結果
| 問題 |
No.1318 ABCD quadruplets
|
| コンテスト | |
| ユーザー |
 fukafukatani
|
| 提出日時 | 2020-12-17 00:44:23 |
| 言語 | Rust (1.83.0 + proconio) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 57,964 bytes |
| コンパイル時間 | 13,964 ms |
| コンパイル使用メモリ | 387,232 KB |
| 実行使用メモリ | 56,232 KB |
| 最終ジャッジ日時 | 2024-09-20 05:38:22 |
| 合計ジャッジ時間 | 18,301 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 10 TLE * 1 -- * 19 |
ソースコード
#![allow(unused_imports)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;
use std::ops::Bound::*;
#[allow(unused_macros)]
macro_rules! debug {
($($e:expr),*) => {
#[cfg(debug_assertions)]
$({
let (e, mut err) = (stringify!($e), std::io::stderr());
writeln!(err, "{} = {:?}", e, $e).unwrap()
})*
};
}
fn main() {
let v = read_vec::<usize>();
let (n, m) = (v[0], v[1]);
let mut coefs = vec![vec![0i64; n + 1]; m * 3 + 1];
for a in 0..=m {
for b in 0..=m {
for c in 0..=m {
let k = a * a + b * b + c * c + a * c + b * c + b * a;
if k <= n {
coefs[a + b + c][k] += 1;
}
}
}
}
// debug!(coefs);
let mut answers = vec![0; 10 * n + 1];
for coef in 0..=3 * m {
let mut k1 = vec![0; n + 1];
for d in 0..=m {
if d * d + coef * d > n {
break;
}
k1[d * d + coef * d] += 1;
}
let result = convolution_i64(&k1, &coefs[coef]);
for i in 0..=n {
answers[i] += result[i];
}
}
for ans in answers.into_iter().take(n + 1) {
println!("{}", ans);
}
}
fn read<T: std::str::FromStr>() -> T {
let mut s = String::new();
std::io::stdin().read_line(&mut s).ok();
s.trim().parse().ok().unwrap()
}
fn read_vec<T: std::str::FromStr>() -> Vec<T> {
read::<String>()
.split_whitespace()
.map(|e| e.parse().ok().unwrap())
.collect()
}
//https://github.com/rust-lang-ja/ac-library-rs
pub mod convolution {
macro_rules! modulus {
($($name:ident),*) => {
$(
#[derive(Copy, Clone, Eq, PartialEq)]
enum $name {}
impl Modulus for $name {
const VALUE: u32 = $name as _;
const HINT_VALUE_IS_PRIME: bool = true;
fn butterfly_cache() -> &'static ::std::thread::LocalKey<::std::cell::RefCell<::std::option::Option<crate::modint::ButterflyCache<Self>>>> {
thread_local! {
static BUTTERFLY_CACHE: ::std::cell::RefCell<::std::option::Option<crate::modint::ButterflyCache<$name>>> = ::std::default::Default::default();
}
&BUTTERFLY_CACHE
}
}
)*
};
}
use crate::{
internal_bit, internal_math,
modint::{ButterflyCache, Modulus, RemEuclidU32, StaticModInt},
};
use std::{
cmp,
convert::{TryFrom, TryInto as _},
fmt,
};
#[allow(clippy::many_single_char_names)]
pub fn convolution<M>(a: &[StaticModInt<M>], b: &[StaticModInt<M>]) -> Vec<StaticModInt<M>>
where
M: Modulus,
{
if a.is_empty() || b.is_empty() {
return vec![];
}
let (n, m) = (a.len(), b.len());
if cmp::min(n, m) <= 60 {
let (n, m, a, b) = if n < m { (m, n, b, a) } else { (n, m, a, b) };
let mut ans = vec![StaticModInt::new(0); n + m - 1];
for i in 0..n {
for j in 0..m {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
let (mut a, mut b) = (a.to_owned(), b.to_owned());
let z = 1 << internal_bit::ceil_pow2((n + m - 1) as _);
a.resize(z, StaticModInt::raw(0));
butterfly(&mut a);
b.resize(z, StaticModInt::raw(0));
butterfly(&mut b);
for (a, b) in a.iter_mut().zip(&b) {
*a *= b;
}
butterfly_inv(&mut a);
a.resize(n + m - 1, StaticModInt::raw(0));
let iz = StaticModInt::new(z).inv();
for a in &mut a {
*a *= iz;
}
a
}
pub fn convolution_raw<T, M>(a: &[T], b: &[T]) -> Vec<T>
where
T: RemEuclidU32 + TryFrom<u32> + Clone,
T::Error: fmt::Debug,
M: Modulus,
{
let a = a.iter().cloned().map(Into::into).collect::<Vec<_>>();
let b = b.iter().cloned().map(Into::into).collect::<Vec<_>>();
convolution::<M>(&a, &b)
.into_iter()
.map(|z| {
z.val()
.try_into()
.expect("the numeric type is smaller than the modulus")
})
.collect()
}
#[allow(clippy::many_single_char_names)]
pub fn convolution_i64(a: &[i64], b: &[i64]) -> Vec<i64> {
const M1: u64 = 754_974_721; // 2^24
const M2: u64 = 167_772_161; // 2^25
const M3: u64 = 469_762_049; // 2^26
const M2M3: u64 = M2 * M3;
const M1M3: u64 = M1 * M3;
const M1M2: u64 = M1 * M2;
const M1M2M3: u64 = M1M2.wrapping_mul(M3);
modulus!(M1, M2, M3);
if a.is_empty() || b.is_empty() {
return vec![];
}
let (_, i1) = internal_math::inv_gcd(M2M3 as _, M1 as _);
let (_, i2) = internal_math::inv_gcd(M1M3 as _, M2 as _);
let (_, i3) = internal_math::inv_gcd(M1M2 as _, M3 as _);
let c1 = convolution_raw::<i64, M1>(a, b);
let c2 = convolution_raw::<i64, M2>(a, b);
let c3 = convolution_raw::<i64, M3>(a, b);
c1.into_iter()
.zip(c2)
.zip(c3)
.map(|((c1, c2), c3)| {
const OFFSET: &[u64] = &[0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3];
let mut x = [(c1, i1, M1, M2M3), (c2, i2, M2, M1M3), (c3, i3, M3, M1M2)]
.iter()
.map(|&(c, i, m1, m2)| {
c.wrapping_mul(i).rem_euclid(m1 as _).wrapping_mul(m2 as _)
})
.fold(0, i64::wrapping_add);
// B = 2^63, -B <= x, r(real value) < B
// (x, x - M, x - 2M, or x - 3M) = r (mod 2B)
// r = c1[i] (mod MOD1)
// focus on MOD1
// r = x, x - M', x - 2M', x - 3M' (M' = M % 2^64) (mod 2B)
// r = x,
// x - M' + (0 or 2B),
// x - 2M' + (0, 2B or 4B),
// x - 3M' + (0, 2B, 4B or 6B) (without mod!)
