結果
| 問題 |
No.1691 Badugi
|
| コンテスト | |
| ユーザー |
 akakimidori
|
| 提出日時 | 2021-12-25 14:14:24 |
| 言語 | Rust (1.83.0 + proconio) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 16,844 bytes |
| コンパイル時間 | 14,706 ms |
| コンパイル使用メモリ | 378,572 KB |
| 実行使用メモリ | 19,456 KB |
| 最終ジャッジ日時 | 2024-09-21 16:33:00 |
| 合計ジャッジ時間 | 20,357 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 7 TLE * 1 -- * 9 |
コンパイルメッセージ
warning: unused import: `std::io::Write`
--> src/main.rs:515:5
|
515 | use std::io::Write;
| ^^^^^^^^^^^^^^
|
= note: `#[warn(unused_imports)]` on by default
warning: type alias `Set` is never used
--> src/main.rs:518:6
|
518 | type Set<T> = BTreeSet<T>;
| ^^^
|
= note: `#[warn(dead_code)]` on by default
warning: type alias `Deque` is never used
--> src/main.rs:519:6
|
519 | type Deque<T> = VecDeque<T>;
| ^^^^^
ソースコード
//---------- begin union_find ----------
pub struct DSU {
p: Vec<i32>,
}
impl DSU {
pub fn new(n: usize) -> DSU {
assert!(n < std::i32::MAX as usize);
DSU { p: vec![-1; n] }
}
pub fn init(&mut self) {
self.p.iter_mut().for_each(|p| *p = -1);
}
pub fn root(&self, mut x: usize) -> usize {
assert!(x < self.p.len());
while self.p[x] >= 0 {
x = self.p[x] as usize;
}
x
}
pub fn same(&self, x: usize, y: usize) -> bool {
assert!(x < self.p.len() && y < self.p.len());
self.root(x) == self.root(y)
}
pub fn unite(&mut self, x: usize, y: usize) -> Option<(usize, usize)> {
assert!(x < self.p.len() && y < self.p.len());
let mut x = self.root(x);
let mut y = self.root(y);
if x == y {
return None;
}
if self.p[x] > self.p[y] {
std::mem::swap(&mut x, &mut y);
}
self.p[x] += self.p[y];
self.p[y] = x as i32;
Some((x, y))
}
pub fn parent(&self, x: usize) -> Option<usize> {
assert!(x < self.p.len());
let p = self.p[x];
if p >= 0 {
Some(p as usize)
} else {
None
}
}
pub fn sum<F>(&self, mut x: usize, mut f: F) -> usize
where
F: FnMut(usize),
{
while let Some(p) = self.parent(x) {
f(x);
x = p;
}
x
}
pub fn size(&self, x: usize) -> usize {
assert!(x < self.p.len());
let r = self.root(x);
(-self.p[r]) as usize
}
}
//---------- end union_find ----------
// ---------- begin max flow (Dinic) ----------
mod maxflow {
pub trait MaxFlowCapacity:
Copy + Ord + std::ops::Add<Output = Self> + std::ops::Sub<Output = Self>
{
fn zero() -> Self;
fn inf() -> Self;
}
macro_rules! impl_primitive_integer_capacity {
($x:ty, $y:expr) => {
impl MaxFlowCapacity for $x {
fn zero() -> Self {
0
}
fn inf() -> Self {
$y
}
}
};
}
impl_primitive_integer_capacity!(u32, std::u32::MAX);
impl_primitive_integer_capacity!(u64, std::u64::MAX);
impl_primitive_integer_capacity!(i32, std::i32::MAX);
impl_primitive_integer_capacity!(i64, std::i64::MAX);
#[derive(Clone)]
struct Edge<Cap> {
to_: u32,
inv_: u32,
cap_: Cap,
}
impl<Cap> Edge<Cap> {
fn new(to: usize, inv: usize, cap: Cap) -> Self {
Edge {
to_: to as u32,
inv_: inv as u32,
cap_: cap,
}
}
fn to(&self) -> usize {
self.to_ as usize
}
fn inv(&self) -> usize {
self.inv_ as usize
}
}
impl<Cap: MaxFlowCapacity> Edge<Cap> {
fn add(&mut self, cap: Cap) {
self.cap_ = self.cap_ + cap;
}
