#717072 (Rust) No.1364 [Renaming] Road to Cherry from Zelkova

• 問題: No.1364 [Renaming] Road to Cherry from Zelkova
• ユーザー: koba-e964
• 提出日時: 2021-11-17 20:40:23
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 189 ms / 2,500 ms
• コード長: 10,616 bytes
• コンパイル時間: 14,543 ms
• コンパイル使用メモリ: 387,684 KB
• 実行使用メモリ: 48,784 KB
• 最終ジャッジ日時: 2024-06-06 10:45:56
• 合計ジャッジ時間: 20,607 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

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	2 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	2 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	10 ms; 5,376 KB
testcase_09	AC	5 ms; 5,376 KB
testcase_10	AC	8 ms; 5,376 KB
testcase_11	AC	37 ms; 5,376 KB
testcase_12	AC	7 ms; 5,376 KB
testcase_13	AC	141 ms; 23,416 KB
testcase_14	AC	122 ms; 20,912 KB
testcase_15	AC	126 ms; 24,708 KB
testcase_16	AC	88 ms; 17,040 KB
testcase_17	AC	61 ms; 17,296 KB
testcase_18	AC	189 ms; 31,844 KB
testcase_19	AC	170 ms; 31,836 KB
testcase_20	AC	181 ms; 31,844 KB
testcase_21	AC	178 ms; 31,840 KB
testcase_22	AC	178 ms; 31,844 KB
testcase_23	AC	39 ms; 10,452 KB
testcase_24	AC	24 ms; 5,376 KB
testcase_25	AC	68 ms; 13,720 KB
testcase_26	AC	103 ms; 18,472 KB
testcase_27	AC	69 ms; 12,672 KB
testcase_28	AC	46 ms; 10,748 KB
testcase_29	AC	66 ms; 11,904 KB
testcase_30	AC	52 ms; 10,864 KB
testcase_31	AC	45 ms; 10,908 KB
testcase_32	AC	54 ms; 9,972 KB
testcase_33	AC	95 ms; 16,512 KB
testcase_34	AC	102 ms; 18,692 KB
testcase_35	AC	145 ms; 28,024 KB
testcase_36	AC	129 ms; 25,344 KB
testcase_37	AC	54 ms; 9,904 KB
testcase_38	AC	85 ms; 18,412 KB
testcase_39	AC	89 ms; 18,460 KB
testcase_40	AC	86 ms; 18,284 KB
testcase_41	AC	88 ms; 18,824 KB
testcase_42	AC	88 ms; 18,464 KB
testcase_43	AC	111 ms; 48,784 KB
testcase_44	AC	93 ms; 24,064 KB
testcase_45	AC	93 ms; 28,672 KB
testcase_46	AC	16 ms; 12,804 KB
testcase_47	AC	1 ms; 5,376 KB

ソースコード

// 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, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) };
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

/// Verified by https://atcoder.jp/contests/abc198/submissions/21774342
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> Default for ModInt<M> {
        fn default() -> Self { Self::new_internal(0) }
    }
    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>;

// Strong connected components.
// Verified by: yukicoder No.470 (http://yukicoder.me/submissions/145785)
//              ABC214-H (https://atcoder.jp/contests/abc214/submissions/25082618)
struct SCC {
    n: usize,
    ncc: usize,
    g: Vec<Vec<usize>>, // graph in adjacent list
    rg: Vec<Vec<usize>>, // reverse graph
    cmp: Vec<usize>, // topological order
}