// (r - x) = 0, (0)
// - M' + (0 or 2B), (1)
// -2M' + (0 or 2B or 4B), (2)
// -3M' + (0 or 2B or 4B or 6B) (3) (mod MOD1)
// we checked that
// ((1) mod MOD1) mod 5 = 2
// ((2) mod MOD1) mod 5 = 3
// ((3) mod MOD1) mod 5 = 4
let mut diff = c1 - internal_math::safe_mod(x, M1 as _);
if diff < 0 {
diff += M1 as i64;
}
x = x.wrapping_sub(OFFSET[diff.rem_euclid(5) as usize] as _);
x
})
.collect()
}
#[allow(clippy::many_single_char_names)]
fn butterfly<M: Modulus>(a: &mut [StaticModInt<M>]) {
let n = a.len();
let h = internal_bit::ceil_pow2(n as u32);
M::butterfly_cache().with(|cache| {
let mut cache = cache.borrow_mut();
let ButterflyCache { sum_e, .. } = cache.get_or_insert_with(prepare);
for ph in 1..=h {
let w = 1 << (ph - 1);
let p = 1 << (h - ph);
let mut now = StaticModInt::<M>::new(1);
for s in 0..w {
let offset = s << (h - ph + 1);
for i in 0..p {
let l = a[i + offset];
let r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[(!s).trailing_zeros() as usize];
}
}
});
}
#[allow(clippy::many_single_char_names)]
fn butterfly_inv<M: Modulus>(a: &mut [StaticModInt<M>]) {
let n = a.len();
let h = internal_bit::ceil_pow2(n as u32);
M::butterfly_cache().with(|cache| {
let mut cache = cache.borrow_mut();
let ButterflyCache { sum_ie, .. } = cache.get_or_insert_with(prepare);
for ph in (1..=h).rev() {
let w = 1 << (ph - 1);
let p = 1 << (h - ph);
let mut inow = StaticModInt::<M>::new(1);
for s in 0..w {
let offset = s << (h - ph + 1);
for i in 0..p {
let l = a[i + offset];
let r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] = StaticModInt::new(M::VALUE + l.val() - r.val()) * inow;
}
inow *= sum_ie[(!s).trailing_zeros() as usize];
}
}
});
}
fn prepare<M: Modulus>() -> ButterflyCache<M> {
let g = StaticModInt::<M>::raw(internal_math::primitive_root(M::VALUE as i32) as u32);
let mut es = [StaticModInt::<M>::raw(0); 30]; // es[i]^(2^(2+i)) == 1
let mut ies = [StaticModInt::<M>::raw(0); 30];
let cnt2 = (M::VALUE - 1).trailing_zeros() as usize;
let mut e = g.pow(((M::VALUE - 1) >> cnt2).into());
let mut ie = e.inv();
for i in (2..=cnt2).rev() {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
let sum_e = es
.iter()
.scan(StaticModInt::new(1), |acc, e| {
*acc *= e;
Some(*acc)
})
.collect();
let sum_ie = ies
.iter()
.scan(StaticModInt::new(1), |acc, ie| {
*acc *= ie;
Some(*acc)
})
.collect();
ButterflyCache { sum_e, sum_ie }
}
#[cfg(test)]
mod tests {
use crate::{
modint::{Mod998244353, Modulus, StaticModInt},
RemEuclidU32,
};
use rand::{rngs::ThreadRng, Rng as _};
use std::{
convert::{TryFrom, TryInto as _},
fmt,
};
//https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L51-L71
#[test]
fn empty() {
assert!(super::convolution_raw::<i32, Mod998244353>(&[], &[]).is_empty());
assert!(super::convolution_raw::<i32, Mod998244353>(&[], &[1, 2]).is_empty());
assert!(super::convolution_raw::<i32, Mod998244353>(&[1, 2], &[]).is_empty());
assert!(super::convolution_raw::<i32, Mod998244353>(&[1], &[]).is_empty());
assert!(super::convolution_raw::<i64, Mod998244353>(&[], &[]).is_empty());
assert!(super::convolution_raw::<i64, Mod998244353>(&[], &[1, 2]).is_empty());
assert!(super::convolution::<Mod998244353>(&[], &[]).is_empty());
assert!(super::convolution::<Mod998244353>(&[], &[1.into(), 2.into()]).is_empty());
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L73-L85
#[test]
fn mid() {
const N: usize = 1234;
const M: usize = 2345;
let mut rng = rand::thread_rng();
let mut gen_values = |n| gen_values::<Mod998244353>(&mut rng, n);
let (a, b) = (gen_values(N), gen_values(M));
assert_eq!(conv_naive(&a, &b), super::convolution(&a, &b));
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L87-L118
#[test]
fn simple_s_mod() {
const M1: u32 = 998_244_353;
const M2: u32 = 924_844_033;
modulus!(M1, M2);
fn test<M: Modulus>(rng: &mut ThreadRng) {
let mut gen_values = |n| gen_values::<Mod998244353>(rng, n);
for (n, m) in (1..20).flat_map(|i| (1..20).map(move |j| (i, j))) {
let (a, b) = (gen_values(n), gen_values(m));
assert_eq!(conv_naive(&a, &b), super::convolution(&a, &b));
}
}
let mut rng = rand::thread_rng();
test::<M1>(&mut rng);
test::<M2>(&mut rng);
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L120-L150
#[test]
fn simple_int() {
simple_raw::<i32>();
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L152-L182
#[test]
fn simple_uint() {
simple_raw::<u32>();
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L184-L214
#[test]
fn simple_ll() {
simple_raw::<i64>();
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L216-L246
#[test]
fn simple_ull() {
simple_raw::<u64>();
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L249-L279
#[test]
fn simple_int128() {
simple_raw::<i128>();
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L281-L311
#[test]
fn simple_uint128() {
simple_raw::<u128>();
}
fn simple_raw<T>()
where
T: TryFrom<u32> + Copy + RemEuclidU32,
T::Error: fmt::Debug,
{
const M1: u32 = 998_244_353;
const M2: u32 = 924_844_033;
modulus!(M1, M2);
fn test<T, M>(rng: &mut ThreadRng)
where
