::T {
(l.0 + r.0, l.1 + r.1)
}
fn eval(&self, x: &Self::T, f: &Self::E) -> Self::T {
(x.0 * *f, x.1 * *f)
}
fn merge(&self, g: &Self::E, h: &Self::E) -> Self::E {
*g * *h
}
fn e(&self) -> Self::T {
(Dual::zero(), Dual::zero())
}
fn id(&self) -> Self::E {
Dual::one()
}
}
fn main() {
run();
}
#[derive(Clone, Copy, Default, Debug)]
pub struct Dual<T>(T, T);
impl<T> Dual<T> {
pub fn new(a: T, b: T) -> Self {
Self(a, b)
}
}
impl<T> Zero for Dual<T>
where
T: Zero,
{
fn zero() -> Self {
Self::new(T::zero(), T::zero())
}
fn is_zero(&self) -> bool {
self.0.is_zero() && self.1.is_zero()
}
}
impl<T> One for Dual<T>
where
T: One + Zero + Clone,
{
fn one() -> Self {
Self::new(T::one(), T::zero())
}
fn is_one(&self) -> bool {
self.0.is_one() && self.1.is_zero()
}
}
impl<T> Add for Dual<T>
where
T: Add<Output = T>,
{
type Output = Self;
fn add(self, rhs: Self) -> Self {
Self::new(self.0 + rhs.0, self.1 + rhs.1)
}
}
impl<T> Sub for Dual<T>
where
T: Sub<Output = T>,
{
type Output = Self;
fn sub(self, rhs: Self) -> Self {
Self::new(self.0 - rhs.0, self.1 - rhs.1)
}
}
impl<T> Mul for Dual<T>
where
T: Clone + Add<Output = T> + Mul<Output = T>,
{
type Output = Self;
fn mul(self, rhs: Self) -> Self {
Self::new(
self.0.clone() * rhs.0.clone(),
self.0 * rhs.1 + self.1 * rhs.0,
)
}
}
// ---------- 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 Lazy Segment Tree ----------
pub trait TE {
type T: Clone;
type E: Clone;
fn fold(&self, l: &Self::T, r: &Self::T) -> Self::T;
fn eval(&self, x: &Self::T, f: &Self::E) -> Self::T;
fn merge(&self, g: &Self::E, h: &Self::E) -> Self::E;
fn e(&self) -> Self::T;
fn id(&self) -> Self::E;
}
pub struct LazySegmentTree<R: TE> {
n: usize,
size: usize,
bit: u32,
op: R,
data: Vec<(R::T, R::E)>,
}
impl<R: TE> LazySegmentTree<R> {
pub fn new(n: usize, op: R) -> Self {
assert!(n > 0);
let size = n.next_power_of_two();
let bit = size.trailing_zeros();
let data = vec![(op.e(), op.id()); 2 * size];
Self {
n,
size,
bit,
op,
data,
}
}
pub fn build<I>(init: I, n: usize, op: R) -> Self
where
I: Iterator<Item = R::T>,
{
let mut seg = Self::new(n, op);
for (data, ini) in seg.data[seg.size..].iter_mut().zip(init) {
data.0 = ini;
}
for i in (1..seg.size).rev() {
seg.pull(i);
}
seg
}
pub fn update(&mut self, l: usize, r: usize, f: R::E) {
assert!(l <= r && r <= self.n);
if l == r {
return;
}
self.push_range(l, r);
let mut s = l + self.size;
let mut t = r + self.size;
while s < t {
if s & 1 == 1 {
self.apply(s, &f);
s += 1;
}
if t & 1 == 1 {
t -= 1;
self.apply(t, &f);
}
s >>= 1;
t >>= 1;
}
let l = l + self.size;
let r = r + self.size;
for k in 1..=self.bit {
if (l >> k) << k != l {
self.pull(l >> k);
}
if (r >> k) << k != r {
self.pull((r - 1) >> k);
}
}
}
pub fn find(&mut self, l: usize, r: usize) -> R::T {
assert!(l <= r && r <= self.n);
if l == r {
