#516607 (Rust) No.1124 Earthquake Safety

• 問題: No.1124 Earthquake Safety
• ユーザー: akakimidori
• 提出日時: 2020-07-22 23:04:03
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 324 ms / 3,000 ms
• コード長: 12,587 bytes
• コンパイル時間: 12,396 ms
• コンパイル使用メモリ: 378,488 KB
• 実行使用メモリ: 48,596 KB
• 最終ジャッジ日時: 2024-06-23 00:20:12
• 合計ジャッジ時間: 22,783 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	2 ms; 5,248 KB
testcase_03	AC	1 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	5 ms; 5,376 KB
testcase_08	AC	105 ms; 15,680 KB
testcase_09	AC	267 ms; 44,200 KB
testcase_10	AC	134 ms; 43,452 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	309 ms; 44,220 KB
testcase_15	AC	287 ms; 44,224 KB
testcase_16	AC	324 ms; 44,352 KB
testcase_17	AC	228 ms; 44,360 KB
testcase_18	AC	221 ms; 44,220 KB
testcase_19	AC	219 ms; 44,220 KB
testcase_20	AC	204 ms; 44,056 KB
testcase_21	AC	213 ms; 44,220 KB
testcase_22	AC	207 ms; 44,224 KB
testcase_23	AC	195 ms; 44,732 KB
testcase_24	AC	194 ms; 43,708 KB
testcase_25	AC	184 ms; 43,836 KB
testcase_26	AC	188 ms; 43,712 KB
testcase_27	AC	181 ms; 43,712 KB
testcase_28	AC	181 ms; 44,220 KB
testcase_29	AC	185 ms; 44,988 KB
testcase_30	AC	179 ms; 44,988 KB
testcase_31	AC	185 ms; 44,992 KB
testcase_32	AC	193 ms; 45,128 KB
testcase_33	AC	169 ms; 43,580 KB
testcase_34	AC	162 ms; 43,548 KB
testcase_35	AC	173 ms; 43,580 KB
testcase_36	AC	164 ms; 43,580 KB
testcase_37	AC	185 ms; 45,860 KB
testcase_38	AC	178 ms; 45,372 KB
testcase_39	AC	167 ms; 45,116 KB
testcase_40	AC	172 ms; 46,400 KB
testcase_41	AC	170 ms; 45,368 KB
testcase_42	AC	172 ms; 46,268 KB
testcase_43	AC	177 ms; 47,292 KB
testcase_44	AC	178 ms; 47,036 KB
testcase_45	AC	169 ms; 46,264 KB
testcase_46	AC	177 ms; 46,884 KB
testcase_47	AC	183 ms; 46,144 KB
testcase_48	AC	197 ms; 46,108 KB
testcase_49	AC	227 ms; 48,596 KB
testcase_50	AC	1 ms; 5,376 KB
testcase_51	AC	1 ms; 5,376 KB
testcase_52	AC	1 ms; 5,376 KB
testcase_53	AC	1 ms; 5,376 KB
testcase_54	AC	1 ms; 5,376 KB
testcase_55	AC	1 ms; 5,376 KB
testcase_56	AC	1 ms; 5,376 KB
testcase_57	AC	1 ms; 5,376 KB

ソースコード

// ---------- begin Rerooting ----------
pub trait RerootingOperator {
    type Value: Clone;
    type Edge: Clone;
    fn init(&mut self, v: usize) -> Self::Value;
    fn merge(&mut self, p: &Self::Value, c: &Self::Value, e: &Self::Edge) -> Self::Value;
}

pub struct Rerooting<R: RerootingOperator> {
    manager: R,
    size: usize,
    edge: Vec<(usize, usize, R::Edge, R::Edge)>,
}