T: TryFrom<u32> + Copy + RemEuclidU32,
T::Error: fmt::Debug,
M: Modulus,
{
let mut gen_raw_values = |n| gen_raw_values::<u32, Mod998244353>(rng, n);
for (n, m) in (1..20).flat_map(|i| (1..20).map(move |j| (i, j))) {
let (a, b) = (gen_raw_values(n), gen_raw_values(m));
assert_eq!(
conv_raw_naive::<_, M>(&a, &b),
super::convolution_raw::<_, M>(&a, &b),
);
}
}
let mut rng = rand::thread_rng();
test::<T, M1>(&mut rng);
test::<T, M2>(&mut rng);
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L315-L329
#[test]
fn conv_ll() {
let mut rng = rand::thread_rng();
for (n, m) in (1..20).flat_map(|i| (1..20).map(move |j| (i, j))) {
let mut gen = |n: usize| -> Vec<_> {
(0..n).map(|_| rng.gen_range(-500_000, 500_000)).collect()
};
let (a, b) = (gen(n), gen(m));
assert_eq!(conv_i64_naive(&a, &b), super::convolution_i64(&a, &b));
}
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L331-L356
#[test]
fn conv_ll_bound() {
const M1: u64 = 754_974_721; // 2^24
const M2: u64 = 167_772_161; // 2^25
const M3: u64 = 469_762_049; // 2^26
const M2M3: u64 = M2 * M3;
const M1M3: u64 = M1 * M3;
const M1M2: u64 = M1 * M2;
modulus!(M1, M2, M3);
for i in -1000..=1000 {
let a = vec![0u64.wrapping_sub(M1M2 + M1M3 + M2M3) as i64 + i];
let b = vec![1];
assert_eq!(a, super::convolution_i64(&a, &b));
}
for i in 0..1000 {
let a = vec![i64::min_value() + i];
let b = vec![1];
assert_eq!(a, super::convolution_i64(&a, &b));
}
for i in 0..1000 {
let a = vec![i64::max_value() - i];
let b = vec![1];
assert_eq!(a, super::convolution_i64(&a, &b));
}
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L358-L371
#[test]
fn conv_641() {
const M: u32 = 641;
modulus!(M);
let mut rng = rand::thread_rng();
let mut gen_values = |n| gen_values::<M>(&mut rng, n);
let (a, b) = (gen_values(64), gen_values(65));
assert_eq!(conv_naive(&a, &b), super::convolution(&a, &b));
}
// https://github.com/atcoder/ac-library/blob/8250de484ae0ab597391db58040a602e0dc1a419/test/unittest/convolution_test.cpp#L373-L386
#[test]
fn conv_18433() {
const M: u32 = 18433;
modulus!(M);
let mut rng = rand::thread_rng();
let mut gen_values = |n| gen_values::<M>(&mut rng, n);
let (a, b) = (gen_values(1024), gen_values(1025));
assert_eq!(conv_naive(&a, &b), super::convolution(&a, &b));
}
#[allow(clippy::many_single_char_names)]
fn conv_naive<M: Modulus>(
a: &[StaticModInt<M>],
b: &[StaticModInt<M>],
) -> Vec<StaticModInt<M>> {
let (n, m) = (a.len(), b.len());
let mut c = vec![StaticModInt::raw(0); n + m - 1];
for (i, j) in (0..n).flat_map(|i| (0..m).map(move |j| (i, j))) {
c[i + j] += a[i] * b[j];
}
c
}
fn conv_raw_naive<T, M>(a: &[T], b: &[T]) -> Vec<T>
where
T: TryFrom<u32> + Copy + RemEuclidU32,
T::Error: fmt::Debug,
M: Modulus,
{
conv_naive::<M>(
&a.iter().copied().map(Into::into).collect::<Vec<_>>(),
&b.iter().copied().map(Into::into).collect::<Vec<_>>(),
)
.into_iter()
.map(|x| x.val().try_into().unwrap())
.collect()
}
#[allow(clippy::many_single_char_names)]
fn conv_i64_naive(a: &[i64], b: &[i64]) -> Vec<i64> {
let (n, m) = (a.len(), b.len());
let mut c = vec![0; n + m - 1];
for (i, j) in (0..n).flat_map(|i| (0..m).map(move |j| (i, j))) {
c[i + j] += a[i] * b[j];
}
c
}
fn gen_values<M: Modulus>(rng: &mut ThreadRng, n: usize) -> Vec<StaticModInt<M>> {
(0..n).map(|_| rng.gen_range(0, M::VALUE).into()).collect()
}
fn gen_raw_values<T, M>(rng: &mut ThreadRng, n: usize) -> Vec<T>
where
T: TryFrom<u32>,
T::Error: fmt::Debug,
M: Modulus,
{
(0..n)
.map(|_| rng.gen_range(0, M::VALUE).try_into().unwrap())
.collect()
}
}
}
pub mod internal_bit {
// Skipped:
//
// - `bsf` = `__builtin_ctz`: is equivalent to `{integer}::trailing_zeros`
#[allow(dead_code)]
pub(crate) fn ceil_pow2(n: u32) -> u32 {
32 - n.saturating_sub(1).leading_zeros()
}
#[cfg(test)]
mod tests {
#[test]
fn ceil_pow2() {
// https://github.com/atcoder/ac-library/blob/2088c8e2431c3f4d29a2cfabc6529fe0a0586c48/test/unittest/bit_test.cpp
assert_eq!(0, super::ceil_pow2(0));
assert_eq!(0, super::ceil_pow2(1));
assert_eq!(1, super::ceil_pow2(2));
assert_eq!(2, super::ceil_pow2(3));
assert_eq!(2, super::ceil_pow2(4));
assert_eq!(3, super::ceil_pow2(5));
assert_eq!(3, super::ceil_pow2(6));
assert_eq!(3, super::ceil_pow2(7));
assert_eq!(3, super::ceil_pow2(8));
assert_eq!(4, super::ceil_pow2(9));
assert_eq!(30, super::ceil_pow2(1 << 30));
assert_eq!(31, super::ceil_pow2((1 << 30) + 1));
assert_eq!(32, super::ceil_pow2(u32::max_value()));
}
}
}
pub mod internal_math {
// remove this after dependencies has been added
#![allow(dead_code)]
use std::mem::swap;
/// # Arguments
/// * `m` `1 <= m`
///
/// # Returns
/// x mod m
/* const */
pub(crate) fn safe_mod(mut x: i64, m: i64) -> i64 {
x %= m;
if x < 0 {
x += m;
}
x
}
/// Fast modular by barrett reduction
/// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
/// NOTE: reconsider after Ice Lake
pub(crate) struct Barrett {
pub(crate) _m: u32,
pub(crate) im: u64,
}
impl Barrett {
/// # Arguments
/// * `m` `1 <= m`
/// (Note: `m <= 2^31` should also hold, which is undocumented in the original library.
