#506107 (Rust) No.1103 Directed Length Sum

• 問題: No.1103 Directed Length Sum
• ユーザー: akakimidori
• 提出日時: 2020-07-03 21:58:59
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 814 ms / 3,000 ms
• コード長: 10,158 bytes
• コンパイル時間: 11,342 ms
• コンパイル使用メモリ: 393,208 KB
• 実行使用メモリ: 129,640 KB
• 最終ジャッジ日時: 2024-09-17 00:48:02
• 合計ジャッジ時間: 19,072 ms
• ジャッジサーバーID （参考情報）: judge3 / judge2

ファイルパターン	結果
sample	AC * 2
other	AC * 22

ソースコード

// ---------- 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 RuntimeMod;
    static mut RUNTIME_MOD: u32 = 0;
    impl Modulo for RuntimeMod {
        fn modulo() -> u32 {
            unsafe { RUNTIME_MOD }
        }
    }

    #[allow(dead_code)]
    impl RuntimeMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                RUNTIME_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)
        }
    }

    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)
        }
    }

    #[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: u32) -> 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() - 2)
        }
    }

    // ---------- begin Precalc ----------
    #[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 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 ----------
}
// ---------- begin Tree DP ----------
struct TreeDP<Edge, Value, Init, Merge> {
    size: usize,
    graph: Vec<Vec<(usize, Edge)>>,
    init: Init,
    merge: Merge,
    phantom: std::marker::PhantomData<Value>,
}

impl<Edge, Value, Init, Merge> TreeDP<Edge, Value, Init, Merge>
where Edge: Clone,
      Value: Clone,
      Init: Fn(usize) -> Value,
      Merge: Fn(Value, Value, &Edge) -> Value,
{
    fn new(size: usize, init: Init, merge: Merge) -> Self {
        TreeDP {
            size: size,
            graph: vec![vec![]; size],
            init: init,
            merge: merge,
            phantom: std::marker::PhantomData,
        }
    }
    fn add_edge(&mut self, a: usize, b: usize, c: Edge) {
        assert!(a < self.size && b < self.size && a != b);
        self.graph[a].push((b, c.clone()));
        self.graph[b].push((a, c));
    }
    fn solve(&self, root: usize) -> Value {
        let size = self.size;
        let graph = &self.graph;
        let mut topo = vec![];
        let mut parent = vec![root; size];
        let mut stack = vec![root];
        while let Some(v) = stack.pop() {
            topo.push(v);
            for e in graph[v].iter() {
                if e.0 != parent[v] {
                    parent[e.0] = v;
                    stack.push(e.0);
                }
            }
        }
        assert!(topo.len() == size);
        let mut dp: Vec<Option<Value>> = (0..size).map(|_| None).collect();
        for &v in topo.iter().rev() {
            let mut now = (self.init)(v);
            for u in graph[v].iter() {
                if u.0 == parent[v] {
                    continue;
                }
                let b = dp[u.0].take().unwrap();
                now = (self.merge)(now, b, &u.1);
            }
            dp[v] = Some(now);
        }
        dp[root].take().unwrap()
    }
}
// ---------- end Tree DP ----------
//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>;

fn run() {
    input! {
        n: usize,
        e: [(usize1, usize1); n - 1],
    }
    type T = (ModInt, ModInt, ModInt);
    type E = ();
    let init = |_v: usize| -> T {
        (ModInt::zero(), ModInt::zero(), ModInt::one())
    };
    let merge = |a: T, b: T, _c: &E| -> T {
        (a.0 + b.0 + b.1 + b.2, a.1 + b.1 + b.2, a.2 + b.2)
    };
    let mut solver = TreeDP::new(n, init, merge);
    let mut child = vec![false; n];
    for (a, b) in e {
        child[b] = true;
        solver.add_edge(a, b, ());
    }
    let root = child.iter().position(|c| !*c).unwrap();
    let ans = solver.solve(root).0;
    println!("{}", ans);
}

fn main() {
    run();
}