fn sub(&mut self, cap: Cap) {
self.cap_ = self.cap_ - cap;
}
fn cap(&self) -> Cap {
self.cap_
}
}
pub struct Graph<Cap> {
graph: Vec<Vec<Edge<Cap>>>,
}
#[allow(dead_code)]
pub struct EdgeIndex {
src: usize,
dst: usize,
x: usize,
y: usize,
}
impl<Cap: MaxFlowCapacity> Graph<Cap> {
pub fn new(size: usize) -> Self {
Self {
graph: vec![vec![]; size],
}
}
pub fn add_edge(&mut self, src: usize, dst: usize, cap: Cap) -> EdgeIndex {
assert!(src.max(dst) < self.graph.len());
assert!(cap >= Cap::zero());
assert!(src != dst);
let x = self.graph[src].len();
let y = self.graph[dst].len();
self.graph[src].push(Edge::new(dst, y, cap));
self.graph[dst].push(Edge::new(src, x, Cap::zero()));
EdgeIndex { src, dst, x, y }
}
// src, dst, used, intial_capacity
#[allow(dead_code)]
pub fn get_edge(&self, e: &EdgeIndex) -> (usize, usize, Cap, Cap) {
let max = self.graph[e.src][e.x].cap() + self.graph[e.dst][e.y].cap();
let used = self.graph[e.dst][e.y].cap();
(e.src, e.dst, used, max)
}
pub fn flow(&mut self, src: usize, dst: usize) -> Cap {
let size = self.graph.len();
assert!(src.max(dst) < size);
assert!(src != dst);
let mut queue = std::collections::VecDeque::new();
let mut level = vec![0; size];
let mut it = vec![0; size];
let mut ans = Cap::zero();
loop {
(|| {
level.clear();
level.resize(size, 0);
level[src] = 1;
queue.clear();
queue.push_back(src);
while let Some(v) = queue.pop_front() {
let d = level[v] + 1;
for e in self.graph[v].iter() {
let u = e.to();
if e.cap() > Cap::zero() && level[u] == 0 {
level[u] = d;
if u == dst {
return;
}
queue.push_back(u);
}
}
}
})();
if level[dst] == 0 {
break;
}
it.clear();
it.resize(size, 0);
loop {
let f = self.dfs(dst, src, Cap::inf(), &mut it, &level);
if f == Cap::zero() {
break;
}
ans = ans + f;
}
}
ans
}
fn dfs(&mut self, v: usize, src: usize, cap: Cap, it: &mut [usize], level: &[u32]) -> Cap {
if v == src {
return cap;
}
while let Some((u, inv)) = self.graph[v].get(it[v]).map(|p| (p.to(), p.inv())) {
if level[u] + 1 == level[v] && self.graph[u][inv].cap() > Cap::zero() {
let cap = cap.min(self.graph[u][inv].cap());
let c = self.dfs(u, src, cap, it, level);
if c > Cap::zero() {
self.graph[v][it[v]].add(c);
self.graph[u][inv].sub(c);
return c;
}
}
it[v] += 1;
}
Cap::zero()
}
}
}
// ---------- end max flow (Dinic) ----------
// ---------- begin ModInt ----------
mod modint {
#[allow(dead_code)]
pub struct Mod;
impl ConstantModulo for Mod {
const MOD: u32 = 998_244_353;
}
use std::marker::*;
use std::ops::*;
pub trait Modulo {
fn modulo() -> u32;
}
pub trait ConstantModulo {
const MOD: u32;
}
impl<T> Modulo for T
where
T: ConstantModulo,
{
fn modulo() -> u32 {
T::MOD
}
}
pub struct ModInt<T>(pub u32, PhantomData<T>);
impl<T> Clone for ModInt<T> {
fn clone(&self) -> Self {
ModInt::new_unchecked(self.0)
}
}
impl<T> Copy for ModInt<T> {}
impl<T: Modulo> Add for ModInt<T> {
type Output = ModInt<T>;
fn add(self, rhs: Self) -> Self::Output {
let mut d = self.0 + rhs.0;
if d >= T::modulo() {
d -= T::modulo();
}
ModInt::new_unchecked(d)
}
}
impl<T: Modulo> AddAssign for ModInt<T> {
