結果
問題 | No.2435 Order All Company |
ユーザー | koba-e964 |
提出日時 | 2023-08-21 10:32:50 |
言語 | Rust (1.77.0 + proconio) |
結果 |
AC
|
実行時間 | 27 ms / 2,000 ms |
コード長 | 6,654 bytes |
コンパイル時間 | 19,373 ms |
コンパイル使用メモリ | 379,368 KB |
実行使用メモリ | 5,248 KB |
最終ジャッジ日時 | 2024-12-14 20:48:50 |
合計ジャッジ時間 | 16,354 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 1 ms
5,248 KB |
testcase_01 | AC | 1 ms
5,248 KB |
testcase_02 | AC | 1 ms
5,248 KB |
testcase_03 | AC | 1 ms
5,248 KB |
testcase_04 | AC | 2 ms
5,248 KB |
testcase_05 | AC | 27 ms
5,248 KB |
testcase_06 | AC | 27 ms
5,248 KB |
testcase_07 | AC | 17 ms
5,248 KB |
testcase_08 | AC | 26 ms
5,248 KB |
testcase_09 | AC | 27 ms
5,248 KB |
testcase_10 | AC | 2 ms
5,248 KB |
testcase_11 | AC | 1 ms
5,248 KB |
testcase_12 | AC | 2 ms
5,248 KB |
testcase_13 | AC | 2 ms
5,248 KB |
testcase_14 | AC | 18 ms
5,248 KB |
testcase_15 | AC | 20 ms
5,248 KB |
testcase_16 | AC | 15 ms
5,248 KB |
testcase_17 | AC | 27 ms
5,248 KB |
testcase_18 | AC | 13 ms
5,248 KB |
testcase_19 | AC | 11 ms
5,248 KB |
testcase_20 | AC | 12 ms
5,248 KB |
testcase_21 | AC | 13 ms
5,248 KB |
testcase_22 | AC | 18 ms
5,248 KB |
testcase_23 | AC | 8 ms
5,248 KB |
testcase_24 | AC | 14 ms
5,248 KB |
testcase_25 | AC | 18 ms
5,248 KB |
testcase_26 | AC | 15 ms
5,248 KB |
testcase_27 | AC | 18 ms
5,248 KB |
testcase_28 | AC | 12 ms
5,248 KB |
testcase_29 | AC | 15 ms
5,248 KB |
testcase_30 | AC | 15 ms
5,248 KB |
testcase_31 | AC | 1 ms
5,248 KB |
testcase_32 | AC | 1 ms
5,248 KB |
testcase_33 | AC | 1 ms
5,248 KB |
testcase_34 | AC | 1 ms
5,248 KB |
testcase_35 | AC | 4 ms
5,248 KB |
ソースコード
// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>() }; ($next:expr, usize1) => (read_value!($next, usize) - 1); ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); read_value!($next, [$t; len]) }}; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } /// Verified by https://atcoder.jp/contests/abc198/submissions/21774342 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> } impl<M: Mod> ModInt<M> { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl<M: Mod> Default for ModInt<M> { fn default() -> Self { Self::new_internal(0) } } impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl<M: Mod> Neg for ModInt<M> { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl<M> ::std::fmt::Display for ModInt<M> { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl<M: Mod> From<i64> for ModInt<M> { fn from(x: i64) -> Self { Self::new(x) } } } // mod mod_int macro_rules! define_mod { ($struct_name: ident, $modulo: expr) => { #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)] pub struct $struct_name {} impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } } } } const MOD: i64 = 998_244_353; define_mod!(P, MOD); type MInt = mod_int::ModInt<P>; // O(n^3) fn determinant(a: &[Vec<MInt>]) -> MInt { let n = a.len(); assert_eq!(a[0].len(), n); let mut a = a.to_vec(); let mut pos = vec![]; let mut r = 0; let mut ans = MInt::new(1); for i in 0..n { for j in 0..r { let idx = pos[j]; let val = a[i][idx]; for k in 0..n { a[i][k] = a[i][k] - a[j][k] * val; } } let mut c = 0; while c < n && a[i][c] == 0.into() { c += 1; } if c >= n { return MInt::new(0); } if r != i { a.swap(r, i); ans = -ans; } pos.push(c); let aic = a[r][c]; let aicinv = aic.inv(); a[r][c] = 1.into(); for j in c + 1..n { a[r][j] *= aicinv; } ans *= aic; for j in r + 1..n { let ajc = a[j][c]; a[j][c] = 0.into(); for k in c + 1..n { let val = ajc * a[r][k]; a[j][k] -= val; } } r += 1; } ans } // O(n^3) fn count_spanning_trees(mat: &[Vec<MInt>]) -> MInt { let n = mat.len(); let mut sub = vec![vec![MInt::new(0); n - 1]; n - 1]; for i in 0..n - 1 { let mut sum = MInt::new(0); for j in 0..n { if i != j { sum += mat[i][j]; if j < n - 1 { sub[i][j] = -mat[i][j]; } } } sub[i][i] = sum; } determinant(&sub) } // https://yukicoder.me/problems/no/2435 (3.5) // 包除原理を使えば 2^K <= 32 回の計算でできる。1 回の計算は行列木定理で O(N^3 + \sum t_i) できる。 // Tags: matrix-tree-theorem, counting-spanning-trees fn main() { input! { n: usize, k: usize, ab: [[(usize1, usize1)]; k], } let mut ans = MInt::new(0); for bits in 0usize..1 << k { let mut e = vec![vec![MInt::new(0); n]; n]; for i in 0..k { if (bits & 1 << i) == 0 { for &(a, b) in &ab[i] { e[a][b] += 1; e[b][a] += 1; } } } let sub = count_spanning_trees(&e); if bits.count_ones() % 2 == 1 { ans -= sub; } else { ans += sub; } } println!("{}", ans); }