結果
問題 | No.1411 Hundreds of Conditions Sequences |
ユーザー |
![]() |
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 62 |
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
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, addimpl SubAssign, sub_assign, subimpl MulAssign, mul_assign, mulimpl 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, addimpl Sub, subimpl Mul, mulimpl Div, div}}use std::{fmt::{Debug, Display},hash::Hash,iter,marker::PhantomData,ops,};// NOTE: `crate::` がないとうまく展開できません。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) -> SelfwhereI: 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) -> SelfwhereI: 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) -> SelfwhereI: 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) -> SelfwhereI: 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) なる、互いに素な (a, b) を一組探して、(g, a, b) を返します。//// | 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::` があるとうまく展開できません。impl Mod for $t {const MOD: i64 = $mod;}// NOTE: `$crate::` があるとうまく展開できません。$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 のみにすると速そうです。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("入力が終了したのですが。")}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(); // 入力が UTF-8 でないときにエラーだそうです。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(),"行の途中で呼ばないでいただきたいです。現在のトークンキュー: {:?}",&self.queue);self.load();}pub fn end(&mut self) {self.load();assert!(self.queue.is_empty(), "入力はまだあります!");}pub fn parse<T: Token>(&mut self) -> T::Output {T::parse(&self.token())}pub fn parse_collect<T: Token, B>(&mut self, n: usize) -> BwhereB: 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>>whereT: 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 TwhereT: 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};}}// }}}