/// See the [pull reqeust commment](https://github.com/rust-lang-ja/ac-library-rs/pull/3#discussion_r484661007)
/// for more details.)
pub(crate) fn new(m: u32) -> Barrett {
Barrett {
_m: m,
im: (-1i64 as u64 / m as u64).wrapping_add(1),
}
}
/// # Returns
/// `m`
pub(crate) fn umod(&self) -> u32 {
self._m
}
/// # Parameters
/// * `a` `0 <= a < m`
/// * `b` `0 <= b < m`
///
/// # Returns
/// a * b % m
#[allow(clippy::many_single_char_names)]
pub(crate) fn mul(&self, a: u32, b: u32) -> u32 {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
let mut z = a as u64;
z *= b as u64;
let x = (((z as u128) * (self.im as u128)) >> 64) as u64;
let mut v = z.wrapping_sub(x.wrapping_mul(self._m as u64)) as u32;
if self._m <= v {
v = v.wrapping_add(self._m);
}
v
}
}
/// # Parameters
/// * `n` `0 <= n`
/// * `m` `1 <= m`
///
/// # Returns
/// `(x ** n) % m`
/* const */
#[allow(clippy::many_single_char_names)]
pub(crate) fn pow_mod(x: i64, mut n: i64, m: i32) -> i64 {
if m == 1 {
return 0;
}
let _m = m as u32;
let mut r: u64 = 1;
let mut y: u64 = safe_mod(x, m as i64) as u64;
while n != 0 {
if (n & 1) > 0 {
r = (r * y) % (_m as u64);
}
y = (y * y) % (_m as u64);
n >>= 1;
}
r as i64
}
/// Reference:
/// M. Forisek and J. Jancina,
/// Fast Primality Testing for Integers That Fit into a Machine Word
///
/// # Parameters
/// * `n` `0 <= n`
/* const */
pub(crate) fn is_prime(n: i32) -> bool {
let n = n as i64;
match n {
_ if n <= 1 => return false,
2 | 7 | 61 => return true,
_ if n % 2 == 0 => return false,
_ => {}
}
let mut d = n - 1;
while d % 2 == 0 {
d /= 2;
}
for &a in &[2, 7, 61] {
let mut t = d;
let mut y = pow_mod(a, t, n as i32);
while t != n - 1 && y != 1 && y != n - 1 {
y = y * y % n;
t <<= 1;
}
if y != n - 1 && t % 2 == 0 {
return false;
}
}
true
}
// omitted
// template <int n> constexpr bool is_prime = is_prime_constexpr(n);
/// # Parameters
/// * `b` `1 <= b`
///
/// # Returns
/// (g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
/* const */
#[allow(clippy::many_single_char_names)]
pub(crate) fn inv_gcd(a: i64, b: i64) -> (i64, i64) {
let a = safe_mod(a, b);
if a == 0 {
return (b, 0);
}
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
let mut s = b;
let mut t = a;
let mut m0 = 0;
let mut m1 = 1;
while t != 0 {
let u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
swap(&mut s, &mut t);
swap(&mut m0, &mut m1);
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
if m0 < 0 {
m0 += b / s;
}
(s, m0)
}
/// Compile time (currently not) primitive root
/// @param m must be prime
/// @return primitive root (and minimum in now)
/* const */
pub(crate) fn primitive_root(m: i32) -> i32 {
match m {
2 => return 1,
167_772_161 => return 3,
469_762_049 => return 3,
754_974_721 => return 11,
998_244_353 => return 3,
_ => {}
}
let mut divs = [0; 20];
divs[0] = 2;
let mut cnt = 1;
let mut x = (m - 1) / 2;
while x % 2 == 0 {
x /= 2;
}
for i in (3..std::i32::MAX).step_by(2) {
if i as i64 * i as i64 > x as i64 {
break;
}
if x % i == 0 {
divs[cnt] = i;
cnt += 1;
while x % i == 0 {
x /= i;
}
}
}
if x > 1 {
divs[cnt] = x;
cnt += 1;
}
let mut g = 2;
loop {
if (0..cnt).all(|i| pow_mod(g, ((m - 1) / divs[i]) as i64, m) != 1) {
break g as i32;
}
g += 1;
}
}
// omitted
// template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
#[cfg(test)]
mod tests {
#![allow(clippy::unreadable_literal)]
#![allow(clippy::cognitive_complexity)]
use crate::internal_math::{inv_gcd, is_prime, pow_mod, primitive_root, safe_mod, Barrett};
use std::collections::HashSet;
#[test]
fn test_safe_mod() {
assert_eq!(safe_mod(0, 3), 0);
assert_eq!(safe_mod(1, 3), 1);
assert_eq!(safe_mod(2, 3), 2);
assert_eq!(safe_mod(3, 3), 0);
assert_eq!(safe_mod(4, 3), 1);
assert_eq!(safe_mod(5, 3), 2);
assert_eq!(safe_mod(73, 11), 7);
assert_eq!(safe_mod(2306249155046129918, 6620319213327), 1374210749525);
assert_eq!(safe_mod(-1, 3), 2);
assert_eq!(safe_mod(-2, 3), 1);
assert_eq!(safe_mod(-3, 3), 0);
assert_eq!(safe_mod(-4, 3), 2);
assert_eq!(safe_mod(-5, 3), 1);
assert_eq!(safe_mod(-7170500492396019511, 777567337), 333221848);
}
#[test]
fn test_barrett() {
let b = Barrett::new(7);
assert_eq!(b.umod(), 7);
assert_eq!(b.mul(2, 3), 6);
assert_eq!(b.mul(4, 6), 3);
assert_eq!(b.mul(5, 0), 0);
let b = Barrett::new(998244353);
assert_eq!(b.umod(), 998244353);
assert_eq!(b.mul(2, 3), 6);
assert_eq!(b.mul(3141592, 653589), 919583920);
assert_eq!(b.mul(323846264, 338327950), 568012980);
// make `z - x * self._m as u64` overflow.
