結果
問題 | No.1222 -101 |
ユーザー |
|
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 35 |
ソースコード
#[allow(unused_imports)]use std::cmp::*;#[allow(unused_imports)]use std::collections::*;use std::io::{Write, BufWriter};// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8macro_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/3968098mod 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 >= 0pub 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_intmacro_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 { $modulo } }}}const MOD: i64 = 1_000_000_007;define_mod!(P, MOD);type MInt = mod_int::ModInt<P>;fn dfs(g: &[Vec<(usize, i32)>], v: usize,vis: &mut [bool], pot: &mut [i32], cur: i32) -> Result<i64, ()> {if vis[v] {return [Err(()), Ok(0)][usize::from(cur == pot[v])];}vis[v] = true;pot[v] = cur;let mut sum = 1;for &(w, c) in &g[v] {let sub = dfs(g, w, vis, pot, cur * c)?;sum += sub;}Ok(sum)}// The author read the editorial.// Tags: dp-with-intervals, atypical-transitions, dp-optimizationfn solve() {let out = std::io::stdout();let mut out = BufWriter::new(out.lock());macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}#[allow(unused)]macro_rules! putvec {($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: -1let 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: -1let 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 MBlet thd = std::thread::Builder::new().stack_size(stack_size);thd.spawn(|| solve()).unwrap().join().unwrap();}