結果
| 問題 | No.1507 Road Blocked |
| ユーザー |
 to-omer
|
| 提出日時 | 2021-05-14 22:29:51 |
| 言語 | Rust (1.77.0 + proconio) |
| 結果 |
AC
|
| 実行時間 | 55 ms / 2,000 ms |
| コード長 | 42,561 bytes |
| コンパイル時間 | 12,255 ms |
| コンパイル使用メモリ | 378,076 KB |
| 実行使用メモリ | 39,552 KB |
| 最終ジャッジ日時 | 2024-10-02 02:10:16 |
| 合計ジャッジ時間 | 15,024 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
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
5,248 KB |
| testcase_01 | AC | 1 ms
5,248 KB |
| testcase_02 | AC | 1 ms
5,248 KB |
| testcase_03 | AC | 48 ms
39,552 KB |
| testcase_04 | AC | 55 ms
13,312 KB |
| testcase_05 | AC | 54 ms
13,312 KB |
| testcase_06 | AC | 40 ms
13,288 KB |
| testcase_07 | AC | 39 ms
13,312 KB |
| testcase_08 | AC | 38 ms
13,312 KB |
| testcase_09 | AC | 37 ms
13,440 KB |
| testcase_10 | AC | 37 ms
13,292 KB |
| testcase_11 | AC | 38 ms
13,184 KB |
| testcase_12 | AC | 38 ms
13,312 KB |
| testcase_13 | AC | 37 ms
13,312 KB |
| testcase_14 | AC | 39 ms
13,312 KB |
| testcase_15 | AC | 39 ms
13,184 KB |
| testcase_16 | AC | 39 ms
13,312 KB |
| testcase_17 | AC | 40 ms
13,312 KB |
| testcase_18 | AC | 37 ms
13,304 KB |
| testcase_19 | AC | 40 ms
13,312 KB |
| testcase_20 | AC | 39 ms
13,312 KB |
| testcase_21 | AC | 39 ms
13,312 KB |
| testcase_22 | AC | 42 ms
13,304 KB |
| testcase_23 | AC | 39 ms
13,296 KB |
| testcase_24 | AC | 40 ms
13,184 KB |
| testcase_25 | AC | 42 ms
13,312 KB |
| testcase_26 | AC | 39 ms
13,312 KB |
| testcase_27 | AC | 38 ms
13,312 KB |
| testcase_28 | AC | 38 ms
13,312 KB |
| testcase_29 | AC | 38 ms
13,312 KB |
| testcase_30 | AC | 39 ms
13,312 KB |
| testcase_31 | AC | 38 ms
13,164 KB |
| testcase_32 | AC | 41 ms
13,312 KB |
ソースコード
fn main() {
#![allow(unused_imports, unused_macros)]
prepare_io!(_in_buf, scanner, _out);
macro_rules ! print { ($ ($ arg : tt) *) => (:: std :: write ! (_out , $ ($ arg) *) . expect ("io error")) }
macro_rules ! println { ($ ($ arg : tt) *) => (:: std :: writeln ! (_out , $ ($ arg) *) . expect ("io error")) }
scan!(scanner, n, (g, _): {TreeGraphScanner::<Usize1>::new(n)});
let r =
ReRooting::<(AdditiveOperation<usize>, AdditiveOperation<usize>), _>::new(&g, |d, _, o| {
(d.0 + d.1, d.1 + o.is_some() as usize)
});
let distsum = (0..n).map(|u| r.dp[u].0).sum::<usize>();
let ans = M::from(distsum) / (M::from(n - 1) * M::from(n) * M::from(n - 1));
println!("{}", M::one() - ans);
}
pub type M = mint_basic::MInt998244353;
#[macro_export]
macro_rules! prepare_io {
($ in_buf : ident , $ scanner : ident , $ out : ident) => {
use std::io::{stdout, BufWriter, Write as _};
let $in_buf = read_stdin_all_unchecked();
let mut $scanner = Scanner::new(&$in_buf);
let $out = stdout();
let mut $out = BufWriter::new($out.lock());
};
}
pub fn echo<T: std::fmt::Display>(
mut writer: impl std::io::Write,
iter: impl IntoIterator<Item = T>,
sep: impl std::fmt::Display,
) -> std::io::Result<()> {
let mut iter = iter.into_iter();
if let Some(item) = iter.next() {
write!(writer, "{}", item)?;
}
for item in iter {
write!(writer, "{}{}", sep, item)?;
}
writeln!(writer)
}
pub fn read_stdin_all_unchecked() -> String {
use std::io::Read as _;
let mut buf = Vec::new();
std::io::stdin().read_to_end(&mut buf).expect("io error");
unsafe { String::from_utf8_unchecked(buf) }
}
pub fn read_stdin_line() -> String {
let mut s = String::new();
std::io::stdin().read_line(&mut s).expect("io error");
s
}
pub use scanner_impls::{IterScan, MarkedIterScan, Scanner};
mod scanner_impls {
pub trait IterScan: Sized {
type Output;
fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output>;
}
pub trait MarkedIterScan: Sized {
type Output;
fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output>;
}
#[derive(Clone, Debug)]
pub struct Scanner<'a> {
iter: std::str::SplitAsciiWhitespace<'a>,
}
impl<'a> Scanner<'a> {
#[inline]
pub fn new(s: &'a str) -> Self {
let iter = s.split_ascii_whitespace();
Self { iter }
}
#[inline]
pub fn scan<T>(&mut self) -> <T as IterScan>::Output
where
T: IterScan,
{
<T as IterScan>::scan(&mut self.iter).expect("scan error")
}
#[inline]
pub fn mscan<T>(&mut self, marker: T) -> <T as MarkedIterScan>::Output
where
T: MarkedIterScan,
{
marker.mscan(&mut self.iter).expect("scan error")
}
#[inline]
pub fn scan_vec<T>(&mut self, size: usize) -> Vec<<T as IterScan>::Output>
where
T: IterScan,
{
(0..size)
.map(|_| <T as IterScan>::scan(&mut self.iter).expect("scan error"))
.collect()
}
#[inline]
pub fn iter<'b, T>(&'b mut self) -> ScannerIter<'a, 'b, T>
where
T: IterScan,
