結果

問題 No.1411 Hundreds of Conditions Sequences
ユーザー ngtkanangtkana
提出日時 2020-12-02 00:19:33
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 668 ms / 2,000 ms
コード長 19,830 bytes
コンパイル時間 25,298 ms
コンパイル使用メモリ 401,432 KB
実行使用メモリ 23,228 KB
最終ジャッジ日時 2024-09-22 10:55:25
合計ジャッジ時間 36,778 ms
ジャッジサーバーID
(参考情報)
judge5 / judge4
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 * 62
権限があれば一括ダウンロードができます
コンパイルメッセージ
warning: unused imports: `Leaf`, `Tuple`, `VecLen`
   --> src/main.rs:376:37
    |
376 |         pub use self::multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen};
    |                                     ^^^^                                 ^^^^^  ^^^^^^
    |
    = note: `#[warn(unused_imports)]` on by default

warning: unused import: `with_str`
   --> src/main.rs:631:35
    |
631 |     pub use self::i::{with_stdin, with_str};
    |                                   ^^^^^^^^

warning: unused imports: `ParserTuple`, `Parser`, `RawTuple`, `Token`, `Usize1`
   --> src/main.rs:634:28
    |
634 |         pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
    |                            ^^^^^^  ^^^^^^^^^^^  ^^^^^^^^  ^^^^^  ^^^^^^

ソースコード

diff #
プレゼンテーションモードにする

use std::collections::HashMap;
type Fp = fp::F1000000007;
fn main() {
let mut buf = ngtio::with_stdin();
let n = buf.usize();
let a = buf.vec::<u64>(n);
let div = a
.iter()
.map(|&x| factorize::factorize(x))
.collect::<Vec<_>>();
let cnt = {
let mut cnt = HashMap::new();
for &(p, m) in div.iter().flatten() {
let m = m as usize;
let vec = cnt.entry(p).or_insert(Vec::new());
while vec.len() <= m {
vec.push(0);
}
vec[m] += 1;
}
cnt
};
let prod = a.iter().map(|&x| Fp::new(x as i64)).product::<Fp>();
let ratio = cnt
.iter()
.map(|(&p, v)| Fp::new(p as i64).pow(weight(v)).inv())
.product::<Fp>();
for (div, &x) in div.iter().zip(a.iter()) {
let ratio = ratio
* div
.iter()
.copied()
.map(|(p, m)| {
let mut v = cnt.get(&p).unwrap().clone();
let orig = weight(&v);
v[m as usize] -= 1;
let new = weight(&v);
Fp::new(p as i64).pow(orig - new)
})
.product::<Fp>();
let ans = prod * Fp::new(x as i64).inv() * (Fp::new(1) - ratio);
println!("{}", ans);
}
}
fn weight(v: &[u32]) -> u64 {
v.iter()
.enumerate()
.map(|(i, &x)| i as u64 * x as u64)
.sum::<u64>()
- v.iter()
.enumerate()
.rev()
.find(|&(_, &x)| x != 0)
.map_or(0, |(pos, _)| pos as u64)
}
// factorize {{{
#[allow(dead_code)]
mod factorize {
pub fn factorize(mut n: u64) -> Vec<(u64, u32)> {
let mut vec = Vec::new();
for p in 2.. {
if n < p * p {
break;
}
if n % p == 0 {
let mut m = 0;
while n % p == 0 {
n /= p;
m += 1;
}
vec.push((p, m));
}
}
if n != 1 {
vec.push((n, 1));
}
vec
}
}
// }}}
// fp {{{
#[allow(dead_code)]
mod fp {
mod arith {
use super::{Fp, Mod};
use std::ops::*;
impl<T: Mod> Add for Fp<T> {
type Output = Self;
fn add(self, rhs: Self) -> Self {
let res = self.0 + rhs.0;
Self::unchecked(if T::MOD <= res { res - T::MOD } else { res })
}
}
impl<T: Mod> Sub for Fp<T> {
type Output = Self;
fn sub(self, rhs: Self) -> Self {
let res = self.0 - rhs.0;
Self::unchecked(if res < 0 { res + T::MOD } else { res })
}
}
impl<T: Mod> Mul for Fp<T> {
type Output = Self;
fn mul(self, rhs: Self) -> Self {
Self::new(self.0 * rhs.0)
}
}
#[allow(clippy::suspicious_arithmetic_impl)]
impl<T: Mod> Div for Fp<T> {