// Thanks @koba-e964 (at https://github.com/rust-lang-ja/ac-library-rs/pull/3#discussion_r484932161)
let b = Barrett::new(2147483647);
assert_eq!(b.umod(), 2147483647);
assert_eq!(b.mul(1073741824, 2147483645), 2147483646);
}
#[test]
fn test_pow_mod() {
assert_eq!(pow_mod(0, 0, 1), 0);
assert_eq!(pow_mod(0, 0, 3), 1);
assert_eq!(pow_mod(0, 0, 723), 1);
assert_eq!(pow_mod(0, 0, 998244353), 1);
assert_eq!(pow_mod(0, 0, i32::max_value()), 1);
assert_eq!(pow_mod(0, 1, 1), 0);
assert_eq!(pow_mod(0, 1, 3), 0);
assert_eq!(pow_mod(0, 1, 723), 0);
assert_eq!(pow_mod(0, 1, 998244353), 0);
assert_eq!(pow_mod(0, 1, i32::max_value()), 0);
assert_eq!(pow_mod(0, i64::max_value(), 1), 0);
assert_eq!(pow_mod(0, i64::max_value(), 3), 0);
assert_eq!(pow_mod(0, i64::max_value(), 723), 0);
assert_eq!(pow_mod(0, i64::max_value(), 998244353), 0);
assert_eq!(pow_mod(0, i64::max_value(), i32::max_value()), 0);
assert_eq!(pow_mod(1, 0, 1), 0);
assert_eq!(pow_mod(1, 0, 3), 1);
assert_eq!(pow_mod(1, 0, 723), 1);
assert_eq!(pow_mod(1, 0, 998244353), 1);
assert_eq!(pow_mod(1, 0, i32::max_value()), 1);
assert_eq!(pow_mod(1, 1, 1), 0);
assert_eq!(pow_mod(1, 1, 3), 1);
assert_eq!(pow_mod(1, 1, 723), 1);
assert_eq!(pow_mod(1, 1, 998244353), 1);
assert_eq!(pow_mod(1, 1, i32::max_value()), 1);
assert_eq!(pow_mod(1, i64::max_value(), 1), 0);
assert_eq!(pow_mod(1, i64::max_value(), 3), 1);
assert_eq!(pow_mod(1, i64::max_value(), 723), 1);
assert_eq!(pow_mod(1, i64::max_value(), 998244353), 1);
assert_eq!(pow_mod(1, i64::max_value(), i32::max_value()), 1);
assert_eq!(pow_mod(i64::max_value(), 0, 1), 0);
assert_eq!(pow_mod(i64::max_value(), 0, 3), 1);
assert_eq!(pow_mod(i64::max_value(), 0, 723), 1);
assert_eq!(pow_mod(i64::max_value(), 0, 998244353), 1);
assert_eq!(pow_mod(i64::max_value(), 0, i32::max_value()), 1);
assert_eq!(pow_mod(i64::max_value(), i64::max_value(), 1), 0);
assert_eq!(pow_mod(i64::max_value(), i64::max_value(), 3), 1);
assert_eq!(pow_mod(i64::max_value(), i64::max_value(), 723), 640);
assert_eq!(
pow_mod(i64::max_value(), i64::max_value(), 998244353),
683296792
);
assert_eq!(
pow_mod(i64::max_value(), i64::max_value(), i32::max_value()),
1
);
assert_eq!(pow_mod(2, 3, 1_000_000_007), 8);
assert_eq!(pow_mod(5, 7, 1_000_000_007), 78125);
assert_eq!(pow_mod(123, 456, 1_000_000_007), 565291922);
}
#[test]
fn test_is_prime() {
assert!(!is_prime(0));
assert!(!is_prime(1));
assert!(is_prime(2));
assert!(is_prime(3));
assert!(!is_prime(4));
assert!(is_prime(5));
assert!(!is_prime(6));
assert!(is_prime(7));
assert!(!is_prime(8));
assert!(!is_prime(9));
// assert!(is_prime(57));
assert!(!is_prime(57));
assert!(!is_prime(58));
assert!(is_prime(59));
assert!(!is_prime(60));
assert!(is_prime(61));
assert!(!is_prime(62));
assert!(!is_prime(701928443));
assert!(is_prime(998244353));
assert!(!is_prime(1_000_000_000));
assert!(is_prime(1_000_000_007));
assert!(is_prime(i32::max_value()));
}
#[test]
fn test_is_prime_sieve() {
let n = 1_000_000;
let mut prime = vec![true; n];
prime[0] = false;
prime[1] = false;
for i in 0..n {
assert_eq!(prime[i], is_prime(i as i32));
if prime[i] {
for j in (2 * i..n).step_by(i) {
prime[j] = false;
}
}
}
}
#[test]
fn test_inv_gcd() {
for &(a, b, g) in &[
(0, 1, 1),
(0, 4, 4),
(0, 7, 7),
(2, 3, 1),
(-2, 3, 1),
(4, 6, 2),
(-4, 6, 2),
(13, 23, 1),
(57, 81, 3),
(12345, 67890, 15),
(-3141592 * 6535, 3141592 * 8979, 3141592),
(i64::max_value(), i64::max_value(), i64::max_value()),
(i64::min_value(), i64::max_value(), 1),
] {
let (g_, x) = inv_gcd(a, b);
assert_eq!(g, g_);
let b_ = b as i128;
assert_eq!(((x as i128 * a as i128) % b_ + b_) % b_, g as i128 % b_);
}
}
#[test]
fn test_primitive_root() {
for &p in &[
2,
3,
5,
7,
233,
200003,
998244353,
1_000_000_007,
i32::max_value(),
] {
assert!(is_prime(p));
let g = primitive_root(p);
if p != 2 {
assert_ne!(g, 1);
}
let q = p - 1;
for i in (2..i32::max_value()).take_while(|i| i * i <= q) {
if q % i != 0 {
break;
}
for &r in &[i, q / i] {
assert_ne!(pow_mod(g as i64, r as i64, p), 1);
}
}
assert_eq!(pow_mod(g as i64, q as i64, p), 1);
if p < 1_000_000 {
assert_eq!(
(0..p - 1)
.scan(1, |i, _| {
*i = *i * g % p;
Some(*i)
})
.collect::<HashSet<_>>()
.len() as i32,
p - 1
);
}
}
}
}
}
pub mod modint {
//! Structs that treat the modular arithmetic.
//!
//! # Major changes from the original ACL
//!
//! - Converted the struct names to PascalCase.
//! - Renamed `mod` → `modulus`.
//! - Moduli are `u32`, not `i32`.
//! - `Id`s are `usize`, not `i32`.
//! - The default `Id` is `0`, not `-1`.
//! - The type of the argument of `pow` is `u64`, not `i64`.
//! - Modints implement `FromStr` and `Display`. Modints in the original ACL don't have `operator<<` or `operator>>`.
use crate::internal_math;
use std::{
cell::RefCell,
convert::{Infallible, TryInto as _},
fmt,
hash::{Hash, Hasher},
iter::{Product, Sum},
marker::PhantomData,
ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
str::FromStr,
thread::LocalKey,
};
pub type ModInt1000000007 = StaticModInt<Mod1000000007>;
pub type ModInt998244353 = StaticModInt<Mod998244353>;
pub type ModInt = DynamicModInt<DefaultId>;
/// Corresponds to `atcoder::static_modint` in the original ACL.
#[derive(Copy, Clone, Eq, PartialEq)]
#[repr(transparent)]
pub struct StaticModInt<M> {
val: u32,
phantom: PhantomData<fn() -> M>,
}
impl<M: Modulus> StaticModInt<M> {
/// Corresponds to `atcoder::static_modint::mod` in the original ACL.
#[inline(always)]
pub fn modulus() -> u32 {
M::VALUE
}
/// Creates a new `StaticModInt`.
#[inline]
pub fn new<T: RemEuclidU32>(val: T) -> Self {
Self::raw(val.rem_euclid_u32(M::VALUE))
}
/// Corresponds to `atcoder::static_modint::raw` in the original ACL.
#[inline]
pub fn raw(val: u32) -> Self {
Self {
val,
phantom: PhantomData,
}
}
/// Corresponds to `atcoder::static_modint::val` in the original ACL.
#[inline]
pub fn val(self) -> u32 {
self.val
}
/// Corresponds to `atcoder::static_modint::pow` in the original ACL.
#[inline]
pub fn pow(self, n: u64) -> Self {
<Self as ModIntBase>::pow(self, n)
}
/// Corresponds to `atcoder::static_modint::inv` in the original ACL.
///
/// # Panics
///
/// Panics if the multiplicative inverse does not exist.