{
ScannerIter {
inner: self,
_marker: std::marker::PhantomData,
}
}
}
macro_rules ! iter_scan_impls { ($ ($ t : ty) *) => { $ (impl IterScan for $ t { type Output = Self ; # [inline] fn scan <'a , I : Iterator < Item = &'a str >> (iter : & mut I) -> Option < Self > { iter . next () ?. parse ::<$ t > () . ok () } }) * } ; }
iter_scan_impls ! (char u8 u16 u32 u64 usize i8 i16 i32 i64 isize f32 f64 u128 i128 String);
macro_rules ! iter_scan_tuple_impl { ($ ($ T : ident) *) => { impl <$ ($ T : IterScan) ,*> IterScan for ($ ($ T ,) *) { type Output = ($ (<$ T as IterScan >:: Output ,) *) ; # [inline] fn scan <'a , It : Iterator < Item = &'a str >> (_iter : & mut It) -> Option < Self :: Output > { Some (($ (<$ T as IterScan >:: scan (_iter) ?,) *)) } } } ; }
iter_scan_tuple_impl!();
iter_scan_tuple_impl!(A);
iter_scan_tuple_impl ! (A B);
iter_scan_tuple_impl ! (A B C);
iter_scan_tuple_impl ! (A B C D);
iter_scan_tuple_impl ! (A B C D E);
iter_scan_tuple_impl ! (A B C D E F);
iter_scan_tuple_impl ! (A B C D E F G);
iter_scan_tuple_impl ! (A B C D E F G H);
iter_scan_tuple_impl ! (A B C D E F G H I);
iter_scan_tuple_impl ! (A B C D E F G H I J);
iter_scan_tuple_impl ! (A B C D E F G H I J K);
pub struct ScannerIter<'a, 'b, T> {
inner: &'b mut Scanner<'a>,
_marker: std::marker::PhantomData<fn() -> T>,
}
impl<'a, 'b, T> Iterator for ScannerIter<'a, 'b, T>
where
T: IterScan,
{
type Item = <T as IterScan>::Output;
#[inline]
fn next(&mut self) -> Option<Self::Item> {
<T as IterScan>::scan(&mut self.inner.iter)
}
}
}
pub use marker_impls::{CharWithBase, Chars, CharsWithBase, Collect, SizedCollect, Usize1};
mod marker_impls {
use super::*;
use std::{
iter::{repeat_with, FromIterator},
marker::PhantomData,
};
#[derive(Debug, Copy, Clone)]
pub struct Usize1;
impl IterScan for Usize1 {
type Output = usize;
#[inline]
fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
<usize as IterScan>::scan(iter)?.checked_sub(1)
}
}
#[derive(Debug, Copy, Clone)]
pub struct CharWithBase(pub char);
impl MarkedIterScan for CharWithBase {
type Output = usize;
#[inline]
fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
Some((<char as IterScan>::scan(iter)? as u8 - self.0 as u8) as usize)
}
}
#[derive(Debug, Copy, Clone)]
pub struct Chars;
impl IterScan for Chars {
type Output = Vec<char>;
#[inline]
fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
Some(iter.next()?.chars().collect())
}
}
#[derive(Debug, Copy, Clone)]
pub struct CharsWithBase(pub char);
impl MarkedIterScan for CharsWithBase {
type Output = Vec<usize>;
#[inline]
fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
Some(
iter.next()?
.chars()
.map(|c| (c as u8 - self.0 as u8) as usize)
.collect(),
)
}
}
#[derive(Debug, Copy, Clone)]
pub struct Collect<T, B = Vec<<T as IterScan>::Output>>
where
T: IterScan,
B: FromIterator<<T as IterScan>::Output>,
{
size: usize,
_marker: PhantomData<fn() -> (T, B)>,
}
impl<T, B> Collect<T, B>
where
T: IterScan,
B: FromIterator<<T as IterScan>::Output>,
{
pub fn new(size: usize) -> Self {
Self {
size,
_marker: PhantomData,
}
}
}
impl<T, B> MarkedIterScan for Collect<T, B>
where
T: IterScan,
B: FromIterator<<T as IterScan>::Output>,
{
type Output = B;
#[inline]
fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
repeat_with(|| <T as IterScan>::scan(iter))
.take(self.size)
.collect()
}
}
#[derive(Debug, Copy, Clone)]
pub struct SizedCollect<T, B = Vec<<T as IterScan>::Output>>
where
T: IterScan,
B: FromIterator<<T as IterScan>::Output>,
{
_marker: PhantomData<fn() -> (T, B)>,
}
impl<T, B> IterScan for SizedCollect<T, B>
where
T: IterScan,
B: FromIterator<<T as IterScan>::Output>,
{
type Output = B;
#[inline]
fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
let size = usize::scan(iter)?;
repeat_with(|| <T as IterScan>::scan(iter))
.take(size)
.collect()
}
}
}
#[macro_export]
macro_rules ! scan_value { ($ scanner : expr , ($ ($ t : tt) ,*)) => { ($ ($ crate :: scan_value ! ($ scanner , $ t)) ,*) } ; ($ scanner : expr , [$ t : tt ; $ len : expr]) => { (0 ..$ len) . map (| _ | $ crate :: scan_value ! ($ scanner , $ t)) . collect ::< Vec < _ >> () } ; ($ scanner : expr , [$ t : ty ; $ len : expr]) => { $ scanner . scan_vec ::<$ t > ($ len) } ; ($ scanner : expr , [$ t : ty]) => { $ scanner . iter ::<$ t > () } ; ($ scanner : expr , { $ e : expr }) => { $ scanner . mscan ($ e) } ; ($ scanner : expr , $ t : ty) => { $ scanner . scan ::<$ t > () } ; }
#[macro_export]