fn add_assign(&mut self, rhs: Self) {
*self = *self + rhs;
}
}
impl<T: Modulo> Sub for ModInt<T> {
type Output = ModInt<T>;
fn sub(self, rhs: Self) -> Self::Output {
let mut d = self.0 - rhs.0;
if d >= T::modulo() {
d += T::modulo();
}
ModInt::new_unchecked(d)
}
}
impl<T: Modulo> SubAssign for ModInt<T> {
fn sub_assign(&mut self, rhs: Self) {
*self = *self - rhs;
}
}
impl<T: Modulo> Mul for ModInt<T> {
type Output = ModInt<T>;
fn mul(self, rhs: Self) -> Self::Output {
let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
ModInt::new_unchecked(v as u32)
}
}
impl<T: Modulo> MulAssign for ModInt<T> {
fn mul_assign(&mut self, rhs: Self) {
*self = *self * rhs;
}
}
impl<T: Modulo> Neg for ModInt<T> {
type Output = ModInt<T>;
fn neg(self) -> Self::Output {
if self.0 == 0 {
Self::zero()
} else {
Self::new_unchecked(T::modulo() - self.0)
}
}
}
impl<T> std::fmt::Display for ModInt<T> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.0)
}
}
impl<T> std::fmt::Debug for ModInt<T> {
fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
write!(f, "{}", self.0)
}
}
impl<T: Modulo> std::str::FromStr for ModInt<T> {
type Err = std::num::ParseIntError;
fn from_str(s: &str) -> Result<Self, Self::Err> {
let val = s.parse::<u32>()?;
Ok(ModInt::new(val))
}
}
impl<T: Modulo> From<usize> for ModInt<T> {
fn from(val: usize) -> ModInt<T> {
ModInt::new_unchecked((val % T::modulo() as usize) as u32)
}
}
impl<T: Modulo> From<u64> for ModInt<T> {
fn from(val: u64) -> ModInt<T> {
ModInt::new_unchecked((val % T::modulo() as u64) as u32)
}
}
impl<T: Modulo> From<i64> for ModInt<T> {
fn from(val: i64) -> ModInt<T> {
let m = T::modulo() as i64;
ModInt::new((val % m + m) as u32)
}
}
#[allow(dead_code)]
impl<T> ModInt<T> {
pub fn new_unchecked(d: u32) -> Self {
ModInt(d, PhantomData)
}
pub fn zero() -> Self {
ModInt::new_unchecked(0)
}
pub fn one() -> Self {
ModInt::new_unchecked(1)
}
pub fn is_zero(&self) -> bool {
self.0 == 0
}
}
#[allow(dead_code)]
impl<T: Modulo> ModInt<T> {
pub fn new(d: u32) -> Self {
ModInt::new_unchecked(d % T::modulo())
}
pub fn pow(&self, mut n: u64) -> Self {
let mut t = Self::one();
let mut s = *self;
while n > 0 {
if n & 1 == 1 {
t *= s;
}
s *= s;
n >>= 1;
}
t
}
pub fn inv(&self) -> Self {
assert!(self.0 != 0);
self.pow(T::modulo() as u64 - 2)
}
}
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
mod precalc {
use super::modint::*;
#[allow(dead_code)]
pub struct Precalc<T> {
inv: Vec<ModInt<T>>,
fact: Vec<ModInt<T>>,
ifact: Vec<ModInt<T>>,
}
#[allow(dead_code)]
impl<T: Modulo> Precalc<T> {
pub fn new(n: usize) -> Precalc<T> {
let mut inv = vec![ModInt::one(); n + 1];
let mut fact = vec![ModInt::one(); n + 1];
let mut ifact = vec![ModInt::one(); n + 1];
for i in 2..(n + 1) {
fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
}
ifact[n] = fact[n].inv();
if n > 0 {
inv[n] = ifact[n] * fact[n - 1];
}
for i in (1..n).rev() {
ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
inv[i] = ifact[i] * fact[i - 1];
}
Precalc {
inv: inv,
fact: fact,
ifact: ifact,
}
}
pub fn inv(&self, n: usize) -> ModInt<T> {
