結果
| 問題 | No.1750 ラムドスウイルスの感染拡大-hard |
| ユーザー |
 manta1130
|
| 提出日時 | 2021-11-19 22:03:00 |
| 言語 | Rust (1.77.0) |
| 結果 |
AC
|
| 実行時間 | 302 ms / 2,000 ms |
| コード長 | 35,734 bytes |
| コンパイル時間 | 1,886 ms |
| コンパイル使用メモリ | 181,752 KB |
| 実行使用メモリ | 4,384 KB |
| 最終ジャッジ日時 | 2023-08-30 08:31:02 |
| 合計ジャッジ時間 | 6,369 ms |
|
ジャッジサーバーID （参考情報） |
judge13 / judge15 |
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
4,380 KB |
| testcase_01 | AC | 1 ms
4,384 KB |
| testcase_02 | AC | 1 ms
4,380 KB |
| testcase_03 | AC | 1 ms
4,376 KB |
| testcase_04 | AC | 8 ms
4,380 KB |
| testcase_05 | AC | 1 ms
4,380 KB |
| testcase_06 | AC | 1 ms
4,376 KB |
| testcase_07 | AC | 1 ms
4,376 KB |
| testcase_08 | AC | 53 ms
4,380 KB |
| testcase_09 | AC | 53 ms
4,380 KB |
| testcase_10 | AC | 53 ms
4,380 KB |
| testcase_11 | AC | 40 ms
4,380 KB |
| testcase_12 | AC | 56 ms
4,380 KB |
| testcase_13 | AC | 53 ms
4,380 KB |
| testcase_14 | AC | 279 ms
4,380 KB |
| testcase_15 | AC | 284 ms
4,376 KB |
| testcase_16 | AC | 288 ms
4,380 KB |
| testcase_17 | AC | 293 ms
4,380 KB |
| testcase_18 | AC | 302 ms
4,376 KB |
| testcase_19 | AC | 288 ms
4,380 KB |
| testcase_20 | AC | 202 ms
4,380 KB |
| testcase_21 | AC | 225 ms
4,380 KB |
| testcase_22 | AC | 40 ms
4,380 KB |
| testcase_23 | AC | 276 ms
4,380 KB |
| testcase_24 | AC | 30 ms
4,376 KB |
| testcase_25 | AC | 73 ms
4,384 KB |
| testcase_26 | AC | 24 ms
4,376 KB |
| testcase_27 | AC | 1 ms
4,376 KB |
| testcase_28 | AC | 3 ms
4,380 KB |
| testcase_29 | AC | 1 ms
4,380 KB |
| testcase_30 | AC | 39 ms
4,380 KB |
| testcase_31 | AC | 36 ms
4,376 KB |
| testcase_32 | AC | 35 ms
4,380 KB |
| testcase_33 | AC | 34 ms
4,380 KB |
コンパイルメッセージ
warning: fields `sum_e` and `sum_ie` are never read
--> Main.rs:735:20
|
734 | pub struct ButterflyCache<M> {
| -------------- fields in this struct
735 | pub(crate) sum_e: Vec<StaticModInt<M>>,
| ^^^^^
736 | pub(crate) sum_ie: Vec<StaticModInt<M>>,
| ^^^^^^
|
= note: `#[warn(dead_code)]` on by default
warning: 1 warning emitted
ソースコード
#[allow(unused_imports)]
use std::io::{stdout, BufWriter, Write};
fn main() {
let out = stdout();
let mut out = BufWriter::new(out.lock());
inputv! {
n:usize,m:usize,t:u64,
}
let mut graph = Matrix::new(n, n, ModInt998244353::new(0));
let mut v = Matrix::new(n, 1, ModInt998244353::new(0));
v[0][0] += 1;
for _ in 0..m {
inputv! {
a:usize,b:usize,
}
graph[a][b] += 1;
graph[b][a] += 1;
}
let graph = graph.pow(t, ModInt998244353::new(1));
let ans = &graph * &v;
writeln!(out, "{}", ans[0][0]).unwrap();
}
//https://github.com/rust-lang-ja/ac-library-rs
//https://github.com/manta1130/competitive-template-rs
use input::*;
use matrix::*;
use modint::*;
pub mod input {
use std::cell::RefCell;
use std::io;
pub const SPLIT_DELIMITER: char = ' ';
pub use std::io::prelude::*;
thread_local! {
pub static INPUT_BUFFER:RefCell<std::collections::VecDeque<String>>=RefCell::new(std::collections::VecDeque::new());
}
#[macro_export]
macro_rules! input_internal {
($x:ident : $t:ty) => {
INPUT_BUFFER.with(|p| {
if p.borrow().len() == 0 {
let temp_str = input_line_str();
let mut split_result_iter = temp_str
.split(SPLIT_DELIMITER)
.map(|q| q.to_string())
.collect::<std::collections::VecDeque<_>>();
p.borrow_mut().append(&mut split_result_iter)
}
});
let mut buf_split_result = String::new();
INPUT_BUFFER.with(|p| buf_split_result = p.borrow_mut().pop_front().unwrap());
let $x: $t = buf_split_result.parse().unwrap();
};
(mut $x:ident : $t:ty) => {
