結果

問題 No.621 3 x N グリッド上のドミノの置き方の数
ユーザー koba-e964koba-e964
提出日時 2021-10-16 16:50:54
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 124 ms / 3,000 ms
コード長 5,204 bytes
コンパイル時間 12,675 ms
コンパイル使用メモリ 385,620 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-09-17 19:28:32
合計ジャッジ時間 19,395 ms
ジャッジサーバーID
(参考情報)
judge2 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 66
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

use std::io::Read;
fn get_word() -> String {
let stdin = std::io::stdin();
let mut stdin=stdin.lock();
let mut u8b: [u8; 1] = [0];
loop {
let mut buf: Vec<u8> = Vec::with_capacity(16);
loop {
let res = stdin.read(&mut u8b);
if res.unwrap_or(0) == 0 || u8b[0] <= b' ' {
break;
} else {
buf.push(u8b[0]);
}
}
if buf.len() >= 1 {
let ret = String::from_utf8(buf).unwrap();
return ret;
}
}
}
#[allow(dead_code)]
fn get<T: std::str::FromStr>() -> T { get_word().parse().ok().unwrap() }
/// 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, 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)]
struct $struct_name {}
impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } }
}
}
const MOD: i64 = 1_000_000_007;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;
// Depends on MInt.rs
// Verified by: https://atcoder.jp/contests/abc199/submissions/22259436
fn squmul(a: &[Vec<MInt>], b: &[Vec<MInt>]) -> Vec<Vec<MInt>> {
let n = a.len();
let mut ret = vec![vec![MInt::new(0); n]; n];
for i in 0..n {
for j in 0..n {
for k in 0..n {
ret[i][k] += a[i][j] * b[j][k];
}
}
}
ret
}
fn squpow(a: &[Vec<MInt>], mut e: i64) -> Vec<Vec<MInt>> {
let n = a.len();
let mut sum = vec![vec![MInt::new(0); n]; n];
for i in 0..n { sum[i][i] = 1.into(); }
let mut cur = a.to_vec();
while e > 0 {
if e % 2 == 1 {
sum = squmul(&sum, &cur);
}
cur = squmul(&cur, &cur);
e /= 2;
}
sum
}
// Tags: matrix-multiplication
fn main() {
let n: i64 = get();
let mut mat = vec![vec![MInt::new(0); 64]; 64];
for pre in 0..8 {
for i in 0..8 {
for j in 0..8 {
if (i & j) != j { continue; }
let diff = i ^ j;
if (diff & 3) == 3 || (diff & 6) == 6 { continue; }
let x = 7 ^ j;
for &k in &[0, 3, 6] {
if (x & k) == k && (diff & pre) == 0 {
mat[8 * i + pre][(7 - j - k) * 8 + (i ^ j)] += 1;
}
}
}
}
}
let ans = squpow(&mat, n);
let mut tot = MInt::new(0);
for &i in &[0, 1, 2, 4, 5] {
for &j in &[0, 1, 2, 4, 5] {
if (i & j) == 0 {
tot += ans[0][i * 8 + j];
}
}
}
println!("{}", tot);
}
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