macro_rules ! scan { ($ scanner : expr) => { } ; ($ scanner : expr ,) => { } ; ($ scanner : expr , mut $ var : tt : $ t : tt) => { let mut $ var = $ crate :: scan_value ! ($ scanner , $ t) ; } ; ($ scanner : expr , $ var : tt : $ t : tt) => { let $ var = $ crate :: scan_value ! ($ scanner , $ t) ; } ; ($ scanner : expr , mut $ var : tt : $ t : tt , $ ($ rest : tt) *) => { let mut $ var = $ crate :: scan_value ! ($ scanner , $ t) ; scan ! ($ scanner , $ ($ rest) *) } ; ($ scanner : expr , $ var : tt : $ t : tt , $ ($ rest : tt) *) => { let $ var = $ crate :: scan_value ! ($ scanner , $ t) ; scan ! ($ scanner , $ ($ rest) *) } ; ($ scanner : expr , mut $ var : tt) => { let mut $ var = $ crate :: scan_value ! ($ scanner , usize) ; } ; ($ scanner : expr , $ var : tt) => { let $ var = $ crate :: scan_value ! ($ scanner , usize) ; } ; ($ scanner : expr , mut $ var : tt , $ ($ rest : tt) *) => { let mut $ var = $ crate :: scan_value ! ($ scanner , usize) ; scan ! ($ scanner , $ ($ rest) *) } ; ($ scanner : expr , $ var : tt , $ ($ rest : tt) *) => { let $ var = $ crate :: scan_value ! ($ scanner , usize) ; scan ! ($ scanner , $ ($ rest) *) } ; }
pub use sparse_graph::{
Adjacency, BidirectionalGraphScanner, BidirectionalSparseGraph, DirectedGraphScanner,
DirectedSparseGraph, SparseGraph, TreeGraphScanner, UndirectedGraphScanner,
UndirectedSparseGraph,
};
pub mod sparse_graph {
use super::*;
use std::{iter, marker::PhantomData, ops, slice};
type Marker<T> = PhantomData<fn() -> T>;
#[derive(Clone, Copy, Debug, Default, Eq, PartialEq, Ord, PartialOrd, Hash)]
pub struct DirectedEdge;
#[derive(Clone, Copy, Debug, Default, Eq, PartialEq, Ord, PartialOrd, Hash)]
pub struct UndirectedEdge;
#[derive(Clone, Copy, Debug, Default, Eq, PartialEq, Ord, PartialOrd, Hash)]
pub struct BidirectionalEdge;
#[derive(Clone, Copy, Debug, Default, Eq, PartialEq, Ord, PartialOrd, Hash)]
pub struct Adjacency {
pub id: usize,
pub to: usize,
}
impl Adjacency {
pub fn new(id: usize, to: usize) -> Adjacency {
Adjacency { id, to }
}
}
/// Static Sparse Graph represented as Compressed Sparse Row.
#[derive(Debug, Clone)]
pub struct SparseGraph<D> {
vsize: usize,
pub start: Vec<usize>,
pub elist: Vec<Adjacency>,
pub edges: Vec<(usize, usize)>,
_marker: Marker<D>,
}
impl<D> SparseGraph<D> {
/// Return the number of vertices.
pub fn vertices_size(&self) -> usize {
self.vsize
}
/// Return the number of edges.
pub fn edges_size(&self) -> usize {
self.edges.len()
}
/// Return an iterator over graph vertices.
pub fn vertices(&self) -> ops::Range<usize> {
0..self.vertices_size()
}
/// Return a slice of adjacency vertices.
pub fn adjacencies(&self, v: usize) -> slice::Iter<'_, Adjacency> {
self.elist[self.start[v]..self.start[v + 1]].iter()
}
}
pub trait SparseGraphConstruction: Sized {
fn construct_graph(vsize: usize, edges: Vec<(usize, usize)>) -> SparseGraph<Self>;
}
impl<D: SparseGraphConstruction> SparseGraph<D> {
/// Construct graph from edges.
pub fn from_edges(vsize: usize, edges: Vec<(usize, usize)>) -> Self {
D::construct_graph(vsize, edges)
}
}
impl SparseGraphConstruction for DirectedEdge {
fn construct_graph(vsize: usize, edges: Vec<(usize, usize)>) -> SparseGraph<Self> {
let mut start: Vec<_> = iter::repeat(0).take(vsize + 1).collect();
let mut elist = Vec::with_capacity(edges.len());
unsafe { elist.set_len(edges.len()) }
for (from, _) in edges.iter().cloned() {
start[from] += 1;
}
for i in 1..=vsize {
start[i] += start[i - 1];
}
for (id, (from, to)) in edges.iter().cloned().enumerate() {
start[from] -= 1;
elist[start[from]] = Adjacency::new(id, to);
}
SparseGraph {
vsize,
start,
elist,
edges,
_marker: PhantomData,
}
}
}
impl SparseGraphConstruction for UndirectedEdge {
fn construct_graph(vsize: usize, edges: Vec<(usize, usize)>) -> SparseGraph<Self> {
let mut start: Vec<_> = iter::repeat(0).take(vsize + 1).collect();
let mut elist = Vec::with_capacity(edges.len() * 2);
unsafe { elist.set_len(edges.len() * 2) }
for (from, to) in edges.iter().cloned() {
start[to] += 1;
start[from] += 1;
}
for i in 1..=vsize {
start[i] += start[i - 1];
}
for (id, (from, to)) in edges.iter().cloned().enumerate() {
start[from] -= 1;
elist[start[from]] = Adjacency::new(id, to);
start[to] -= 1;
elist[start[to]] = Adjacency::new(id, from);
}
SparseGraph {
vsize,
start,
elist,
edges,
_marker: PhantomData,
}
}
}
impl SparseGraphConstruction for BidirectionalEdge {
fn construct_graph(vsize: usize, edges: Vec<(usize, usize)>) -> SparseGraph<Self> {
let mut start: Vec<_> = iter::repeat(0).take(vsize + 1).collect();