#[inline]
pub fn inv(self) -> Self {
if M::HINT_VALUE_IS_PRIME {
if self.val() == 0 {
panic!("attempt to divide by zero");
}
debug_assert!(
internal_math::is_prime(M::VALUE.try_into().unwrap()),
"{} is not a prime number",
M::VALUE,
);
self.pow((M::VALUE - 2).into())
} else {
Self::inv_for_non_prime_modulus(self)
}
}
}
impl<M: Modulus> ModIntBase for StaticModInt<M> {
#[inline(always)]
fn modulus() -> u32 {
Self::modulus()
}
#[inline]
fn raw(val: u32) -> Self {
Self::raw(val)
}
#[inline]
fn val(self) -> u32 {
self.val()
}
#[inline]
fn inv(self) -> Self {
self.inv()
}
}
pub trait Modulus: 'static + Copy + Eq {
const VALUE: u32;
const HINT_VALUE_IS_PRIME: bool;
fn butterfly_cache() -> &'static LocalKey<RefCell<Option<ButterflyCache<Self>>>>;
}
#[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash, Debug)]
pub enum Mod1000000007 {}
impl Modulus for Mod1000000007 {
const VALUE: u32 = 1_000_000_007;
const HINT_VALUE_IS_PRIME: bool = true;
fn butterfly_cache() -> &'static LocalKey<RefCell<Option<ButterflyCache<Self>>>> {
thread_local! {
static BUTTERFLY_CACHE: RefCell<Option<ButterflyCache<Mod1000000007>>> = RefCell::default();
}
&BUTTERFLY_CACHE
}
}
#[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash, Debug)]
pub enum Mod998244353 {}
impl Modulus for Mod998244353 {
const VALUE: u32 = 998_244_353;
const HINT_VALUE_IS_PRIME: bool = true;
fn butterfly_cache() -> &'static LocalKey<RefCell<Option<ButterflyCache<Self>>>> {
thread_local! {
static BUTTERFLY_CACHE: RefCell<Option<ButterflyCache<Mod998244353>>> = RefCell::default();
}
&BUTTERFLY_CACHE
}
}
pub struct ButterflyCache<M> {
pub(crate) sum_e: Vec<StaticModInt<M>>,
pub(crate) sum_ie: Vec<StaticModInt<M>>,
}
#[derive(Copy, Clone, Eq, PartialEq)]
#[repr(transparent)]
pub struct DynamicModInt<I> {
val: u32,
phantom: PhantomData<fn() -> I>,
}
impl<I: Id> DynamicModInt<I> {
#[inline]
pub fn modulus() -> u32 {
I::companion_barrett().with(|bt| bt.borrow().umod())
}
#[inline]
pub fn set_modulus(modulus: u32) {
if modulus == 0 {
panic!("the modulus must not be 0");
}
I::companion_barrett().with(|bt| *bt.borrow_mut() = Barrett::new(modulus))
}
#[inline]
pub fn new<T: RemEuclidU32>(val: T) -> Self {
<Self as ModIntBase>::new(val)
}
#[inline]
pub fn raw(val: u32) -> Self {
Self {
val,
phantom: PhantomData,
}
}
#[inline]
pub fn val(self) -> u32 {
self.val
}
#[inline]
pub fn pow(self, n: u64) -> Self {
<Self as ModIntBase>::pow(self, n)
}
#[inline]
pub fn inv(self) -> Self {
Self::inv_for_non_prime_modulus(self)
}
}
impl<I: Id> ModIntBase for DynamicModInt<I> {
#[inline]
fn modulus() -> u32 {
Self::modulus()
}
#[inline]
fn raw(val: u32) -> Self {
Self::raw(val)
}
#[inline]
fn val(self) -> u32 {
self.val()
}
#[inline]
fn inv(self) -> Self {
self.inv()
}
}
pub trait Id: 'static + Copy + Eq {
// TODO: Make `internal_math::Barret` `Copy`.
fn companion_barrett() -> &'static LocalKey<RefCell<Barrett>>;
}
#[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash, Debug)]
pub enum DefaultId {}
impl Id for DefaultId {
fn companion_barrett() -> &'static LocalKey<RefCell<Barrett>> {
thread_local! {
static BARRETT: RefCell<Barrett> = RefCell::default();
}
&BARRETT
}
}
pub struct Barrett(internal_math::Barrett);
impl Barrett {
#[inline]
pub fn new(m: u32) -> Self {
Self(internal_math::Barrett::new(m))
}
#[inline]
fn umod(&self) -> u32 {
self.0.umod()
}
#[inline]
fn mul(&self, a: u32, b: u32) -> u32 {
self.0.mul(a, b)
}
}
impl Default for Barrett {
#[inline]
fn default() -> Self {
Self(internal_math::Barrett::new(998_244_353))
}
}
pub trait ModIntBase:
Default
+ FromStr
+ From<i8>
+ From<i16>
+ From<i32>
+ From<i64>
+ From<i128>
+ From<u8>
+ From<u16>
+ From<u32>
+ From<u64>
+ From<u128>
+ Copy
+ Eq
+ Hash
+ fmt::Display
+ fmt::Debug
+ Neg<Output = Self>
+ Add<Output = Self>
+ Sub<Output = Self>
+ Mul<Output = Self>
+ Div<Output = Self>
+ AddAssign
+ SubAssign
+ MulAssign
+ DivAssign
{
fn modulus() -> u32;
fn raw(val: u32) -> Self;
fn val(self) -> u32;
fn inv(self) -> Self;
#[inline]
fn new<T: RemEuclidU32>(val: T) -> Self {
Self::raw(val.rem_euclid_u32(Self::modulus()))
}
#[inline]
fn pow(self, mut n: u64) -> Self {
let mut x = self;
let mut r = Self::raw(1);
while n > 0 {
if n & 1 == 1 {
r *= x;
}
x *= x;
n >>= 1;
}
r
}
}
pub trait RemEuclidU32 {
fn rem_euclid_u32(self, modulus: u32) -> u32;
}
macro_rules! impl_rem_euclid_u32_for_small_signed {
($($ty:tt),*) => {
$(
impl RemEuclidU32 for $ty {
#[inline]
fn rem_euclid_u32(self, modulus: u32) -> u32 {
(self as i64).rem_euclid(i64::from(modulus)) as _
}
}
)*
}
}
impl_rem_euclid_u32_for_small_signed!(i8, i16, i32, i64, isize);
impl RemEuclidU32 for i128 {
#[inline]
fn rem_euclid_u32(self, modulus: u32) -> u32 {
self.rem_euclid(i128::from(modulus)) as _
}
}
macro_rules! impl_rem_euclid_u32_for_small_unsigned {
($($ty:tt),*) => {
$(
impl RemEuclidU32 for $ty {
#[inline]
fn rem_euclid_u32(self, modulus: u32) -> u32 {
self as u32 % modulus
}
}
)*
}
}
macro_rules! impl_rem_euclid_u32_for_large_unsigned {
($($ty:tt),*) => {
$(
impl RemEuclidU32 for $ty {
#[inline]
fn rem_euclid_u32(self, modulus: u32) -> u32 {
(self % (modulus as $ty)) as _
}
}
)*
}
}
impl_rem_euclid_u32_for_small_unsigned!(u8, u16, u32);
impl_rem_euclid_u32_for_large_unsigned!(u64, u128);
#[cfg(target_pointer_width = "32")]
impl_rem_euclid_u32_for_small_unsigned!(usize);
#[cfg(target_pointer_width = "64")]
impl_rem_euclid_u32_for_large_unsigned!(usize);
trait InternalImplementations: ModIntBase {
#[inline]
fn inv_for_non_prime_modulus(this: Self) -> Self {
let (gcd, x) = internal_math::inv_gcd(this.val().into(), Self::modulus().into());
if gcd != 1 {
panic!("the multiplicative inverse does not exist");
}
Self::new(x)
}
#[inline]
fn default_impl() -> Self {
Self::raw(0)
}
#[inline]
fn from_str_impl(s: &str) -> Result<Self, Infallible> {
Ok(s.parse::<i64>()
.map(Self::new)
.unwrap_or_else(|_| todo!("parsing as an arbitrary precision integer?")))