impl<R: RerootingOperator> Rerooting<R> {
    pub fn new(size: usize, manager: R) -> Self {
        Rerooting {
            manager: manager,
            size: size,
            edge: vec![],
        }
    }
    #[allow(dead_code)]
    pub fn add_edge(&mut self, a: usize, b: usize, cost: R::Edge) {
        assert!(a < self.size && b < self.size && a != b);
        self.add_edge_bi(a, b, cost.clone(), cost);
    }
    #[allow(dead_code)]
    pub fn add_edge_bi(&mut self, a: usize, b: usize, ab: R::Edge, ba: R::Edge) {
        assert!(a < self.size && b < self.size && a != b);
        self.edge.push((a, b, ab, ba));
    }
    pub fn solve(&mut self) -> Vec<R::Value> {
        let size = self.size;
        let mut graph = vec![vec![]; size];
        for e in self.edge.iter() {
            graph[e.0].push((e.1, e.2.clone()));
            graph[e.1].push((e.0, e.3.clone()));
        }
        let root = 0;
        let mut topo = vec![];
        let mut parent = vec![root; size];
        let mut stack = vec![root];
        let mut parent_edge: Vec<Option<R::Edge>> = (0..size).map(|_| None).collect();
        while let Some(v) = stack.pop() {
            topo.push(v);
            if let Some(k) = graph[v].iter().position(|e| e.0 == parent[v]) {
                let (_, c) = graph[v].remove(k);
                parent_edge[v] = Some(c);
            }
            for e in graph[v].iter() {
                parent[e.0] = v;
                stack.push(e.0);
            }
        }
        assert!(topo.len() == size);
        let manager = &mut self.manager;
        let mut down: Vec<_> = (0..size).map(|v| manager.init(v)).collect();
        for &v in topo.iter().rev() {
            for e in graph[v].iter() {
                down[v] = manager.merge(&down[v], &down[e.0], &e.1);
            }
        }
        let mut up: Vec<_> = (0..size).map(|v| manager.init(v)).collect();
        let mut stack = vec![];
        for &v in topo.iter() {
            if let Some(e) = parent_edge[v].take() {
                let ini = manager.init(v);
                up[v] = manager.merge(&ini, &up[v], &e);
            }
            if !graph[v].is_empty() {
                stack.push((graph[v].as_slice(), up[v].clone()));
                while let Some((g, val)) = stack.pop() {
                    if g.len() == 1 {
                        up[g[0].0] = val;
                    } else {
                        let m = g.len() / 2;
                        let (a, b) = g.split_at(m);
                        for a in [(a, b), (b, a)].iter() {
                            let mut p = val.clone();
                            for a in a.0.iter() {
                                p = manager.merge(&p, &down[a.0], &a.1);
                            }
                            stack.push((a.1, p));
                        }
                    }
                }
            }
            for e in graph[v].iter() {
                up[v] = manager.merge(&up[v], &down[e.0], &e.1);
            }
        }
        up
    }
}
// ---------- end Rerooting ----------
// ---------- 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 ModularInteger<T>(pub u32, PhantomData<T>);

    impl<T> Clone for ModularInteger<T> {
        fn clone(&self) -> Self {
            ModularInteger::new_unchecked(self.0)
        }
    }

    impl<T> Copy for ModularInteger<T> {}

    impl<T: Modulo> Add for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn add(self, rhs: Self) -> Self::Output {
            let mut d = self.0 + rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModularInteger::new_unchecked(d)
        }
    }

    impl<T: Modulo> AddAssign for ModularInteger<T> {
        fn add_assign(&mut self, rhs: Self) {
            *self = *self + rhs;
        }
    }

    impl<T: Modulo> Sub for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn sub(self, rhs: Self) -> Self::Output {
            let mut d = T::modulo() + self.0 - rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModularInteger::new_unchecked(d)
        }
    }

    impl<T: Modulo> SubAssign for ModularInteger<T> {
        fn sub_assign(&mut self, rhs: Self) {
            *self = *self - rhs;
        }
    }

    impl<T: Modulo> Mul for ModularInteger<T> {
        type Output = ModularInteger<T>;
        fn mul(self, rhs: Self) -> Self::Output {
            let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
            ModularInteger::new_unchecked(v as u32)
        }
    }

    impl<T: Modulo> MulAssign for ModularInteger<T> {
        fn mul_assign(&mut self, rhs: Self) {
            *self = *self * rhs;
        }
    }

    impl<T: Modulo> Neg for ModularInteger<T> {
        type Output = ModularInteger<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 ModularInteger<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 ModularInteger<T> {
        type Err = std::num::ParseIntError;
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            let val = s.parse::<u32>()?;
            Ok(ModularInteger::new(val))
        }
    }

