結果

問題 No.1222 -101
ユーザー koba-e964
提出日時 2020-10-15 00:02:24
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 187 ms / 2,000 ms
コード長 9,356 bytes
コンパイル時間 15,273 ms
コンパイル使用メモリ 379,188 KB
実行使用メモリ 38,392 KB
最終ジャッジ日時 2024-07-20 19:33:46
合計ジャッジ時間 20,098 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 * 4
other AC * 35
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

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::{Write, BufWriter};
// 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, [graph1; $len:expr]) => {{
let mut g = vec![vec![]; $len];
let ab = read_value!($next, [(usize1, usize1)]);
for (a, b) in ab {
g[a].push(b);
g[b].push(a);
}
g
}};
($next:expr, ( $($t:tt),* )) => {
( $(read_value!($next, $t)),* )
};
($next:expr, [ $t:tt ; $len:expr ]) => {
(0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
};
($next:expr, chars) => {
read_value!($next, String).chars().collect::<Vec<char>>()
};
($next:expr, usize1) => (read_value!($next, usize) - 1);
($next:expr, [ $t:tt ]) => {{
let len = read_value!($next, usize);
read_value!($next, [$t; len])
}};
($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}
#[allow(unused)]
macro_rules! debug {
($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap());
}
#[allow(unused)]
macro_rules! debugln {
($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap());
}
/// Verified by https://atcoder.jp/contests/arc093/submissions/3968098
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> ::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 { $modulo } }
}
}
const MOD: i64 = 1_000_000_007;
define_mod!(P, MOD);
type MInt = mod_int::ModInt<P>;
fn dfs(g: &[Vec<(usize, i32)>], v: usize,
vis: &mut [bool], pot: &mut [i32], cur: i32) -> Result<i64, ()> {
if vis[v] {
return [Err(()), Ok(0)][usize::from(cur == pot[v])];
}
vis[v] = true;
pot[v] = cur;
let mut sum = 1;
for &(w, c) in &g[v] {
let sub = dfs(g, w, vis, pot, cur * c)?;
sum += sub;
}
Ok(sum)
}
// The author read the editorial.
// Tags: dp-with-intervals, atypical-transitions, dp-optimization
fn solve() {
let out = std::io::stdout();
let mut out = BufWriter::new(out.lock());
macro_rules! puts {
($($format:tt)*) => (let _ = write!(out,$($format)*););
}
#[allow(unused)]
macro_rules! putvec {
($v:expr) => {
for i in 0..$v.len() {
puts!("{}{}", $v[i], if i + 1 == $v.len() {"\n"} else {" "});
}
}
}
input! {
n: usize, m: usize,
lrp: [(usize1, usize1, i32); m],
}
// First, we find in what positions 0 cannot be filled.
let mut non0 = vec![0; n + 1];
for &(l, r, p) in &lrp {
if p != 0 {
non0[l] += 1;
non0[r + 1] -= 1;
}
}
for i in 0..n {
non0[i + 1] += non0[i];
}
// Second, we need the array a and its cumulative max:
// a[r[k]] = if p[k] == 0 { l[k] } else { -inf }
// cum_a[i] := max { l[k] | r[k] < i, p[k] = 0}
// bias: -1
let mut a = vec![0; n];
let mut cum_a = vec![0; n + 1];
for i in 0..m {
let (l, r, p) = lrp[i];
a[r] = if p == 0 { l + 1 } else { 0 };
}
for i in 0..n {
cum_a[i + 1] = a[i];
cum_a[i + 1] = max(cum_a[i + 1], cum_a[i]);
}
// dp[i]: #{x | x[i] = 0, x is a 0-1 assignemnt satisfying certain conditions, with weight 2^{-count(x, 0)}}
// origin: -1
let mut dp = vec![MInt::new(0); n + 2];
let mut acc = vec![MInt::new(0); n + 2];
dp[0] += 1;
acc[0] += 1;
let inv2 = MInt::new(2).inv();
for i in 0..n + 1 {
if non0[i] > 0 {
acc[i + 1] = acc[i];
continue;
}
let val = acc[i] - if cum_a[i] == 0 {
MInt::new(0)
} else {
acc[cum_a[i] - 1]
};
dp[i + 1] = val * inv2;
acc[i + 1] = acc[i] + dp[i + 1];
}
// For a 0-1 assignment x, the number of corresponding arrays is
// 2^{-count(x, 0)} * 2^n * 2^{-#edges in mst of in constraints},
// if there are no contradictions in the constraints.
// We obtain the sum of 2^{-count(x, 0)} * 2^n, which, if multiplied by
// 2^{-#edges in mst of in constraints}, gives the overall answer.
// We unnecessarily counted the 0 at the sentinel at n (dp[n + 1]), so we have to
// multiply the answer by 2.
let mut g = vec![vec![]; n + 1];
for &(l, r, p) in &lrp {
if p != 0 {
g[l].push((r + 1, p));
g[r + 1].push((l, p));
}
}
let mut vis = vec![false; n + 1];
let mut pot = vec![0; n + 1];
let mut edges = 0;
for i in 0..n + 1 {
if vis[i] {
continue;
}
let res = dfs(&g, i, &mut vis, &mut pot, 1);
if res.is_err() {
puts!("0\n");
return;
}
let res = res.unwrap() - 1;
edges += res;
}
puts!("{}\n", dp[n + 1] * MInt::new(2).pow(n as i64 + 1) * inv2.pow(edges));
}
fn main() {
// In order to avoid potential stack overflow, spawn a new thread.
let stack_size = 104_857_600; // 100 MB
let thd = std::thread::Builder::new().stack_size(stack_size);
thd.spawn(|| solve()).unwrap().join().unwrap();
}
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