let mut elist = Vec::with_capacity(edges.len() * 2);
unsafe { elist.set_len(edges.len() * 2) }
for (from, to) in edges.iter().cloned() {
start[to] += 1;
start[from] += 1;
}
for i in 1..=vsize {
start[i] += start[i - 1];
}
for (id, (from, to)) in edges.iter().cloned().enumerate() {
start[from] -= 1;
elist[start[from]] = Adjacency::new(id * 2, to);
start[to] -= 1;
elist[start[to]] = Adjacency::new(id * 2 + 1, from);
}
SparseGraph {
vsize,
start,
elist,
edges,
_marker: PhantomData,
}
}
}
pub type DirectedSparseGraph = SparseGraph<DirectedEdge>;
pub type UndirectedSparseGraph = SparseGraph<UndirectedEdge>;
pub type BidirectionalSparseGraph = SparseGraph<BidirectionalEdge>;
pub struct SparseGraphScanner<U: IterScan<Output = usize>, T: IterScan, D> {
vsize: usize,
esize: usize,
_marker: Marker<(U, T, D)>,
}
impl<U: IterScan<Output = usize>, T: IterScan, D> SparseGraphScanner<U, T, D> {
pub fn new(vsize: usize, esize: usize) -> Self {
Self {
vsize,
esize,
_marker: PhantomData,
}
}
}
impl<U: IterScan<Output = usize>, T: IterScan, D: SparseGraphConstruction> MarkedIterScan
for SparseGraphScanner<U, T, D>
{
type Output = (SparseGraph<D>, Vec<<T as IterScan>::Output>);
fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
let mut edges = Vec::with_capacity(self.esize);
let mut rest = Vec::with_capacity(self.esize);
for _ in 0..self.esize {
edges.push((U::scan(iter)?, U::scan(iter)?));
rest.push(T::scan(iter)?);
}
let graph = SparseGraph::from_edges(self.vsize, edges);
Some((graph, rest))
}
}
pub type DirectedGraphScanner<U, T = ()> = SparseGraphScanner<U, T, DirectedEdge>;
pub type UndirectedGraphScanner<U, T = ()> = SparseGraphScanner<U, T, UndirectedEdge>;
pub type BidirectionalGraphScanner<U, T = ()> = SparseGraphScanner<U, T, BidirectionalEdge>;
pub struct TreeGraphScanner<U: IterScan<Output = usize>, T: IterScan = ()> {
vsize: usize,
_marker: Marker<(U, T)>,
}
impl<U: IterScan<Output = usize>, T: IterScan> TreeGraphScanner<U, T> {
pub fn new(vsize: usize) -> Self {
Self {
vsize,
_marker: PhantomData,
}
}
}
impl<U: IterScan<Output = usize>, T: IterScan> MarkedIterScan for TreeGraphScanner<U, T> {
type Output = (UndirectedSparseGraph, Vec<<T as IterScan>::Output>);
fn mscan<'a, I: Iterator<Item = &'a str>>(self, iter: &mut I) -> Option<Self::Output> {
UndirectedGraphScanner::<U, T>::new(self.vsize, self.vsize - 1).mscan(iter)
}
}
}
/// dynamic programming on all-rooted trees
///
/// caluculate all subtrees (hanging on the edge) in specific ordering,
/// each subtree calculated in the order of merge and rooting
#[derive(Clone, Debug)]
pub struct ReRooting<'a, M: Monoid, F: Fn(&M::T, usize, Option<usize>) -> M::T> {
graph: &'a UndirectedSparseGraph,
/// dp\[v\]: result of v-rooted tree
pub dp: Vec<M::T>,
/// ep\[e\]: result of e-subtree, if e >= n then reversed-e-subtree
pub ep: Vec<M::T>,
/// rooting(data, vid, (Optional)eid): add root node(vid), result subtree is edge(eid)
rooting: F,
}
impl<'a, M, F> ReRooting<'a, M, F>
where
M: Monoid,
F: Fn(&M::T, usize, Option<usize>) -> M::T,
{
pub fn new(graph: &'a UndirectedSparseGraph, rooting: F) -> Self {
let dp = vec![M::unit(); graph.vertices_size()];
let ep = vec![M::unit(); graph.vertices_size() * 2];
let mut self_ = Self {
graph,
dp,
ep,
rooting,
};
self_.rerooting();
self_
}
#[inline]
fn eidx(&self, u: usize, a: &Adjacency) -> usize {
a.id + self.graph.edges_size() * (u > a.to) as usize
}
#[inline]
fn reidx(&self, u: usize, a: &Adjacency) -> usize {
a.id + self.graph.edges_size() * (u < a.to) as usize
}
#[inline]
fn merge(&self, x: &M::T, y: &M::T) -> M::T {
M::operate(x, y)
}
#[inline]
fn add_subroot(&self, x: &M::T, vid: usize, eid: usize) -> M::T {
(self.rooting)(x, vid, Some(eid))
}
#[inline]
fn add_root(&self, x: &M::T, vid: usize) -> M::T {
(self.rooting)(x, vid, None)
}
fn dfs(&mut self, pa: &Adjacency, p: usize) {
let u = pa.to;
let pi = self.eidx(p, pa);
for a in self.graph.adjacencies(u).filter(|a| a.to != p) {
let i = self.eidx(u, a);
self.dfs(a, u);
self.ep[pi] = self.merge(&self.ep[pi], &self.ep[i]);
}
self.ep[pi] = self.add_subroot(&self.ep[pi], u, pa.id);
}
fn efs(&mut self, u: usize, p: usize) {
let m = self.graph.adjacencies(u).len();
let mut left = vec![M::unit(); m + 1];
let mut right = vec![M::unit(); m + 1];
for (k, a) in self.graph.adjacencies(u).enumerate() {
let i = self.eidx(u, a);
left[k + 1] = self.merge(&left[k], &self.ep[i]);
}
for (k, a) in self.graph.adjacencies(u).enumerate().rev() {
let i = self.eidx(u, a);