type Output = Self;
fn div(self, rhs: Self) -> Self {
self * rhs.inv()
}
}
impl<M: Mod> Neg for Fp<M> {
type Output = Self;
fn neg(self) -> Self {
if self.0 == 0 {
Self::unchecked(0)
} else {
Self::unchecked(M::MOD - self.0)
}
}
}
impl<M: Mod> Neg for &Fp<M> {
type Output = Fp<M>;
fn neg(self) -> Self::Output {
if self.0 == 0 {
Fp::unchecked(0)
} else {
Fp::unchecked(M::MOD - self.0)
}
}
}
macro_rules! forward_assign_biop {
($(impl $trait:ident, $fn_assign:ident, $fn:ident)*) => {
$(
impl<M: Mod> $trait for Fp<M> {
fn $fn_assign(&mut self, rhs: Self) {
*self = self.$fn(rhs);
}
}
)*
};
}
forward_assign_biop! {
impl AddAssign, add_assign, add
impl SubAssign, sub_assign, sub
impl MulAssign, mul_assign, mul
impl DivAssign, div_assign, div
}
macro_rules! forward_ref_binop {
($(impl $imp:ident, $method:ident)*) => {
$(
impl<'a, T: Mod> $imp<Fp<T>> for &'a Fp<T> {
type Output = Fp<T>;
fn $method(self, other: Fp<T>) -> Self::Output {
$imp::$method(*self, other)
}
}
impl<'a, T: Mod> $imp<&'a Fp<T>> for Fp<T> {
type Output = Fp<T>;
fn $method(self, other: &Fp<T>) -> Self::Output {
$imp::$method(self, *other)
}
}
impl<'a, T: Mod> $imp<&'a Fp<T>> for &'a Fp<T> {
type Output = Fp<T>;
fn $method(self, other: &Fp<T>) -> Self::Output {
$imp::$method(*self, *other)
}
}
)*
};
}
forward_ref_binop! {
impl Add, add
impl Sub, sub
impl Mul, mul
impl Div, div
}
}
use std::{
fmt::{Debug, Display},
hash::Hash,
iter,
marker::PhantomData,
ops,
};
// NOTE: `crate::`
crate::define_fp!(pub F998244353, Mod998244353, 998244353);
crate::define_fp!(pub F1000000007, Mod1000000007, 1000000007);
#[derive(Clone, PartialEq, Copy, Eq, Hash)]
pub struct Fp<T>(i64, PhantomData<T>);
pub trait Mod: Debug + Clone + PartialEq + Copy + Eq + Hash {
const MOD: i64;
}
impl<T: Mod> Fp<T> {
pub fn new(mut x: i64) -> Self {
x %= T::MOD;
Self::unchecked(if x < 0 { x + T::MOD } else { x })
}
pub fn into_inner(self) -> i64 {
self.0
}
pub fn r#mod() -> i64 {
T::MOD
}
pub fn inv(self) -> Self {
assert_ne!(self.0, 0, "Zero division");
let (sign, x) = if self.0 * 2 < T::MOD {
(1, self.0)
} else {
(-1, T::MOD - self.0)
};
let (g, _a, b) = ext_gcd(T::MOD, x);
let ans = sign * b;
assert_eq!(g, 1);
Self::unchecked(if ans < 0 { ans + T::MOD } else { ans })
}
pub fn frac(x: i64, y: i64) -> Self {
Fp::new(x) / Fp::new(y)
}
pub fn pow(mut self, mut p: u64) -> Self {
let mut ans = Fp::new(1);
while p != 0 {
if p % 2 == 1 {
ans *= self;
}
self *= self;
p /= 2;
}
ans
}
fn unchecked(x: i64) -> Self {
Self(x, PhantomData)
}
}
impl<T: Mod> iter::Sum<Fp<T>> for Fp<T> {
fn sum<I>(iter: I) -> Self
where
I: iter::Iterator<Item = Fp<T>>,
{
iter.fold(Fp::new(0), ops::Add::add)
}
}
impl<'a, T: 'a + Mod> iter::Sum<&'a Fp<T>> for Fp<T> {
fn sum<I>(iter: I) -> Self
where
I: iter::Iterator<Item = &'a Fp<T>>,
{
iter.fold(Fp::new(0), ops::Add::add)
}
}
impl<T: Mod> iter::Product<Fp<T>> for Fp<T> {
fn product<I>(iter: I) -> Self
where
I: iter::Iterator<Item = Fp<T>>,
{
iter.fold(Self::new(1), ops::Mul::mul)
}
}
impl<'a, T: 'a + Mod> iter::Product<&'a Fp<T>> for Fp<T> {
fn product<I>(iter: I) -> Self
where
I: iter::Iterator<Item = &'a Fp<T>>,
{
iter.fold(Self::new(1), ops::Mul::mul)
}
}
impl<T: Mod> Debug for Fp<T> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