INPUT_BUFFER.with(|p| {
if p.borrow().len() == 0 {
let temp_str = input_line_str();
let mut split_result_iter = temp_str
.split(SPLIT_DELIMITER)
.map(|q| q.to_string())
.collect::<std::collections::VecDeque<_>>();
p.borrow_mut().append(&mut split_result_iter)
}
});
let mut buf_split_result = String::new();
INPUT_BUFFER.with(|p| buf_split_result = p.borrow_mut().pop_front().unwrap());
let mut $x: $t = buf_split_result.parse().unwrap();
};
}
pub fn input_buffer_is_empty() -> bool {
let mut empty = false;
INPUT_BUFFER.with(|p| {
if p.borrow().len() == 0 {
empty = true;
}
});
empty
}
#[macro_export]
macro_rules! inputv {
($i:ident : $t:ty) => {
input_internal!{$i : $t}
};
(mut $i:ident : $t:ty) => {
input_internal!{mut $i : $t}
};
($i:ident : $t:ty $(,)*) => {
input_internal!{$i : $t}
};
(mut $i:ident : $t:ty $(,)*) => {
input_internal!{mut $i : $t}
};
(mut $i:ident : $t:ty,$($q:tt)*) => {
input_internal!{mut $i : $t}
inputv!{$($q)*}
};
($i:ident : $t:ty,$($q:tt)*) => {
input_internal!{$i : $t}
inputv!{$($q)*}
};
}
pub fn input_all() {
INPUT_BUFFER.with(|p| {
if p.borrow().len() == 0 {
let mut temp_str = String::new();
std::io::stdin().read_to_string(&mut temp_str).unwrap();
let mut split_result_iter = temp_str
.split_whitespace()
.map(|q| q.to_string())
.collect::<std::collections::VecDeque<_>>();
p.borrow_mut().append(&mut split_result_iter)
}
});
}
pub fn input_line_str() -> String {
let mut s = String::new();
io::stdin().read_line(&mut s).unwrap();
s.trim().to_string()
}
#[allow(clippy::match_wild_err_arm)]
pub fn input_vector<T>() -> Vec<T>
where
T: std::str::FromStr,
{
let mut v: Vec<T> = Vec::new();
let s = input_line_str();
let split_result = s.split(SPLIT_DELIMITER);
for z in split_result {
let buf = match z.parse() {
Ok(r) => r,
Err(_) => panic!("Parse Error",),
};
v.push(buf);
}
v
}
#[allow(clippy::match_wild_err_arm)]
pub fn input_vector_row<T>(n: usize) -> Vec<T>
where
T: std::str::FromStr,
{
let mut v = Vec::with_capacity(n);
for _ in 0..n {
let buf = match input_line_str().parse() {
Ok(r) => r,
Err(_) => panic!("Parse Error",),
};
v.push(buf);
}
v
}
pub trait ToCharVec {
fn to_charvec(&self) -> Vec<char>;
}
impl ToCharVec for String {
fn to_charvec(&self) -> Vec<char> {
self.to_string().chars().collect::<Vec<_>>()
}
}
}
pub mod internal_math {
#![allow(dead_code)]
use std::mem::swap;
/* const */
pub(crate) fn safe_mod(mut x: i64, m: i64) -> i64 {
x %= m;
if x < 0 {
x += m;
}
x
}
pub(crate) struct Barrett {
pub(crate) _m: u32,
pub(crate) im: u64,
}
impl Barrett {
pub(crate) fn new(m: u32) -> Barrett {
Barrett {
_m: m,
im: (-1i64 as u64 / m as u64).wrapping_add(1),
}
}
pub(crate) fn umod(&self) -> u32 {
self._m
}
#[allow(clippy::many_single_char_names)]
pub(crate) fn mul(&self, a: u32, b: u32) -> u32 {
mul_mod(a, b, self._m, self.im)
}
}
#[allow(clippy::many_single_char_names)]
pub(crate) fn mul_mod(a: u32, b: u32, m: u32, im: u64) -> u32 {
let mut z = a as u64;
z *= b as u64;
let x = (((z as u128) * (im as u128)) >> 64) as u64;
let mut v = z.wrapping_sub(x.wrapping_mul(m as u64)) as u32;
if m <= v {
v = v.wrapping_add(m);
}
v
}
/* 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
}
/* 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
}
/* 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);
}
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
swap(&mut s, &mut t);
swap(&mut m0, &mut m1);
}
if m0 < 0 {
m0 += b / s;
}
(s, m0)
}
/* 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;
}
}
}