right[k] = self.merge(&right[k + 1], &self.ep[i]);
}
self.dp[u] = self.add_root(&left[m], u);
for (k, a) in self.graph.adjacencies(u).enumerate() {
if a.to != p {
let i = self.reidx(u, a);
self.ep[i] = self.merge(&left[k], &right[k + 1]);
self.ep[i] = self.add_subroot(&self.ep[i], u, a.id);
self.efs(a.to, u);
}
}
}
fn rerooting(&mut self) {
for a in self.graph.adjacencies(0) {
self.dfs(a, 0);
}
self.efs(0, std::usize::MAX);
}
}
/// binary operaion: $T \circ T \to T$
pub trait Magma {
/// type of operands: $T$
type T: Clone;
/// binary operaion: $\circ$
fn operate(x: &Self::T, y: &Self::T) -> Self::T;
#[inline]
fn reverse_operate(x: &Self::T, y: &Self::T) -> Self::T {
Self::operate(y, x)
}
#[inline]
fn operate_assign(x: &mut Self::T, y: &Self::T) {
*x = Self::operate(x, y);
}
}
/// $\forall a,\forall b,\forall c \in T, (a \circ b) \circ c = a \circ (b \circ c)$
pub trait Associative {}
/// associative binary operation
pub trait SemiGroup: Magma + Associative {}
impl<S: Magma + Associative> SemiGroup for S {}
/// $\exists e \in T, \forall a \in T, e \circ a = a \circ e = e$
pub trait Unital: Magma {
/// identity element: $e$
fn unit() -> Self::T;
#[inline]
fn is_unit(x: &Self::T) -> bool
where
<Self as Magma>::T: PartialEq,
{
x == &Self::unit()
}
#[inline]
fn set_unit(x: &mut Self::T) {
*x = Self::unit();
}
}
/// associative binary operation and an identity element
pub trait Monoid: SemiGroup + Unital {
/// binary exponentiation: $x^n = x\circ\ddots\circ x$
fn pow(mut x: Self::T, mut n: usize) -> Self::T {
let mut res = Self::unit();
while n > 0 {
if n & 1 == 1 {
res = Self::operate(&res, &x);
}
x = Self::operate(&x, &x);
n >>= 1;
}
res
}
}
impl<M: SemiGroup + Unital> Monoid for M {}
/// $\exists e \in T, \forall a \in T, \exists b,c \in T, b \circ a = a \circ c = e$
pub trait Invertible: Magma {
/// $a$ where $a \circ x = e$
fn inverse(x: &Self::T) -> Self::T;
#[inline]
fn rinv_operate(x: &Self::T, y: &Self::T) -> Self::T {
Self::operate(x, &Self::inverse(y))
}
}
/// associative binary operation and an identity element and inverse elements
pub trait Group: Monoid + Invertible {}
impl<G: Monoid + Invertible> Group for G {}
/// $\forall a,\forall b \in T, a \circ b = b \circ a$
pub trait Commutative {}
/// commutative monoid
pub trait AbelianMonoid: Monoid + Commutative {}
impl<M: Monoid + Commutative> AbelianMonoid for M {}
/// commutative group
pub trait AbelianGroup: Group + Commutative {}
impl<G: Group + Commutative> AbelianGroup for G {}
/// $\forall a \in T, a \circ a = a$
pub trait Idempotent {}
/// idempotent monoid
pub trait IdempotentMonoid: Monoid + Idempotent {}
impl<M: Monoid + Idempotent> IdempotentMonoid for M {}
#[macro_export]
macro_rules ! monoid_fold { ($ m : ty) => { <$ m as Unital >:: unit () } ; ($ m : ty ,) => { <$ m as Unital >:: unit () } ; ($ m : ty , $ f : expr) => { $ f } ; ($ m : ty , $ f : expr , $ ($ ff : expr) ,*) => { <$ m as Magma >:: operate (& ($ f) , & monoid_fold ! ($ m , $ ($ ff) ,*)) } ; }
/// $+$
pub struct AdditiveOperation<T: Clone + Zero + std::ops::Add<Output = T>> {
_marker: std::marker::PhantomData<fn() -> T>,
}
mod additive_operation_impl {
use super::*;
use std::ops::{Add, Neg, Sub};
impl<T: Clone + Zero + Add<Output = T>> Magma for AdditiveOperation<T> {
type T = T;
#[inline]
fn operate(x: &Self::T, y: &Self::T) -> Self::T {
x.clone() + y.clone()
}
}
impl<T: Clone + Zero + Add<Output = T>> Unital for AdditiveOperation<T> {
#[inline]
fn unit() -> Self::T {
Zero::zero()
}
}
impl<T: Clone + Zero + Add<Output = T>> Associative for AdditiveOperation<T> {}
impl<T: Clone + Zero + Add<Output = T>> Commutative for AdditiveOperation<T> {}
impl<T: Clone + Zero + Add<Output = T> + Sub<Output = T> + Neg<Output = T>> Invertible
for AdditiveOperation<T>
{
#[inline]
fn inverse(x: &Self::T) -> Self::T {
-x.clone()
}
#[inline]
fn rinv_operate(x: &Self::T, y: &Self::T) -> Self::T {
x.clone() - y.clone()
}
}
}
pub trait Zero: Sized {
fn zero() -> Self;
#[inline]
fn is_zero(&self) -> bool
where
Self: PartialEq,
{
self == &Self::zero()
}
#[inline]
fn set_zero(&mut self) {
*self = Self::zero();
}
}
pub trait One: Sized {
fn one() -> Self;
#[inline]
fn is_one(&self) -> bool
where
Self: PartialEq,
{
self == &Self::one()
}
#[inline]
fn set_one(&mut self) {
*self = Self::one();
}
}
macro_rules ! zero_one_impls { ($ ({ $ Trait : ident $ method : ident $ ($ t : ty) *, $ e : expr }) *) => { $ ($ (impl $ Trait for $ t { fn $ method () -> Self { $ e } }) *) * } ; }