}
#[inline]
fn hash_impl(this: &Self, state: &mut impl Hasher) {
this.val().hash(state)
}
#[inline]
fn display_impl(this: &Self, f: &mut fmt::Formatter) -> fmt::Result {
fmt::Display::fmt(&this.val(), f)
}
#[inline]
fn debug_impl(this: &Self, f: &mut fmt::Formatter) -> fmt::Result {
fmt::Debug::fmt(&this.val(), f)
}
#[inline]
fn neg_impl(this: Self) -> Self {
Self::sub_impl(Self::raw(0), this)
}
#[inline]
fn add_impl(lhs: Self, rhs: Self) -> Self {
let modulus = Self::modulus();
let mut val = lhs.val() + rhs.val();
if val >= modulus {
val -= modulus;
}
Self::raw(val)
}
#[inline]
fn sub_impl(lhs: Self, rhs: Self) -> Self {
let modulus = Self::modulus();
let mut val = lhs.val().wrapping_sub(rhs.val());
if val >= modulus {
val = val.wrapping_add(modulus)
}
Self::raw(val)
}
fn mul_impl(lhs: Self, rhs: Self) -> Self;
#[inline]
fn div_impl(lhs: Self, rhs: Self) -> Self {
Self::mul_impl(lhs, rhs.inv())
}
}
impl<M: Modulus> InternalImplementations for StaticModInt<M> {
#[inline]
fn mul_impl(lhs: Self, rhs: Self) -> Self {
Self::raw((u64::from(lhs.val()) * u64::from(rhs.val()) % u64::from(M::VALUE)) as u32)
}
}
impl<I: Id> InternalImplementations for DynamicModInt<I> {
#[inline]
fn mul_impl(lhs: Self, rhs: Self) -> Self {
I::companion_barrett().with(|bt| Self::raw(bt.borrow().mul(lhs.val, rhs.val)))
}
}
macro_rules! impl_basic_traits {
() => {};
(impl <$generic_param:ident : $generic_param_bound:tt> _ for $self:ty; $($rest:tt)*) => {
impl <$generic_param: $generic_param_bound> Default for $self {
#[inline]
fn default() -> Self {
Self::default_impl()
}
}
impl <$generic_param: $generic_param_bound> FromStr for $self {
type Err = Infallible;
#[inline]
fn from_str(s: &str) -> Result<Self, Infallible> {
Self::from_str_impl(s)
}
}
impl<$generic_param: $generic_param_bound, V: RemEuclidU32> From<V> for $self {
#[inline]
fn from(from: V) -> Self {
Self::new(from)
}
}
#[allow(clippy::derive_hash_xor_eq)]
impl<$generic_param: $generic_param_bound> Hash for $self {
#[inline]
fn hash<H: Hasher>(&self, state: &mut H) {
Self::hash_impl(self, state)
}
}
impl<$generic_param: $generic_param_bound> fmt::Display for $self {
#[inline]
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
Self::display_impl(self, f)
}
}
impl<$generic_param: $generic_param_bound> fmt::Debug for $self {
#[inline]
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
Self::debug_impl(self, f)
}
}
impl<$generic_param: $generic_param_bound> Neg for $self {
type Output = $self;
#[inline]
fn neg(self) -> $self {
Self::neg_impl(self)
}
}
impl<$generic_param: $generic_param_bound> Neg for &'_ $self {
type Output = $self;
#[inline]
fn neg(self) -> $self {
<$self>::neg_impl(*self)
}
}
impl_basic_traits!($($rest)*);
};
}
impl_basic_traits! {
impl <M: Modulus> _ for StaticModInt<M> ;
impl <I: Id > _ for DynamicModInt<I>;
}
macro_rules! impl_bin_ops {
() => {};
(for<$generic_param:ident : $generic_param_bound:tt> <$lhs_ty:ty> ~ <$rhs_ty:ty> -> $output:ty { { $lhs_body:expr } ~ { $rhs_body:expr } } $($rest:tt)*) => {
impl <$generic_param: $generic_param_bound> Add<$rhs_ty> for $lhs_ty {
type Output = $output;
#[inline]
fn add(self, rhs: $rhs_ty) -> $output {
<$output>::add_impl(apply($lhs_body, self), apply($rhs_body, rhs))
}
}
impl <$generic_param: $generic_param_bound> Sub<$rhs_ty> for $lhs_ty {
type Output = $output;
#[inline]
fn sub(self, rhs: $rhs_ty) -> $output {
<$output>::sub_impl(apply($lhs_body, self), apply($rhs_body, rhs))
}
}
impl <$generic_param: $generic_param_bound> Mul<$rhs_ty> for $lhs_ty {
type Output = $output;
#[inline]
fn mul(self, rhs: $rhs_ty) -> $output {
<$output>::mul_impl(apply($lhs_body, self), apply($rhs_body, rhs))
}
}
impl <$generic_param: $generic_param_bound> Div<$rhs_ty> for $lhs_ty {
type Output = $output;
#[inline]
fn div(self, rhs: $rhs_ty) -> $output {
<$output>::div_impl(apply($lhs_body, self), apply($rhs_body, rhs))
}
}
impl_bin_ops!($($rest)*);
};
}
macro_rules! impl_assign_ops {
() => {};
(for<$generic_param:ident : $generic_param_bound:tt> <$lhs_ty:ty> ~= <$rhs_ty:ty> { _ ~= { $rhs_body:expr } } $($rest:tt)*) => {
impl <$generic_param: $generic_param_bound> AddAssign<$rhs_ty> for $lhs_ty {
#[inline]
fn add_assign(&mut self, rhs: $rhs_ty) {
*self = *self + apply($rhs_body, rhs);
}
}
impl <$generic_param: $generic_param_bound> SubAssign<$rhs_ty> for $lhs_ty {
#[inline]
fn sub_assign(&mut self, rhs: $rhs_ty) {
*self = *self - apply($rhs_body, rhs);
}
}
impl <$generic_param: $generic_param_bound> MulAssign<$rhs_ty> for $lhs_ty {
#[inline]
fn mul_assign(&mut self, rhs: $rhs_ty) {
*self = *self * apply($rhs_body, rhs);
