結果

問題 No.1847 Good Sequence
ユーザー koba-e964koba-e964
提出日時 2022-02-20 03:40:16
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 495 ms / 3,000 ms
コード長 6,566 bytes
コンパイル時間 12,888 ms
コンパイル使用メモリ 391,068 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-06-29 10:44:36
合計ジャッジ時間 17,384 ms
ジャッジサーバーID
(参考情報)
judge4 / judge2
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ファイルパターン 結果
other AC * 41
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ソースコード

diff #
プレゼンテーションモードにする

use std::cmp::*;
// 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 ; $len:expr ]) => {
(0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
};
($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> ::std::fmt::Debug for ModInt<M> {
fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
let (mut a, mut b, _) = red(self.x, M::m());
if b < 0 {
a = -a;
b = -b;
}
write!(f, "{}/{}", a, b)
}
}
impl<M: Mod> From<i64> for ModInt<M> {
fn from(x: i64) -> Self { Self::new(x) }
}
// Finds the simplest fraction x/y congruent to r mod p.
// The return value (x, y, z) satisfies x = y * r + z * p.
fn red(r: i64, p: i64) -> (i64, i64, i64) {
if r.abs() <= 10000 {
return (r, 1, 0);
}
let mut nxt_r = p % r;
let mut q = p / r;
if 2 * nxt_r >= r {
nxt_r -= r;
q += 1;
}
if 2 * nxt_r <= -r {
nxt_r += r;
q -= 1;
}
let (x, z, y) = red(nxt_r, r);
(x, y - q * z, z)
}
} // 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
}
fn main() {
input! {
l: i64, n: usize, m: usize,
k: [usize; m],
}
let mut pop = vec![false; n];
for k in k {
pop[k - 1] = true;
}
let mut mat = vec![vec![MInt::new(0); 2 + n * (n + 1)]; 2 + n * (n + 1)];
for i in 0..n {
mat[0][2 + i * (n + 1)] += 1;
mat[1][1] += 1;
}
for i in 0..n {
for j in 0..n + 1 {
let v = 2 + i * (n + 1) + j;
for x in 0..n {
if i == x {
mat[v][2 + i * (n + 1) + min(j + 1, n)]
+= 1;
} else if j == i && pop[j] {
mat[v][1] += 1;
} else {
mat[v][2 + x * (n + 1)] += 1;
}
}
}
}
let pw = squpow(&mat, l);
let mut tot = pw[0][1];
for i in 0..n {
if pop[i] {
tot += pw[0][2 + i * (n + 1) + i];
}
}
println!("{}", tot);
}
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