impl SCC {
    fn new(n: usize) -> Self {
        SCC {
            n: n,
            ncc: n + 1,
            g: vec![Vec::new(); n],
            rg: vec![Vec::new(); n],
            cmp: vec![0; n],
        }
    }
    fn add_edge(&mut self, from: usize, to: usize) {
        self.g[from].push(to);
        self.rg[to].push(from);
    }
    fn dfs(&self, v: usize, used: &mut [bool], vs: &mut Vec<usize>) {
        used[v] = true;
        for &w in self.g[v].iter() {
            if !used[w] {
               self.dfs(w, used, vs);
            }
        }
        vs.push(v);
    }
    fn rdfs(&self, v: usize, k: usize,
            used: &mut [bool], cmp: &mut [usize]) {
        used[v] = true;
        cmp[v] = k;
        for &w in self.rg[v].iter() {
            if !used[w] {
                self.rdfs(w, k, used, cmp);
            }
        }
    }
    fn scc(&mut self) -> usize {
        let n = self.n;
        let mut used = vec![false; n];
        let mut vs = Vec::new();
        let mut cmp = vec![0; n];
        for v in 0 .. n {
            if !used[v] { self.dfs(v, &mut used, &mut vs); }
        }
        for u in used.iter_mut() {
            *u = false;
        }
        let mut k = 0;
        for &t in vs.iter().rev() {
            if !used[t] { self.rdfs(t, k, &mut used, &mut cmp); k += 1; }
        }
        self.ncc = k;
        self.cmp = cmp;
        k
    }
    #[allow(dead_code)]
    fn top_order(&self) -> Vec<usize> {
        assert!(self.ncc <= self.n);
        self.cmp.clone()
    }
    /*
     * Returns a dag whose vertices are scc's, and whose edges are those of the original graph.
     */
    #[allow(dead_code)]
    fn dag(&self) -> Vec<Vec<usize>> {
        assert!(self.ncc <= self.n);
        let ncc = self.ncc;
        let mut ret = vec![vec![]; ncc];
        let n = self.n;
        for i in 0 .. n {
            for &to in self.g[i].iter() {
                if self.cmp[i] != self.cmp[to] {
                    assert!(self.cmp[i] < self.cmp[to]);
                    ret[self.cmp[i]].push(self.cmp[to]);
                }
            }
        }
        ret.into_iter().map(|mut v| {
            v.sort_unstable(); v.dedup();
            v
        }).collect()
    }
    #[allow(dead_code)]
    fn rdag(&self) -> Vec<Vec<usize>> {
        assert!(self.ncc <= self.n);
        let ncc = self.ncc;
        let mut ret = vec![vec![]; ncc];
        let n = self.n;
        for i in 0 .. n {
            for &to in self.g[i].iter() {
                if self.cmp[i] != self.cmp[to] {
                    assert!(self.cmp[i] < self.cmp[to]);
                    ret[self.cmp[to]].push(self.cmp[i]);
                }
            }
        }
        ret.into_iter().map(|mut v| {
            v.sort_unstable(); v.dedup();
            v
        }).collect()
    }
}

trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); }
impl<T: PartialOrd> Change for T {
    fn chmax(&mut self, x: T) { if *self < x { *self = x; } }
    fn chmin(&mut self, x: T) { if *self > x { *self = x; } }
}

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();
}

fn reach(v: usize, g: &[Vec<usize>]) -> Vec<bool> {
    let n = g.len();
    let mut vis = vec![false; n];
    let mut que = vec![v];
    while let Some(v) = que.pop() {
        if vis[v] { continue; }
        vis[v] = true;
        for &w in &g[v] {
            que.push(w);
        }
    }
    vis
}

fn dfs(v: usize, g: &[Vec<(usize, i64, i64)>], vis: &mut [bool],
       dp: &mut [(MInt, MInt)]) {
    if vis[v] { return; }
    let n = g.len();
    if v == n - 1 {
        dp[v] = (1.into(), 0.into());
        vis[v] = true;
        return;
    }
    let mut x = MInt::new(0);
    let mut y = MInt::new(0);
    for &(w, l, a) in &g[v] {
        dfs(w, g, vis, dp);
        x += dp[w].0 * a;
        y += (dp[w].1 + dp[w].0 * l) * a;
    }
    dp[v] = (x, y);
    vis[v] = true;
}

// https://yukicoder.me/problems/no/1364 (3)
// SCC して、始点と終点から到達可能な大きさ 2 以上の SCC があれば INF。そうでなければ、到達可能な頂点のみを dfs (メモ化再帰) で辿れば良い。パスの個数と長さの合計を管理する。
fn solve() {
    input! {
        n: usize, m: usize,
        uvla: [(usize, usize, i64, i64); m],
    }
    let mut scc = SCC::new(n + 1);
    for &(u, v, _, _) in &uvla {
        scc.add_edge(u, v);
    }
    let ncc = scc.scc();
    let top_ord = scc.top_order();
    let v1 = reach(top_ord[0], &scc.dag());
    let v2 = reach(top_ord[n], &scc.rdag());
    let mut sz = vec![0; ncc];
    for i in 0..n + 1 {
        sz[top_ord[i]] += 1;
    }
    for i in 0..ncc {
        if v1[i] && v2[i] && sz[i] >= 2 {
            println!("INF");
            return;
        }
    }
    let mut dp = vec![(MInt::new(0), MInt::new(0)); n + 1];
    let mut vis = vec![false; n + 1];
    let mut g = vec![vec![]; n + 1];
    for &(u, v, l, a) in &uvla {
        let nu = top_ord[u];
        let nv = top_ord[v];
        if !v1[nu] || !v2[nu] || !v1[nv] || !v2[nv] { continue; }
        g[u].push((v, l, a));
    }
    dfs(0, &g, &mut vis, &mut dp);
    println!("{}", dp[0].1);
}