pub mod matrix {
use std::fmt;
use std::ops::{Add, AddAssign, Deref, DerefMut, Div, Mul, MulAssign, Sub, SubAssign};
#[derive(Clone, PartialEq, Debug)]
pub struct Matrix<T> {
v: Vec<Vec<T>>,
}
impl<T> Matrix<T>
where
T: Copy,
{
pub fn new(h: usize, w: usize, init: T) -> Matrix<T> {
Matrix {
v: vec![vec![init; w]; h],
}
}
pub fn from(v: Vec<Vec<T>>) -> Matrix<T> {
Matrix { v }
}
pub fn h(&self) -> usize {
self.v.len()
}
pub fn w(&self) -> usize {
self.v[0].len()
}
pub fn chrow(&mut self, a: usize, b: usize) {
self.v.swap(a, b);
}
pub fn chcol(&mut self, a: usize, b: usize) {
for i in 0..self.v.len() {
self.v[i].swap(a, b);
}
}
}
impl<T> fmt::Display for Matrix<T>
where
T: fmt::Debug,
{
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
let mut first = true;
for l in &self.v {
if !first {
writeln!(f).unwrap();
}
first = false;
for k in l {
write!(f, "{:?} ", k).unwrap();
}
}
write!(f, "")
}
}
impl<T> Matrix<T>
where
T: Copy + AddAssign + Sub<Output = T> + Default,
{
pub fn t(&self) -> Matrix<T> {
let mut r = Matrix::new(self.w(), self.h(), T::default());
for i in 0..self.h() {
for j in 0..self.w() {
r[j][i] = self[i][j];
}
}
r
}
}
impl<T> Matrix<T>
where
T: Copy
+ Add<Output = T>
+ Sub<Output = T>
+ MulAssign
+ Mul<Output = T>
+ AddAssign
+ Div<Output = T>
+ Default,
{
pub fn pow(&self, mut p: u64, init: T) -> Matrix<T> {
let mut r = Matrix::new(self.h(), self.w(), T::default());
for i in 0..r.len() {
r[i][i] = init;
}
let mut buf = self.clone();
while p > 0 {
if p & 1 == 1 {
r = &r * &buf;
}
buf = &buf * &buf;
p >>= 1;
}
r
}
}
impl<T> Add for &Matrix<T>
where
T: Copy + Add<Output = T> + Sub<Output = T> + MulAssign + Default,
{
type Output = Matrix<T>;
fn add(self, other: &Matrix<T>) -> Matrix<T> {
assert_eq!(self.h(), other.h());
assert_eq!(self.w(), other.w());
let mut r = Matrix::new(self.h(), self.w(), T::default());
for i in 0..self.h() {
for j in 0..self.w() {
r[i][j] = self[i][j] + other[i][j];
}
}
r
}
}
impl<T> Add<T> for &Matrix<T>
where
T: Copy + AddAssign,
{
type Output = Matrix<T>;
fn add(self, other: T) -> Matrix<T> {
let mut r = self.clone();
for i in 0..self.h() {
for j in 0..self.w() {
r[i][j] += other;
}
}
r
}
}
impl<T> AddAssign<T> for Matrix<T>
where
T: Copy + AddAssign,
{
fn add_assign(&mut self, other: T) {
for i in 0..self.h() {
for j in 0..self.w() {
self[i][j] += other;
}
}
}
}
impl<T> Sub for &Matrix<T>
where
T: Copy + Sub<Output = T> + Default,
{
type Output = Matrix<T>;
fn sub(self, other: &Matrix<T>) -> Matrix<T> {
assert_eq!(self.h(), other.h());
assert_eq!(self.w(), other.w());
let mut r = Matrix::new(self.h(), self.w(), T::default());
for i in 0..self.h() {
for j in 0..self.w() {
r[i][j] = self[i][j] - other[i][j];
}
}
r
}
}
impl<T> Sub<T> for &Matrix<T>
where
T: Copy + SubAssign,
{
type Output = Matrix<T>;
fn sub(self, other: T) -> Matrix<T> {
let mut r = self.clone();
for i in 0..self.h() {
for j in 0..self.w() {
r[i][j] -= other;
}
}
r
}
}
impl<T> SubAssign<T> for Matrix<T>
where
T: Copy + SubAssign,
{
fn sub_assign(&mut self, other: T) {
for i in 0..self.h() {
for j in 0..self.w() {
self[i][j] -= other;
}
}
}
}
impl<T> Mul for &Matrix<T>
where
T: Copy + Sub<Output = T> + AddAssign + Mul<Output = T> + Default,
{
type Output = Matrix<T>;
fn mul(self, other: &Matrix<T>) -> Matrix<T> {
assert_eq!(self.w(), other.h());
let mut r = Matrix::new(self.h(), other.w(), T::default());
for i in 0..r.h() {
for j in 0..r.w() {
for q in 0..self.w() {
r[i][j] += self[i][q] * other[q][j];
}
}