    impl<T: Modulo> From<usize> for ModularInteger<T> {
        fn from(val: usize) -> ModularInteger<T> {
            ModularInteger::new_unchecked((val % T::modulo() as usize) as u32)
        }
    }

    impl<T: Modulo> From<i64> for ModularInteger<T> {
        fn from(val: i64) -> ModularInteger<T> {
            let m = T::modulo() as i64;
            ModularInteger::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModularInteger<T> {
        pub fn new_unchecked(d: u32) -> Self {
            ModularInteger(d, PhantomData)
        }
        pub fn zero() -> Self {
            ModularInteger::new_unchecked(0)
        }
        pub fn one() -> Self {
            ModularInteger::new_unchecked(1)
        }
        pub fn is_zero(&self) -> bool {
            self.0 == 0
        }
    }

    #[allow(dead_code)]
    impl<T: Modulo> ModularInteger<T> {
        pub fn new(d: u32) -> Self {
            ModularInteger::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 Precalc ----------
mod precalc {
    use super::modint::*;
    #[allow(dead_code)]
    pub struct Precalc<T> {
        inv: Vec<ModularInteger<T>>,
        fact: Vec<ModularInteger<T>>,
        ifact: Vec<ModularInteger<T>>,
    }
    #[allow(dead_code)]
    impl<T: Modulo> Precalc<T> {
        pub fn new(n: usize) -> Precalc<T> {
            let mut inv = vec![ModularInteger::one(); n + 1];
            let mut fact = vec![ModularInteger::one(); n + 1];
            let mut ifact = vec![ModularInteger::one(); n + 1];
            for i in 2..(n + 1) {
                fact[i] = fact[i - 1] * ModularInteger::new_unchecked(i as u32);
            }
            ifact[n] = fact[n].inv();
            if n > 0 {
                inv[n] = ifact[n] * fact[n - 1];
            }
            for i in (1..n).rev() {
                ifact[i] = ifact[i + 1] * ModularInteger::new_unchecked((i + 1) as u32);
                inv[i] = ifact[i] * fact[i - 1];
            }
            Precalc {
                inv: inv,
                fact: fact,
                ifact: ifact,
            }
        }
        pub fn inv(&self, n: usize) -> ModularInteger<T> {
            assert!(n > 0);
            self.inv[n]
        }
        pub fn fact(&self, n: usize) -> ModularInteger<T> {
            self.fact[n]
        }
        pub fn ifact(&self, n: usize) -> ModularInteger<T> {
            self.ifact[n]
        }
        pub fn perm(&self, n: usize, k: usize) -> ModularInteger<T> {
            if k > n {
                return ModularInteger::zero();
            }
            self.fact[n] * self.ifact[n - k]
        }
        pub fn comb(&self, n: usize, k: usize) -> ModularInteger<T> {
            if k > n {
                return ModularInteger::zero();
            }
            self.fact[n] * self.ifact[k] * self.ifact[n - k]
        }
    }
}
// ---------- end Precalc ----------
//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
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")
    };
}

//

use modint::*;
type ModInt = ModularInteger<Mod>;

struct R {
    inv: ModInt,
}

impl RerootingOperator for R {
    // P^2, sum P, PxPy
    type Value = (ModInt, ModInt, ModInt);
    type Edge = ();
    fn init(&mut self, _v: usize) -> Self::Value {
        (ModInt::one(), ModInt::one(), ModInt::zero())
    }
    fn merge(&mut self, p: &Self::Value, c: &Self::Value, _e: &Self::Edge) -> Self::Value {
        (p.0 + self.inv * c.0, p.1 + self.inv * c.1, p.2 + self.inv * c.2 + p.1 * c.1)
    }
}

fn run() {
    input! {
        n: usize,
        e: [(usize1, usize1); n - 1],
    }
    let mut solver = Rerooting::new(n, R{inv: ModInt::new(2).inv()});
    for (a, b) in e {
        solver.add_edge(a, b, ());
    }
    let ans = solver.solve().into_iter().fold(ModInt::zero(), |s, a| s + a.0 + a.2) * ModInt::new(2).pow((n - 1) as u64);
    println!("{}", ans);
}

fn main() {
    run();
}