return self.op.e();
}
self.push_range(l, r);
let mut l = l + self.size;
let mut r = r + self.size;
let mut p = self.op.e();
let mut q = self.op.e();
while l < r {
if l & 1 == 1 {
p = self.op.fold(&p, &self.data[l].0);
l += 1;
}
if r & 1 == 1 {
r -= 1;
q = self.op.fold(&self.data[r].0, &q);
}
l >>= 1;
r >>= 1;
}
self.op.fold(&p, &q)
}
pub fn set_at(&mut self, x: usize, v: R::T) {
assert!(x < self.n);
let x = x + self.size;
for k in (1..=self.bit).rev() {
self.push(x >> k);
}
self.data[x].0 = v;
for k in 1..=self.bit {
self.pull(x >> k);
}
}
fn push_range(&mut self, l: usize, r: usize) {
let l = l + self.size;
let r = r + self.size;
for k in (1..(self.bit + 1)).rev() {
if (l >> k) << k != l {
self.push(l >> k);
}
if (r >> k) << k != r {
self.push((r - 1) >> k);
}
}
}
fn apply(&mut self, x: usize, f: &R::E) {
self.data[x].0 = self.op.eval(&self.data[x].0, f);
self.data[x].1 = self.op.merge(&self.data[x].1, f);
}
fn push(&mut self, x: usize) {
let f = std::mem::replace(&mut self.data[x].1, self.op.id());
self.apply(2 * x, &f);
self.apply(2 * x + 1, &f);
}
fn pull(&mut self, x: usize) {
self.data[x].0 = self.op.fold(&self.data[2 * x].0, &self.data[2 * x + 1].0);
}
}
// ---------- end Lazy Segment Tree ----------
use std::ops::*;
// ---------- begin trait ----------
pub trait Zero: Sized + Add<Self, Output = Self> {
fn zero() -> Self;
fn is_zero(&self) -> bool;
}
pub trait One: Sized + Mul<Self, Output = Self> {
fn one() -> Self;
fn is_one(&self) -> bool;
}
pub trait SemiRing: Zero + One {}
pub trait Ring: SemiRing + Sub<Output = Self> + Neg<Output = Self> {}
pub trait Field: Ring + Div<Output = Self> {}
impl<T> SemiRing for T where T: Zero + One {}
impl<T> Ring for T where T: SemiRing + Sub<Output = Self> + Neg<Output = Self> {}
impl<T> Field for T where T: Ring + Div<Output = Self> {}
// ---------- end trait ----------
// ---------- begin modint ----------
pub const fn pow_mod(mut r: u32, mut n: u32, m: u32) -> u32 {
let mut t = 1;
while n > 0 {
if n & 1 == 1 {
t = (t as u64 * r as u64 % m as u64) as u32;
}
r = (r as u64 * r as u64 % m as u64) as u32;
n >>= 1;
}
t
}
pub const fn primitive_root(p: u32) -> u32 {
let mut m = p - 1;
let mut f = [1; 30];
let mut k = 0;
let mut d = 2;
while d * d <= m {
if m % d == 0 {
f[k] = d;
k += 1;
}
while m % d == 0 {
m /= d;
}
d += 1;
}
if m > 1 {
f[k] = m;
k += 1;
}
let mut g = 1;
while g < p {
let mut ok = true;
let mut i = 0;
while i < k {
ok &= pow_mod(g, (p - 1) / f[i], p) > 1;
i += 1;
}
if ok {
break;
}
g += 1;
}
g
}
pub const fn is_prime(n: u32) -> bool {
if n <= 1 {
return false;
}
let mut d = 2;
while d * d <= n {
if n % d == 0 {
return false;
}
d += 1;
}
true
}
#[derive(Clone, Copy, PartialEq, Eq)]
pub struct ModInt<const M: u32>(u32);
impl<const M: u32> ModInt<{ M }> {
const REM: u32 = {
let mut t = 1u32;