zero_one_impls ! ({ Zero zero u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 , 0 } { Zero zero f32 f64 , 0. } { One one u8 u16 u32 u64 usize i8 i16 i32 i64 isize u128 i128 , 1 } { One one f32 f64 , 1. });
mod tuple_operation_impl {
#![allow(unused_variables)]
use super::*;
macro_rules ! impl_tuple_operation { ($ ($ M : ident) *, $ ($ i : tt) *) => { impl <$ ($ M : Magma) ,*> Magma for ($ ($ M ,) *) { type T = ($ (<$ M as Magma >:: T ,) *) ; # [inline] fn operate (x : & Self :: T , y : & Self :: T) -> Self :: T { ($ (<$ M as Magma >:: operate (& x .$ i , & y .$ i) ,) *) } } impl <$ ($ M : Unital) ,*> Unital for ($ ($ M ,) *) { # [inline] fn unit () -> Self :: T { ($ (<$ M as Unital >:: unit () ,) *) } } impl <$ ($ M : Associative) ,*> Associative for ($ ($ M ,) *) { } impl <$ ($ M : Commutative) ,*> Commutative for ($ ($ M ,) *) { } impl <$ ($ M : Idempotent) ,*> Idempotent for ($ ($ M ,) *) { } impl <$ ($ M : Invertible) ,*> Invertible for ($ ($ M ,) *) { # [inline] fn inverse (x : & Self :: T) -> Self :: T { ($ (<$ M as Invertible >:: inverse (& x .$ i) ,) *) } } } ; }
impl_tuple_operation ! (,);
impl_tuple_operation!(A, 0);
impl_tuple_operation ! (A B , 0 1);
impl_tuple_operation ! (A B C , 0 1 2);
impl_tuple_operation ! (A B C D , 0 1 2 3);
impl_tuple_operation ! (A B C D E , 0 1 2 3 4);
impl_tuple_operation ! (A B C D E F , 0 1 2 3 4 5);
impl_tuple_operation ! (A B C D E F G , 0 1 2 3 4 5 6);
impl_tuple_operation ! (A B C D E F G H , 0 1 2 3 4 5 6 7);
impl_tuple_operation ! (A B C D E F G H I , 0 1 2 3 4 5 6 7 8);
impl_tuple_operation ! (A B C D E F G H I J , 0 1 2 3 4 5 6 7 8 9);
}
pub mod mint_basic {
use super::*;
#[macro_export]
macro_rules ! define_basic_mintbase { ($ name : ident , $ m : expr , $ basety : ty , $ signedty : ty , $ upperty : ty , [$ ($ unsigned : ty) ,*] , [$ ($ signed : ty) ,*]) => { pub struct $ name ; impl MIntBase for $ name { type Inner = $ basety ; # [inline] fn get_mod () -> Self :: Inner { $ m } # [inline] fn mod_zero () -> Self :: Inner { 0 } # [inline] fn mod_one () -> Self :: Inner { 1 } # [inline] fn mod_add (x : Self :: Inner , y : Self :: Inner) -> Self :: Inner { let z = x + y ; let m = Self :: get_mod () ; if z >= m { z - m } else { z } } # [inline] fn mod_sub (x : Self :: Inner , y : Self :: Inner) -> Self :: Inner { if x < y { x + Self :: get_mod () - y } else { x - y } } # [inline] fn mod_mul (x : Self :: Inner , y : Self :: Inner) -> Self :: Inner { (x as $ upperty * y as $ upperty % Self :: get_mod () as $ upperty) as $ basety } # [inline] fn mod_div (x : Self :: Inner , y : Self :: Inner) -> Self :: Inner { Self :: mod_mul (x , Self :: mod_inv (y)) } # [inline] fn mod_neg (x : Self :: Inner) -> Self :: Inner { if x == 0 { 0 } else { Self :: get_mod () - x } } fn mod_inv (x : Self :: Inner) -> Self :: Inner { let p = Self :: get_mod () as $ signedty ; let (mut a , mut b) = (x as $ signedty , p) ; let (mut u , mut x) = (1 , 0) ; while a != 0 { let k = b / a ; x -= k * u ; b -= k * a ; std :: mem :: swap (& mut x , & mut u) ; std :: mem :: swap (& mut b , & mut a) ; } (if x < 0 { x + p } else { x }) as _ } } $ (impl MIntConvert <$ unsigned > for $ name { # [inline] fn from (x : $ unsigned) -> Self :: Inner { (x % < Self as MIntBase >:: get_mod () as $ unsigned) as $ basety } # [inline] fn into (x : Self :: Inner) -> $ unsigned { x as $ unsigned } # [inline] fn mod_into () -> $ unsigned { < Self as MIntBase >:: get_mod () as $ unsigned } }) * $ (impl MIntConvert <$ signed > for $ name { # [inline] fn from (x : $ signed) -> Self :: Inner { let x = x % < Self as MIntBase >:: get_mod () as $ signed ; if x < 0 { (x + < Self as MIntBase >:: get_mod () as $ signed) as $ basety } else { x as $ basety } } # [inline] fn into (x : Self :: Inner) -> $ signed { x as $ signed } # [inline] fn mod_into () -> $ signed { < Self as MIntBase >:: get_mod () as $ signed } }) * } ; }
#[macro_export]
macro_rules ! define_basic_mint32 { ($ ([$ name : ident , $ m : expr , $ mint_name : ident]) ,*) => { $ (crate :: define_basic_mintbase ! ($ name , $ m , u32 , i32 , u64 , [u32 , u64 , u128 , usize] , [i32 , i64 , i128 , isize]) ; pub type $ mint_name = MInt <$ name >;) * } ; }
define_basic_mint32!(
[Modulo998244353, 998_244_353, MInt998244353],
[Modulo1000000007, 1_000_000_007, MInt1000000007],
[Modulo1000000009, 1_000_000_009, MInt1000000009],
[
DynModuloU32,
DYN_MODULUS_U32.with(|cell| unsafe { *cell.get() }),
DynMIntU32
]
);