let (x, y, _z) = reduce(self.0, T::MOD);
let (x, y) = match y.signum() {
1 => (x, y),
-1 => (-x, -y),
_ => unreachable!(),
};
if y == 1 {
write!(f, "{}", x)
} else {
write!(f, "{}/{}", x, y)
}
}
}
impl<T: Mod> Display for Fp<T> {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
write!(f, "{}", self.0)
}
}
// ax + by = gcd(x, y) (a, b) (g, a, b)
//
// | 0 -x | | y -x | | x 0 |
// | 1 b | = | a b | | y 1 |
fn ext_gcd(x: i64, y: i64) -> (i64, i64, i64) {
let (b, g) = {
let mut x = x;
let mut y = y;
let mut u = 0;
let mut v = 1;
while x != 0 {
let q = y / x;
y -= q * x;
v -= q * u;
std::mem::swap(&mut x, &mut y);
std::mem::swap(&mut u, &mut v);
}
(v, y)
};
assert_eq!((g - b * y) % x, 0);
let a = (g - b * y) / x;
(g, a, b)
}
fn reduce(a: i64, m: i64) -> (i64, i64, i64) {
if a.abs() < 10_000 {
(a, 1, 0)
} else {
let mut q = m.div_euclid(a);
let mut r = m.rem_euclid(a);
if a <= 2 * r {
q += 1;
r -= a;
}
let (x, z, y) = reduce(r, a);
(x, y - q * z, z)
}
}
#[macro_export]
macro_rules! define_fp {
($vis:vis $fp:ident, $t:ident, $mod:expr) => {
#[derive(Debug, Clone, PartialEq, Copy, Eq, Hash)]
$vis struct $t;
// NOTE: `$crate::`
impl Mod for $t {
const MOD: i64 = $mod;
}
// NOTE: `$crate::`
$vis type $fp = Fp<$t>;
}
}
}
// }}}
// ngtio {{{
#[allow(dead_code)]
mod ngtio {
#![warn(missing_docs)]
mod i {
use std::{
io::{self, BufRead},
iter,
};
pub use self::multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen};
pub use self::token::{Token, Usize1};
pub fn with_stdin() -> Tokenizer<io::BufReader<io::Stdin>> {
io::BufReader::new(io::stdin()).tokenizer()
}
pub fn with_str(src: &str) -> Tokenizer<&[u8]> {
src.as_bytes().tokenizer()
}
pub struct Tokenizer<S: BufRead> {
queue: Vec<String>, // FIXME: String
scanner: S,
}
macro_rules! prim_method {
($name:ident: $T:ty) => {
#[allow(missing_docs)]
pub fn $name(&mut self) -> $T {
<$T>::leaf().parse(self)
}
};
($name:ident) => {
prim_method!($name: $name);
};
}
macro_rules! prim_methods {
($name:ident: $T:ty; $($rest:tt)*) => {
prim_method!($name:$T);
prim_methods!($($rest)*);
};
($name:ident; $($rest:tt)*) => {
prim_method!($name);
prim_methods!($($rest)*);
};
() => ()
}
impl<S: BufRead> Tokenizer<S> {
pub fn token(&mut self) -> String {
self.load();
self.queue.pop().expect("")
}
pub fn new(scanner: S) -> Self {
Self {
queue: Vec::new(),
scanner,
}
}
fn load(&mut self) {
while self.queue.is_empty() {
let mut s = String::new();
let length = self.scanner.read_line(&mut s).unwrap(); // UTF-8
if length == 0 {
break;
}
self.queue = s.split_whitespace().rev().map(str::to_owned).collect();
}
}
pub fn skip_line(&mut self) {
assert!(
self.queue.is_empty(),
": {:?}",
&self.queue
);
self.load();
}
pub fn end(&mut self) {
self.load();
assert!(self.queue.is_empty(), "");
}
pub fn parse<T: Token>(&mut self) -> T::Output {
T::parse(&self.token())
}
pub fn parse_collect<T: Token, B>(&mut self, n: usize) -> B
where
B: iter::FromIterator<T::Output>,
{
iter::repeat_with(|| self.parse::<T>()).take(n).collect()
}
pub fn tuple<T: RawTuple>(&mut self) -> <T::LeafTuple as Parser>::Output {
T::leaf_tuple().parse(self)
}
pub fn vec<T: Token>(&mut self, len: usize) -> Vec<T::Output> {
T::leaf().vec(len).parse(self)
}
pub fn vec_tuple<T: RawTuple>(
&mut self,
len: usize,
) -> Vec<<T::LeafTuple as Parser>::Output> {