let mut s = !M + 1;
let mut n = !0u32 >> 2;
while n > 0 {
if n & 1 == 1 {
t = t.wrapping_mul(s);
}
s = s.wrapping_mul(s);
n >>= 1;
}
t
};
const INI: u64 = ((1u128 << 64) % M as u128) as u64;
const IS_PRIME: () = assert!(is_prime(M));
const PRIMITIVE_ROOT: u32 = primitive_root(M);
const ORDER: usize = 1 << (M - 1).trailing_zeros();
const fn reduce(x: u64) -> u32 {
let _ = Self::IS_PRIME;
let b = (x as u32 * Self::REM) as u64;
let t = x + b * M as u64;
let mut c = (t >> 32) as u32;
if c >= M {
c -= M;
}
c as u32
}
const fn multiply(a: u32, b: u32) -> u32 {
Self::reduce(a as u64 * b as u64)
}
pub const fn new(v: u32) -> Self {
assert!(v < M);
Self(Self::reduce(v as u64 * Self::INI))
}
pub const fn const_mul(&self, rhs: Self) -> Self {
Self(Self::multiply(self.0, rhs.0))
}
pub const fn pow(&self, mut n: u64) -> Self {
let mut t = Self::new(1);
let mut r = *self;
while n > 0 {
if n & 1 == 1 {
t = t.const_mul(r);
}
r = r.const_mul(r);
n >>= 1;
}
t
}
pub const fn inv(&self) -> Self {
assert!(self.0 != 0);
self.pow(M as u64 - 2)
}
pub const fn get(&self) -> u32 {
Self::reduce(self.0 as u64)
}
pub const fn zero() -> Self {
Self::new(0)
}
pub const fn one() -> Self {
Self::new(1)
}
}
impl<const M: u32> Add for ModInt<{ M }> {
type Output = Self;
fn add(self, rhs: Self) -> Self::Output {
let mut v = self.0 + rhs.0;
if v >= M {
v -= M;
}
Self(v)
}
}
impl<const M: u32> Sub for ModInt<{ M }> {
type Output = Self;
fn sub(self, rhs: Self) -> Self::Output {
let mut v = self.0 - rhs.0;
if self.0 < rhs.0 {
v += M;
}
Self(v)
}
}
impl<const M: u32> Mul for ModInt<{ M }> {
type Output = Self;
fn mul(self, rhs: Self) -> Self::Output {
self.const_mul(rhs)
}
}
impl<const M: u32> Div for ModInt<{ M }> {
type Output = Self;
fn div(self, rhs: Self) -> Self::Output {
self * rhs.inv()
}
}
impl<const M: u32> AddAssign for ModInt<{ M }> {
fn add_assign(&mut self, rhs: Self) {
*self = *self + rhs;
}
}
impl<const M: u32> SubAssign for ModInt<{ M }> {
fn sub_assign(&mut self, rhs: Self) {
*self = *self - rhs;
}
}
impl<const M: u32> MulAssign for ModInt<{ M }> {
fn mul_assign(&mut self, rhs: Self) {
*self = *self * rhs;
}
}
impl<const M: u32> DivAssign for ModInt<{ M }> {
fn div_assign(&mut self, rhs: Self) {
*self = *self / rhs;
}
}
impl<const M: u32> Neg for ModInt<{ M }> {
type Output = Self;
fn neg(self) -> Self::Output {
if self.0 == 0 {
self
} else {
Self(M - self.0)
}
}
}
impl<const M: u32> std::fmt::Display for ModInt<{ M }> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.get())
}
}
impl<const M: u32> std::fmt::Debug for ModInt<{ M }> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.get())
}
}
impl<const M: u32> std::str::FromStr for ModInt<{ M }> {
type Err = std::num::ParseIntError;
fn from_str(s: &str) -> Result<Self, Self::Err> {
let val = s.parse::<u32>()?;
