結果

問題 No.1275 綺麗な式
ユーザー akakimidoriakakimidori
提出日時 2020-10-30 22:27:30
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 1 ms / 2,000 ms
コード長 8,977 bytes
コンパイル時間 13,363 ms
コンパイル使用メモリ 379,648 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-22 01:41:05
合計ジャッジ時間 15,485 ms
ジャッジサーバーID
(参考情報)
judge5 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 2
other AC * 60
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

// ---------- begin Matrix ----------
#[allow(dead_code)]
mod matrix {
use std::ops::{Add, Mul};
pub trait SemiRing: Add<Output = Self> + Mul<Output = Self> + Copy {
fn zero() -> Self;
fn one() -> Self;
}
pub const SIZE: usize = 2;
#[derive(Clone)]
pub struct SquareMatrix<T: SemiRing> {
buf: [[T; SIZE]; SIZE],
}
impl<T: SemiRing> SquareMatrix<T> {
pub fn zero() -> Self {
let z = T::zero();
SquareMatrix {
buf: [[z; SIZE]; SIZE],
}
}
pub fn identity() -> Self {
let mut m = Self::zero();
for i in 0..SIZE {
m.buf[i][i] = T::one();
}
m
}
pub fn set_at(&mut self, i: usize, j: usize, v: T) {
self.buf[i][j] = v;
}
pub fn get_at(&self, i: usize, j: usize) -> T {
self.buf[i][j]
}
pub fn matmul(&self, rhs: &Self) -> Self {
let mut res = Self::zero();
for (x, a) in res.buf.iter_mut().zip(self.buf.iter()) {
for (a, b) in a.iter().zip(rhs.buf.iter()) {
for (x, b) in x.iter_mut().zip(b.iter()) {
*x = *x + *a * *b;
}
}
}
res
}
pub fn matadd(&self, rhs: &Self) -> Self {
let mut c = Self::zero();
for (c, (a, b)) in c.buf.iter_mut().zip(self.buf.iter().zip(rhs.buf.iter())) {
for (c, (a, b)) in c.iter_mut().zip(a.iter().zip(b.iter())) {
*c = *a + *b;
}
}
c
}
pub fn matpow(&self, mut n: usize) -> Self {
let mut t = Self::identity();
let mut s = self.clone();
while n > 0 {
if n & 1 == 1 {
t = t.matmul(&s);
}
s = s.matmul(&s);
n >>= 1;
}
t
}
}
}
// ---------- end Matrix ----------
// ---------- begin ModInt ----------
mod modint {
#[allow(dead_code)]
pub struct Mod;
impl ConstantModulo for Mod {
const MOD: u32 = 1_000_000_007;
}
#[allow(dead_code)]
pub struct StaticMod;
static mut STATIC_MOD: u32 = 0;
impl Modulo for StaticMod {
fn modulo() -> u32 {
unsafe { STATIC_MOD }
}
}
#[allow(dead_code)]
impl StaticMod {
pub fn set_modulo(p: u32) {
unsafe {
STATIC_MOD = p;
}
}
}
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 = T::modulo() + 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: 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)
}
}
#[allow(dead_code)]
pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 {
let mut t = 1 % m;
let mut s = r % m;
while n > 0 {
if n & 1 == 1 {
t = t * s % m;
}
s = s * s % m;
n >>= 1;
}
t
}
}
// ---------- end ModInt ----------
// ---------- 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 modint::*;
type M = ModInt<Mod>;
use matrix::*;
type Mat = SquareMatrix<M>;
impl SemiRing for M {
fn zero() -> Self {
M::zero()
}
fn one() -> Self {
M::one()
}
}
fn run() {
input! {
a: M,
b: M,
n: usize,
}
let mut mat = Mat::zero();
mat.set_at(0, 0, a * M::new(2));
mat.set_at(0, 1, -(a * a - b));
mat.set_at(1, 0, M::one());
let pow = mat.matpow(n);
let ans = pow.get_at(1, 0) * M::new(2) * a + pow.get_at(1, 1) * M::new(2);
println!("{}", ans);
}
fn main() {
run();
}
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