}
}
impl <$generic_param: $generic_param_bound> DivAssign<$rhs_ty> for $lhs_ty {
#[inline]
fn div_assign(&mut self, rhs: $rhs_ty) {
*self = *self / apply($rhs_body, rhs);
}
}
impl_assign_ops!($($rest)*);
};
}
#[inline]
fn apply<F: FnOnce(X) -> O, X, O>(f: F, x: X) -> O {
f(x)
}
impl_bin_ops! {
for<M: Modulus> <StaticModInt<M> > ~ <StaticModInt<M> > -> StaticModInt<M> { { |x| x } ~ { |x| x } }
for<M: Modulus> <StaticModInt<M> > ~ <&'_ StaticModInt<M> > -> StaticModInt<M> { { |x| x } ~ { |&x| x } }
for<M: Modulus> <&'_ StaticModInt<M> > ~ <StaticModInt<M> > -> StaticModInt<M> { { |&x| x } ~ { |x| x } }
for<M: Modulus> <&'_ StaticModInt<M> > ~ <&'_ StaticModInt<M> > -> StaticModInt<M> { { |&x| x } ~ { |&x| x } }
for<I: Id > <DynamicModInt<I> > ~ <DynamicModInt<I> > -> DynamicModInt<I> { { |x| x } ~ { |x| x } }
for<I: Id > <DynamicModInt<I> > ~ <&'_ DynamicModInt<I>> -> DynamicModInt<I> { { |x| x } ~ { |&x| x } }
for<I: Id > <&'_ DynamicModInt<I>> ~ <DynamicModInt<I> > -> DynamicModInt<I> { { |&x| x } ~ { |x| x } }
for<I: Id > <&'_ DynamicModInt<I>> ~ <&'_ DynamicModInt<I>> -> DynamicModInt<I> { { |&x| x } ~ { |&x| x } }
}
impl_assign_ops! {
for<M: Modulus> <StaticModInt<M> > ~= <StaticModInt<M> > { _ ~= { |x| x } }
for<M: Modulus> <StaticModInt<M> > ~= <&'_ StaticModInt<M> > { _ ~= { |&x| x } }
for<I: Id > <DynamicModInt<I>> ~= <DynamicModInt<I> > { _ ~= { |x| x } }
for<I: Id > <DynamicModInt<I>> ~= <&'_ DynamicModInt<I>> { _ ~= { |&x| x } }
}
macro_rules! impl_folding {
() => {};
(impl<$generic_param:ident : $generic_param_bound:tt> $trait:ident<_> for $self:ty { fn $method:ident(_) -> _ { _($unit:expr, $op:expr) } } $($rest:tt)*) => {
impl<$generic_param: $generic_param_bound> $trait<Self> for $self {
#[inline]
fn $method<S>(iter: S) -> Self
where
S: Iterator<Item = Self>,
{
iter.fold($unit, $op)
}
}
impl<'a, $generic_param: $generic_param_bound> $trait<&'a Self> for $self {
#[inline]
fn $method<S>(iter: S) -> Self
where
S: Iterator<Item = &'a Self>,
{
iter.fold($unit, $op)
}
}
impl_folding!($($rest)*);
};
}
impl_folding! {
impl<M: Modulus> Sum<_> for StaticModInt<M> { fn sum(_) -> _ { _(Self::raw(0), Add::add) } }
impl<M: Modulus> Product<_> for StaticModInt<M> { fn product(_) -> _ { _(Self::raw(1), Mul::mul) } }
impl<I: Id > Sum<_> for DynamicModInt<I> { fn sum(_) -> _ { _(Self::raw(0), Add::add) } }
impl<I: Id > Product<_> for DynamicModInt<I> { fn product(_) -> _ { _(Self::raw(1), Mul::mul) } }
}
#[cfg(test)]
mod tests {
use crate::modint::ModInt1000000007;
#[test]
fn static_modint_new() {
assert_eq!(0, ModInt1000000007::new(0u32).val);
assert_eq!(1, ModInt1000000007::new(1u32).val);
assert_eq!(1, ModInt1000000007::new(1_000_000_008u32).val);
assert_eq!(0, ModInt1000000007::new(0u64).val);
assert_eq!(1, ModInt1000000007::new(1u64).val);
assert_eq!(1, ModInt1000000007::new(1_000_000_008u64).val);
assert_eq!(0, ModInt1000000007::new(0usize).val);
assert_eq!(1, ModInt1000000007::new(1usize).val);
assert_eq!(1, ModInt1000000007::new(1_000_000_008usize).val);
assert_eq!(0, ModInt1000000007::new(0i64).val);
assert_eq!(1, ModInt1000000007::new(1i64).val);
assert_eq!(1, ModInt1000000007::new(1_000_000_008i64).val);
assert_eq!(1_000_000_006, ModInt1000000007::new(-1i64).val);
}
#[test]
fn static_modint_add() {
fn add(lhs: u32, rhs: u32) -> u32 {
(ModInt1000000007::new(lhs) + ModInt1000000007::new(rhs)).val
}
assert_eq!(2, add(1, 1));
assert_eq!(1, add(1_000_000_006, 2));
}
#[test]
fn static_modint_sub() {
fn sub(lhs: u32, rhs: u32) -> u32 {
(ModInt1000000007::new(lhs) - ModInt1000000007::new(rhs)).val
}
assert_eq!(1, sub(2, 1));
assert_eq!(1_000_000_006, sub(0, 1));
}
#[test]
fn static_modint_mul() {
fn mul(lhs: u32, rhs: u32) -> u32 {
(ModInt1000000007::new(lhs) * ModInt1000000007::new(rhs)).val
}
assert_eq!(1, mul(1, 1));
assert_eq!(4, mul(2, 2));
assert_eq!(999_999_937, mul(100_000, 100_000));
}
#[test]
fn static_modint_prime_div() {
fn div(lhs: u32, rhs: u32) -> u32 {
(ModInt1000000007::new(lhs) / ModInt1000000007::new(rhs)).val
}
assert_eq!(0, div(0, 1));
assert_eq!(1, div(1, 1));
assert_eq!(1, div(2, 2));
assert_eq!(23_809_524, div(1, 42));
}
#[test]
fn static_modint_sum() {
fn sum(values: &[i64]) -> ModInt1000000007 {
values.iter().copied().map(ModInt1000000007::new).sum()
}
assert_eq!(ModInt1000000007::new(-3), sum(&[-1, 2, -3, 4, -5]));
}
#[test]
fn static_modint_product() {
fn product(values: &[i64]) -> ModInt1000000007 {
values.iter().copied().map(ModInt1000000007::new).product()
}
assert_eq!(ModInt1000000007::new(-120), product(&[-1, 2, -3, 4, -5]));
}
}
}
use convolution::*;
use modint::*;