Ok(ModInt::new(val))
}
}
impl<const M: u32> From<usize> for ModInt<{ M }> {
fn from(val: usize) -> ModInt<{ M }> {
ModInt::new((val % M as usize) as u32)
}
}
// ---------- end modint ----------
// ---------- begin precalc ----------
pub struct Precalc<const MOD: u32> {
fact: Vec<ModInt<MOD>>,
ifact: Vec<ModInt<MOD>>,
inv: Vec<ModInt<MOD>>,
}
impl<const MOD: u32> Precalc<MOD> {
pub fn new(size: usize) -> Self {
let mut fact = vec![ModInt::one(); size + 1];
let mut ifact = vec![ModInt::one(); size + 1];
let mut inv = vec![ModInt::one(); size + 1];
for i in 2..=size {
fact[i] = fact[i - 1] * ModInt::from(i);
}
ifact[size] = fact[size].inv();
for i in (2..=size).rev() {
inv[i] = ifact[i] * fact[i - 1];
ifact[i - 1] = ifact[i] * ModInt::from(i);
}
Self { fact, ifact, inv }
}
pub fn fact(&self, n: usize) -> ModInt<MOD> {
self.fact[n]
}
pub fn ifact(&self, n: usize) -> ModInt<MOD> {
self.ifact[n]
}
pub fn inv(&self, n: usize) -> ModInt<MOD> {
assert!(0 < n);
self.inv[n]
}
pub fn perm(&self, n: usize, k: usize) -> ModInt<MOD> {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[n - k]
}
pub fn binom(&self, n: usize, k: usize) -> ModInt<MOD> {
if n < k {
return ModInt::zero();
}
self.fact[n] * self.ifact[k] * self.ifact[n - k]
}
}
// ---------- end precalc ----------
impl<const M: u32> Zero for ModInt<{ M }> {
fn zero() -> Self {
Self::zero()
}
fn is_zero(&self) -> bool {
self.0 == 0
}
}
impl<const M: u32> One for ModInt<{ M }> {
fn one() -> Self {
Self::one()
}
fn is_one(&self) -> bool {
self.get() == 1
}
}
// ---------- begin array op ----------
struct NTTPrecalc<const M: u32> {
sum_e: [ModInt<{ M }>; 30],
sum_ie: [ModInt<{ M }>; 30],
}
impl<const M: u32> NTTPrecalc<{ M }> {
const fn new() -> Self {
let cnt2 = (M - 1).trailing_zeros() as usize;
let root = ModInt::new(ModInt::<{ M }>::PRIMITIVE_ROOT);
let zeta = root.pow((M - 1) as u64 >> cnt2);
let mut es = [ModInt::zero(); 30];
let mut ies = [ModInt::zero(); 30];
let mut sum_e = [ModInt::zero(); 30];
let mut sum_ie = [ModInt::zero(); 30];
let mut e = zeta;
let mut ie = e.inv();
let mut i = cnt2;
while i >= 2 {
es[i - 2] = e;
ies[i - 2] = ie;
e = e.const_mul(e);
ie = ie.const_mul(ie);
i -= 1;
}
let mut now = ModInt::one();
let mut inow = ModInt::one();
let mut i = 0;
while i < cnt2 - 1 {
sum_e[i] = es[i].const_mul(now);
sum_ie[i] = ies[i].const_mul(inow);
now = ies[i].const_mul(now);
inow = es[i].const_mul(inow);
i += 1;
}
Self { sum_e, sum_ie }
}
}
struct NTTPrecalcHelper<const MOD: u32>;
impl<const MOD: u32> NTTPrecalcHelper<MOD> {
const A: NTTPrecalc<MOD> = NTTPrecalc::new();
}
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 + One + 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![T::zero(); self.len() + rhs.len() - 1];
for (i, a) in self.iter().enumerate() {