T::leaf_tuple().vec(len).parse(self)
}
pub fn vec2<T: Token>(&mut self, height: usize, width: usize) -> Vec<Vec<T::Output>> {
T::leaf().vec(width).vec(height).parse(self)
}
pub fn vec2_tuple<T>(
&mut self,
height: usize,
width: usize,
) -> Vec<Vec<<T::LeafTuple as Parser>::Output>>
where
T: RawTuple,
{
T::leaf_tuple().vec(width).vec(height).parse(self)
}
prim_methods! {
u8; u16; u32; u64; u128; usize;
i8; i16; i32; i64; i128; isize;
char; string: String;
}
}
mod token {
use super::multi_token::Leaf;
use std::{any, fmt, marker, str};
pub trait Token: Sized {
type Output;
fn parse(s: &str) -> Self::Output;
fn leaf() -> Leaf<Self> {
Leaf(marker::PhantomData)
}
}
impl<T> Token for T
where
T: str::FromStr,
<T as str::FromStr>::Err: fmt::Debug,
{
type Output = T;
fn parse(s: &str) -> Self::Output {
s.parse().unwrap_or_else(|_| {
panic!("Parse error!: ({}: {})", s, any::type_name::<T>(),)
})
}
}
pub struct Usize1 {}
impl Token for Usize1 {
type Output = usize;
fn parse(s: &str) -> Self::Output {
usize::parse(s)
.checked_sub(1)
.expect("Parse error! (Zero substruction error of Usize1)")
}
}
}
mod multi_token {
use super::{Token, Tokenizer};
use std::{io::BufRead, iter, marker};
pub trait Parser: Sized {
type Output;
fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output;
fn vec(self, len: usize) -> VecLen<Self> {
VecLen { len, elem: self }
}
}
pub struct Leaf<T>(pub(super) marker::PhantomData<T>);
impl<T: Token> Parser for Leaf<T> {
type Output = T::Output;
fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> T::Output {
server.parse::<T>()
}
}
pub struct VecLen<T> {
pub len: usize,
pub elem: T,
}
impl<T: Parser> Parser for VecLen<T> {
type Output = Vec<T::Output>;
fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output {
iter::repeat_with(|| self.elem.parse(server))
.take(self.len)
.collect()
}
}
pub trait RawTuple {
type LeafTuple: Parser;
fn leaf_tuple() -> Self::LeafTuple;
}
pub trait ParserTuple {
type Tuple: Parser;
fn tuple(self) -> Self::Tuple;
}
pub struct Tuple<T>(pub T);
macro_rules! impl_tuple {
($($t:ident: $T:ident),*) => {
impl<$($T),*> Parser for Tuple<($($T,)*)>
where
$($T: Parser,)*
{
type Output = ($($T::Output,)*);
#[allow(unused_variables)]
fn parse<S: BufRead >(&self, server: &mut Tokenizer<S>) -> Self::Output {
match self {
Tuple(($($t,)*)) => {
($($t.parse(server),)*)
}
}
}
}
impl<$($T: Token),*> RawTuple for ($($T,)*) {
type LeafTuple = Tuple<($(Leaf<$T>,)*)>;
fn leaf_tuple() -> Self::LeafTuple {
Tuple(($($T::leaf(),)*))
}
}
impl<$($T: Parser),*> ParserTuple for ($($T,)*) {
type Tuple = Tuple<($($T,)*)>;
fn tuple(self) -> Self::Tuple {
Tuple(self)
}
}
};
}
impl_tuple!();
impl_tuple!(t1: T1);
impl_tuple!(t1: T1, t2: T2);
impl_tuple!(t1: T1, t2: T2, t3: T3);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6);
impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7);
impl_tuple!(
t1: T1,
t2: T2,
t3: T3,
t4: T4,
t5: T5,
t6: T6,
t7: T7,
t8: T8
);
}
trait Scanner: BufRead + Sized {
fn tokenizer(self) -> Tokenizer<Self> {
Tokenizer::new(self)
}
}
impl<R: BufRead> Scanner for R {}
}
pub use self::i::{with_stdin, with_str};
pub mod prelude {
pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
}
}
// }}}
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