}
r
}
}
impl<T> Mul<T> for &Matrix<T>
where
T: Copy + MulAssign,
{
type Output = Matrix<T>;
fn mul(self, other: T) -> Matrix<T> {
let mut r = self.clone();
for i in 0..self.h() {
for j in 0..self.w() {
r[i][j] *= other;
}
}
r
}
}
impl<T> MulAssign<T> for Matrix<T>
where
T: Copy + MulAssign,
{
fn mul_assign(&mut self, other: T) {
for i in 0..self.h() {
for j in 0..self.w() {
self[i][j] *= other;
}
}
}
}
impl<T> Deref for Matrix<T> {
type Target = Vec<Vec<T>>;
fn deref(&self) -> &Vec<Vec<T>> {
&self.v
}
}
impl<T> DerefMut for Matrix<T> {
fn deref_mut(&mut self) -> &mut Vec<Vec<T>> {
&mut self.v
}
}
}
pub mod modint {
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,
sync::atomic::{self, AtomicU32, AtomicU64},
thread::LocalKey,
};
pub type ModInt1000000007 = StaticModInt<Mod1000000007>;
pub type ModInt998244353 = StaticModInt<Mod998244353>;
pub type ModInt = DynamicModInt<DefaultId>;
#[derive(Copy, Clone, Eq, PartialEq)]
#[repr(transparent)]
pub struct StaticModInt<M> {
val: u32,
phantom: PhantomData<fn() -> M>,
}
impl<M: Modulus> StaticModInt<M> {
#[inline(always)]
pub fn modulus() -> u32 {
M::VALUE
}
#[inline]
pub fn new<T: RemEuclidU32>(val: T) -> Self {
Self::raw(val.rem_euclid_u32(M::VALUE))
}
#[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 {
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().umod()
}
#[inline]
pub fn set_modulus(modulus: u32) {
if modulus == 0 {
panic!("the modulus must not be 0");
}
I::companion_barrett().update(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 {
fn companion_barrett() -> &'static Barrett;
}
#[derive(Copy, Clone, Ord, PartialOrd, Eq, PartialEq, Hash, Debug)]
pub enum DefaultId {}
impl Id for DefaultId {
fn companion_barrett() -> &'static Barrett {
static BARRETT: Barrett = Barrett::default();
&BARRETT
}
}
pub struct Barrett {
m: AtomicU32,
im: AtomicU64,
}
impl Barrett {
#[inline]
pub const fn new(m: u32) -> Self {
Self {
m: AtomicU32::new(m),
im: AtomicU64::new((-1i64 as u64 / m as u64).wrapping_add(1)),
}
}
#[inline]
const fn default() -> Self {
Self::new(998_244_353)
}
#[inline]
fn update(&self, m: u32) {
let im = (-1i64 as u64 / m as u64).wrapping_add(1);
self.m.store(m, atomic::Ordering::SeqCst);
self.im.store(im, atomic::Ordering::SeqCst);
}
#[inline]
fn umod(&self) -> u32 {
self.m.load(atomic::Ordering::SeqCst)
}
#[inline]
fn mul(&self, a: u32, b: u32) -> u32 {
let m = self.m.load(atomic::Ordering::SeqCst);
let im = self.im.load(atomic::Ordering::SeqCst);
internal_math::mul_mod(a, b, m, im)
}
}
impl Default for Barrett {
#[inline]
fn default() -> Self {
Self::default()
}
}
pub trait ModIntBase:
Default
+ FromStr
+ From<i8>
+ From<i16>
+ From<i32>
+ From<i64>
+ From<i128>
+ From<isize>
+ From<u8>
+ From<u16>
+ From<u32>
+ From<u64>
+ From<u128>
+ From<usize>
+ 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 {
Self::raw(I::companion_barrett().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 } }
for<M: Modulus, T: RemEuclidU32> <StaticModInt<M> > ~ <T> -> StaticModInt<M> { { |x| x } ~ { StaticModInt::<M>::new } }
for<I: Id , T: RemEuclidU32> <DynamicModInt<I> > ~ <T> -> DynamicModInt<I> { { |x| x } ~ { DynamicModInt::<I>::new } }
}
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 } }
for<M: Modulus, T: RemEuclidU32> <StaticModInt<M> > ~= <T> { _ ~= { StaticModInt::<M>::new } }
for<I: Id, T: RemEuclidU32> <DynamicModInt<I>> ~= <T> { _ ~= { DynamicModInt::<I>::new } }
}
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) } }
}
}