thread_local ! (static DYN_MODULUS_U32 : std :: cell :: UnsafeCell < u32 > = std :: cell :: UnsafeCell :: new (1_000_000_007));
impl DynModuloU32 {
pub fn set_mod(m: u32) {
DYN_MODULUS_U32.with(|cell| unsafe { *cell.get() = m })
}
}
thread_local ! (static DYN_MODULUS_U64 : std :: cell :: UnsafeCell < u64 > = std :: cell :: UnsafeCell :: new (1_000_000_007));
define_basic_mintbase!(
DynModuloU64,
DYN_MODULUS_U64.with(|cell| unsafe { *cell.get() }),
u64,
i64,
u128,
[u64, u128, usize],
[i64, i128, isize]
);
impl DynModuloU64 {
pub fn set_mod(m: u64) {
DYN_MODULUS_U64.with(|cell| unsafe { *cell.get() = m })
}
}
pub type DynMIntU64 = MInt<DynModuloU64>;
pub struct Modulo2;
impl MIntBase for Modulo2 {
type Inner = u32;
#[inline]
fn get_mod() -> Self::Inner {
2
}
#[inline]
fn mod_zero() -> Self::Inner {
0
}
#[inline]
fn mod_one() -> Self::Inner {
1
}
#[inline]
fn mod_add(x: Self::Inner, y: Self::Inner) -> Self::Inner {
x ^ y
}
#[inline]
fn mod_sub(x: Self::Inner, y: Self::Inner) -> Self::Inner {
x ^ y
}
#[inline]
fn mod_mul(x: Self::Inner, y: Self::Inner) -> Self::Inner {
x | y
}
#[inline]
fn mod_div(x: Self::Inner, y: Self::Inner) -> Self::Inner {
assert_ne!(y, 0);
x
}
#[inline]
fn mod_neg(x: Self::Inner) -> Self::Inner {
x
}
#[inline]
fn mod_inv(x: Self::Inner) -> Self::Inner {
assert_ne!(x, 0);
x
}
#[inline]
fn mod_pow(x: Self::Inner, y: usize) -> Self::Inner {
if y == 0 {
1
} else {
x
}
}
}
macro_rules ! impl_to_mint_base_for_modulo2 { ($ name : ident , $ basety : ty , [$ ($ t : ty) ,*]) => { $ (impl MIntConvert <$ t > for $ name { # [inline] fn from (x : $ t) -> Self :: Inner { (x & 1) as $ basety } # [inline] fn into (x : Self :: Inner) -> $ t { x as $ t } # [inline] fn mod_into () -> $ t { 1 } }) * } ; }
impl_to_mint_base_for_modulo2!(
Modulo2,
u32,
[u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize]
);
pub type MInt2 = MInt<Modulo2>;
}
#[repr(transparent)]
pub struct MInt<M>
where
M: MIntBase,
{
x: M::Inner,
_marker: std::marker::PhantomData<fn() -> M>,
}
pub trait MIntBase {
type Inner: Sized + Copy + Eq + std::fmt::Debug + std::hash::Hash;
fn get_mod() -> Self::Inner;
fn mod_zero() -> Self::Inner;
fn mod_one() -> Self::Inner;
fn mod_add(x: Self::Inner, y: Self::Inner) -> Self::Inner;
fn mod_sub(x: Self::Inner, y: Self::Inner) -> Self::Inner;
fn mod_mul(x: Self::Inner, y: Self::Inner) -> Self::Inner;
fn mod_div(x: Self::Inner, y: Self::Inner) -> Self::Inner;
fn mod_neg(x: Self::Inner) -> Self::Inner;
fn mod_inv(x: Self::Inner) -> Self::Inner;
fn mod_pow(x: Self::Inner, y: usize) -> Self::Inner {
let (mut x, mut y, mut z) = (x, y, Self::mod_one());
while y > 0 {
if y & 1 == 1 {
z = Self::mod_mul(z, x);
}
x = Self::mod_mul(x, x);
y >>= 1;
}
z
}
}
pub trait MIntConvert<T = <Self as MIntBase>::Inner>: MIntBase {
fn from(x: T) -> <Self as MIntBase>::Inner;
fn into(x: <Self as MIntBase>::Inner) -> T;
fn mod_into() -> T;
}
mod mint_base {
use super::*;
use std::{
fmt::{self, Debug, Display},
hash::{Hash, Hasher},
iter::{Product, Sum},
marker::PhantomData,
ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
str::FromStr,
};
impl<M> MInt<M>
where
M: MIntConvert,
{
#[inline]
pub fn new(x: M::Inner) -> Self {
Self::new_unchecked(<M as MIntConvert<M::Inner>>::from(x))
}
#[inline]
pub fn inner(self) -> M::Inner {
<M as MIntConvert<M::Inner>>::into(self.x)
}
}
impl<M> MInt<M>
where
M: MIntBase,
{
#[inline]
pub fn new_unchecked(x: M::Inner) -> Self {
Self {
x,
_marker: PhantomData,
}
}
#[inline]
pub fn get_mod() -> M::Inner {
M::get_mod()
}
#[inline]
pub fn pow(self, y: usize) -> Self {
Self::new_unchecked(M::mod_pow(self.x, y))
}
#[inline]
pub fn inv(self) -> Self {
Self::new_unchecked(M::mod_inv(self.x))
}
}
impl<M> Clone for MInt<M>
where
M: MIntBase,
{
#[inline]
fn clone(&self) -> Self {
Self {
x: Clone::clone(&self.x),
_marker: PhantomData,
}
}
}
impl<M> Copy for MInt<M> where M: MIntBase {}
impl<M> Debug for MInt<M>
where
M: MIntBase,
{
fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
Debug::fmt(&self.x, f)
}
}
impl<M> Default for MInt<M>
where
M: MIntBase,
{
#[inline]
fn default() -> Self {
<Self as Zero>::zero()
}
}
impl<M> PartialEq for MInt<M>
where
M: MIntBase,
{
#[inline]
fn eq(&self, other: &Self) -> bool {
PartialEq::eq(&self.x, &other.x)
}
}
impl<M> Eq for MInt<M> where M: MIntBase {}
impl<M> Hash for MInt<M>
where
M: MIntBase,
{
#[inline]
fn hash<H: Hasher>(&self, state: &mut H) {
Hash::hash(&self.x, state)
}
}