assert!(n > 0);
self.inv[n]
}
pub fn fact(&self, n: usize) -> ModInt<T> {
self.fact[n]
}
pub fn ifact(&self, n: usize) -> ModInt<T> {
self.ifact[n]
}
pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[n - k]
}
pub fn comb(&self, n: usize, k: usize) -> ModInt<T> {
if k > n {
return ModInt::zero();
}
self.fact[n] * self.ifact[k] * self.ifact[n - k]
}
}
}
// ---------- end Precalc ----------
use modint::*;
type M = ModInt<Mod>;
// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
macro_rules! input {
(source = $s:expr, $($r:tt)*) => {
let mut iter = $s.split_whitespace();
input_inner!{iter, $($r)*}
};
($($r:tt)*) => {
let s = {
use std::io::Read;
let mut s = String::new();
std::io::stdin().read_to_string(&mut s).unwrap();
s
};
let mut iter = s.split_whitespace();
input_inner!{iter, $($r)*}
};
}
macro_rules! input_inner {
($iter:expr) => {};
($iter:expr, ) => {};
($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
let $var = read_value!($iter, $t);
input_inner!{$iter $($r)*}
};
}
macro_rules! read_value {
($iter:expr, ( $($t:tt),* )) => {
( $(read_value!($iter, $t)),* )
};
($iter:expr, [ $t:tt ; $len:expr ]) => {
(0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
};
($iter:expr, chars) => {
read_value!($iter, String).chars().collect::<Vec<char>>()
};
($iter:expr, bytes) => {
read_value!($iter, String).bytes().collect::<Vec<u8>>()
};
($iter:expr, usize1) => {
read_value!($iter, usize) - 1
};
($iter:expr, $t:ty) => {
$iter.next().unwrap().parse::<$t>().expect("Parse error")
};
}
// ---------- end input macro ----------
use std::collections::*;
use std::io::Write;
type Map<K, V> = BTreeMap<K, V>;
type Set<T> = BTreeSet<T>;
type Deque<T> = VecDeque<T>;
fn run() {
let mut trans = Map::new();
for l in 1..=3 {
for r in 1..=3 {
for bit in 0usize..(1 << (l * r)) {
let mut dsu = DSU::new(l + r);
let mut g = maxflow::Graph::new(l + r + 2);
let src = l + r;
let dst = src + 1;
for i in 0..l {
for j in 0..r {
let x = i * r + j;
if bit >> x & 1 == 1 {
dsu.unite(i, l + j);
g.add_edge(i, l + j, 1u32);
}
}
}
for i in 0..l {
g.add_edge(src, i, 1);
}
for i in 0..r {
g.add_edge(l + i, dst, 1);
}
if dsu.size(0) == l + r {
let cnt = bit.count_ones() as usize;
let f = g.flow(src, dst) as usize;
if cnt <= f + 2 {
*trans.entry((l, r, cnt, f)).or_insert(M::zero()) += M::one();
}
}
}
}
}
input!(n: usize, m: usize, k: usize);
let pc = precalc::Precalc::new(n + m + k);
let mut dp = Map::new();
for l in 0..3 {
for r in 0..3 {
if k - 2 + l <= n && k - 2 + r <= n {
dp.insert(
(k - 2 + l, k - 2 + r, k, k - 2),
pc.comb(n, k - 2 + l) * pc.comb(m, k - 2 + r),
);
}
}
}
let mut ans = M::zero();
while let Some((&key, &value)) = dp.iter().next_back() {
dp.remove(&key);
if key == (0, 0, 0, 0) {
ans += value;
}
let (n, m, e, f) = key;
if e < f || f + 2 < e || f > n.min(m) {
continue;
}
for (&(a, b, c, d), &w) in trans.iter() {
if n >= a && m >= b && e >= c && f >= d {
*dp.entry((n - a, m - b, e - c, f - d)).or_insert(M::zero()) +=
pc.comb(n - 1, a - 1) * pc.comb(m, b) * w * value;
}
}
}
println!("{}", ans);
}
fn main() {
run();
}