for (res, b) in res[i..].iter_mut().zip(rhs.iter()) {
*res = *res + *a * *b;
}
}
res
}
}
// transform でlen=1を指定すればNTTになる
pub trait ArrayConvolution {
type Item;
fn transform(&mut self, len: usize);
fn inverse_transform(&mut self, len: usize);
fn convolution(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}
impl<const M: u32> ArrayConvolution for [ModInt<{ M }>] {
type Item = ModInt<{ M }>;
fn transform(&mut self, len: usize) {
let f = self;
let n = f.len();
let k = (n / len).trailing_zeros() as usize;
assert!(len << k == n);
assert!(k <= ModInt::<{ M }>::ORDER);
let pre = &NTTPrecalcHelper::<{ M }>::A;
for ph in 1..=k {
let p = len << (k - ph);
let mut now = ModInt::one();
for (i, f) in f.chunks_exact_mut(2 * p).enumerate() {
let (x, y) = f.split_at_mut(p);
for (x, y) in x.iter_mut().zip(y.iter_mut()) {
let l = *x;
let r = *y * now;
*x = l + r;
*y = l - r;
}
now *= pre.sum_e[(!i).trailing_zeros() as usize];
}
}
}
fn inverse_transform(&mut self, len: usize) {
let f = self;
let n = f.len();
let k = (n / len).trailing_zeros() as usize;
assert!(len << k == n);
assert!(k <= ModInt::<{ M }>::ORDER);
let pre = &NTTPrecalcHelper::<{ M }>::A;
for ph in (1..=k).rev() {
let p = len << (k - ph);
let mut inow = ModInt::one();
for (i, f) in f.chunks_exact_mut(2 * p).enumerate() {
let (x, y) = f.split_at_mut(p);
for (x, y) in x.iter_mut().zip(y.iter_mut()) {
let l = *x;
let r = *y;
*x = l + r;
*y = (l - r) * inow;
}
inow *= pre.sum_ie[(!i).trailing_zeros() as usize];
}
}
let ik = ModInt::new(2).inv().pow(k as u64);
for f in f.iter_mut() {
*f *= ik;
}
}
fn convolution(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
if self.len().min(rhs.len()) <= 32 {
return self.mul(rhs);
}
const PARAM: usize = 10;
let size = self.len() + rhs.len() - 1;
let mut k = 0;
while (size + (1 << k) - 1) >> k > PARAM {
k += 1;
}
let len = (size + (1 << k) - 1) >> k;
let mut f = vec![ModInt::zero(); len << k];
let mut g = vec![ModInt::zero(); len << k];
f[..self.len()].copy_from_slice(self);
g[..rhs.len()].copy_from_slice(rhs);
f.transform(len);
g.transform(len);
let mut buf = [ModInt::zero(); 2 * PARAM - 1];
let buf = &mut buf[..(2 * len - 1)];
let pre = &NTTPrecalcHelper::<{ M }>::A;
let mut now = ModInt::one();
for (i, (f, g)) in f
.chunks_exact_mut(2 * len)
.zip(g.chunks_exact(2 * len))
.enumerate()
{
let mut r = now;
for (f, g) in f.chunks_exact_mut(len).zip(g.chunks_exact(len)) {
buf.fill(ModInt::zero());
for (i, f) in f.iter().enumerate() {
for (buf, g) in buf[i..].iter_mut().zip(g.iter()) {
*buf = *buf + *f * *g;
}
}
f.copy_from_slice(&buf[..len]);
for (f, buf) in f.iter_mut().zip(buf[len..].iter()) {
*f = *f + r * *buf;
}
r = -r;
}
now *= pre.sum_e[(!i).trailing_zeros() as usize];
}
f.inverse_transform(len);
f.truncate(self.len() + rhs.len() - 1);
f
}
}
// ---------- end array op ----------