macro_rules ! impl_mint_from { ($ ($ t : ty) ,*) => { $ (impl < M > From <$ t > for MInt < M > where M : MIntConvert <$ t >, { # [inline] fn from (x : $ t) -> Self { Self :: new_unchecked (< M as MIntConvert <$ t >>:: from (x)) } } impl < M > From < MInt < M >> for $ t where M : MIntConvert <$ t >, { # [inline] fn from (x : MInt < M >) -> $ t { < M as MIntConvert <$ t >>:: into (x . x) } }) * } ; }
impl_mint_from!(u8, u16, u32, u64, u128, usize, i8, i16, i32, i64, i128, isize);
impl<M> Zero for MInt<M>
where
M: MIntBase,
{
#[inline]
fn zero() -> Self {
Self::new_unchecked(M::mod_zero())
}
}
impl<M> One for MInt<M>
where
M: MIntBase,
{
#[inline]
fn one() -> Self {
Self::new_unchecked(M::mod_one())
}
}
impl<M> Add for MInt<M>
where
M: MIntBase,
{
type Output = Self;
#[inline]
fn add(self, rhs: Self) -> Self::Output {
Self::new_unchecked(M::mod_add(self.x, rhs.x))
}
}
impl<M> Sub for MInt<M>
where
M: MIntBase,
{
type Output = Self;
#[inline]
fn sub(self, rhs: Self) -> Self::Output {
Self::new_unchecked(M::mod_sub(self.x, rhs.x))
}
}
impl<M> Mul for MInt<M>
where
M: MIntBase,
{
type Output = Self;
#[inline]
fn mul(self, rhs: Self) -> Self::Output {
Self::new_unchecked(M::mod_mul(self.x, rhs.x))
}
}
impl<M> Div for MInt<M>
where
M: MIntBase,
{
type Output = Self;
#[inline]
fn div(self, rhs: Self) -> Self::Output {
Self::new_unchecked(M::mod_div(self.x, rhs.x))
}
}
impl<M> Neg for MInt<M>
where
M: MIntBase,
{
type Output = Self;
#[inline]
fn neg(self) -> Self::Output {
Self::new_unchecked(M::mod_neg(self.x))
}
}
impl<M> Sum for MInt<M>
where
M: MIntBase,
{
#[inline]
fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(<Self as Zero>::zero(), Add::add)
}
}
impl<M> Product for MInt<M>
where
M: MIntBase,
{
#[inline]
fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
iter.fold(<Self as One>::one(), Mul::mul)
}
}
impl<'a, M: 'a> Sum<&'a MInt<M>> for MInt<M>
where
M: MIntBase,
{
#[inline]
fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(<Self as Zero>::zero(), Add::add)
}
}
impl<'a, M: 'a> Product<&'a MInt<M>> for MInt<M>
where
M: MIntBase,
{
#[inline]
fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
iter.fold(<Self as One>::one(), Mul::mul)
}
}
impl<M> Display for MInt<M>
where
M: MIntConvert,
M::Inner: Display,
{
fn fmt<'a>(&self, f: &mut fmt::Formatter<'a>) -> Result<(), fmt::Error> {
write!(f, "{}", self.inner())
}
}
impl<M> FromStr for MInt<M>
where
M: MIntConvert,
M::Inner: FromStr,
{
type Err = <M::Inner as FromStr>::Err;
#[inline]
fn from_str(s: &str) -> Result<Self, Self::Err> {
s.parse::<M::Inner>().map(Self::new)
}
}
impl<M> IterScan for MInt<M>
where
M: MIntConvert,
M::Inner: FromStr,
{
type Output = Self;
#[inline]
fn scan<'a, I: Iterator<Item = &'a str>>(iter: &mut I) -> Option<Self::Output> {
iter.next()?.parse::<MInt<M>>().ok()
}
}
macro_rules! impl_mint_ref_binop {
($ imp : ident , $ method : ident , $ t : ty) => {
impl<M> $imp<$t> for &$t
where
M: MIntBase,
{
type Output = <$t as $imp<$t>>::Output;
#[inline]
fn $method(self, other: $t) -> <$t as $imp<$t>>::Output {
$imp::$method(*self, other)
}
}
impl<M> $imp<&$t> for $t
where
M: MIntBase,
{
type Output = <$t as $imp<$t>>::Output;
#[inline]
fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
$imp::$method(self, *other)
}
}
impl<M> $imp<&$t> for &$t
where
M: MIntBase,
{
type Output = <$t as $imp<$t>>::Output;
#[inline]
fn $method(self, other: &$t) -> <$t as $imp<$t>>::Output {
$imp::$method(*self, *other)
}
}
};
}
impl_mint_ref_binop!(Add, add, MInt<M>);
impl_mint_ref_binop!(Sub, sub, MInt<M>);
impl_mint_ref_binop!(Mul, mul, MInt<M>);
impl_mint_ref_binop!(Div, div, MInt<M>);
macro_rules! impl_mint_ref_unop {
($ imp : ident , $ method : ident , $ t : ty) => {
impl<M> $imp for &$t
where
M: MIntBase,
{
type Output = <$t as $imp>::Output;
#[inline]
fn $method(self) -> <$t as $imp>::Output {
$imp::$method(*self)
}
}
};
}
impl_mint_ref_unop!(Neg, neg, MInt<M>);
macro_rules! impl_mint_ref_op_assign {
($ imp : ident , $ method : ident , $ t : ty , $ fromimp : ident , $ frommethod : ident) => {
impl<M> $imp<$t> for $t
where
M: MIntBase,
{
#[inline]
fn $method(&mut self, rhs: $t) {
*self = $fromimp::$frommethod(*self, rhs);
}
}
impl<M> $imp<&$t> for $t
where
M: MIntBase,
{
#[inline]
fn $method(&mut self, other: &$t) {
$imp::$method(self, *other);
}
}
};
}
impl_mint_ref_op_assign!(AddAssign, add_assign, MInt<M>, Add, add);
impl_mint_ref_op_assign!(SubAssign, sub_assign, MInt<M>, Sub, sub);
impl_mint_ref_op_assign!(MulAssign, mul_assign, MInt<M>, Mul, mul);
impl_mint_ref_op_assign!(DivAssign, div_assign, MInt<M>, Div, div);
}