#880186 (Rust) No.1983 [Cherry 4th Tune C] 南の島のマーメイド

• 問題: No.1983 [Cherry 4th Tune C] 南の島のマーメイド
• ユーザー: koba-e964
• 提出日時: 2023-06-13 00:15:37
• 言語: Rust (1.77.0)
• 結果: AC
• 実行時間: 337 ms / 4,000 ms
• コード長: 6,755 bytes
• コンパイル時間: 5,571 ms
• コンパイル使用メモリ: 165,420 KB
• 実行使用メモリ: 105,924 KB
• 最終ジャッジ日時: 2023-09-02 17:10:32
• 合計ジャッジ時間: 20,031 ms
• ジャッジサーバーID （参考情報）: judge13 / judge15

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 4,372 KB
testcase_01	AC	1 ms; 4,372 KB
testcase_02	AC	2 ms; 4,368 KB
testcase_03	AC	1 ms; 4,372 KB
testcase_04	AC	1 ms; 4,368 KB
testcase_05	AC	1 ms; 4,368 KB
testcase_06	AC	1 ms; 4,368 KB
testcase_07	AC	1 ms; 4,368 KB
testcase_08	AC	5 ms; 4,372 KB
testcase_09	AC	7 ms; 4,372 KB
testcase_10	AC	11 ms; 4,492 KB
testcase_11	AC	11 ms; 4,372 KB
testcase_12	AC	6 ms; 4,368 KB
testcase_13	AC	165 ms; 30,008 KB
testcase_14	AC	194 ms; 33,424 KB
testcase_15	AC	206 ms; 44,140 KB
testcase_16	AC	83 ms; 27,352 KB
testcase_17	AC	195 ms; 35,680 KB
testcase_18	AC	186 ms; 43,592 KB
testcase_19	AC	261 ms; 51,888 KB
testcase_20	AC	192 ms; 41,228 KB
testcase_21	AC	213 ms; 40,744 KB
testcase_22	AC	255 ms; 42,800 KB
testcase_23	AC	321 ms; 57,392 KB
testcase_24	AC	326 ms; 56,308 KB
testcase_25	AC	337 ms; 56,812 KB
testcase_26	AC	327 ms; 57,060 KB
testcase_27	AC	331 ms; 56,116 KB
testcase_28	AC	329 ms; 56,556 KB
testcase_29	AC	328 ms; 56,856 KB
testcase_30	AC	334 ms; 56,108 KB
testcase_31	AC	329 ms; 56,080 KB
testcase_32	AC	324 ms; 56,184 KB
testcase_33	AC	1 ms; 4,368 KB
testcase_34	AC	89 ms; 26,264 KB
testcase_35	AC	196 ms; 77,808 KB
testcase_36	AC	169 ms; 41,548 KB
testcase_37	AC	1 ms; 4,372 KB
testcase_38	AC	41 ms; 4,368 KB
testcase_39	AC	243 ms; 105,924 KB
testcase_40	AC	188 ms; 55,984 KB

ソースコード

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, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) };
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    ($next:expr, usize1) => (read_value!($next, usize) - 1);
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

// Verified by: https://codeforces.com/contest/700/submission/165850980
// This function uses O(n) stack space.
mod tecomp {
    use std::cmp::min;
    const INF: usize = 1 << 28;
    fn dfs<EIdx: Copy + PartialEq>(v: usize, paridx: EIdx, g: &[Vec<(usize, EIdx)>],
           ord: &mut [usize], low: &mut [usize], k: &mut usize,
           bridges: &mut Vec<EIdx>) {
        ord[v] = *k;
        low[v] = *k;
        *k += 1;
        for &(w, eidx) in g[v].iter() {
            if paridx == eidx { continue; }
            if ord[w] < ord[v] {
                low[v] = min(low[v], ord[w]);
            } else if ord[w] == INF {
                dfs(w, eidx, g, ord, low, k, bridges);
                low[v] = min(low[v], low[w]);
                if ord[v] < low[w] {
                    bridges.push(eidx);
                }
            }
        }
    }
    fn dfs_comp<EIdx: Copy>(
        v: usize, g: &[Vec<(usize, EIdx)>],
        ord: &[usize], low: &[usize],
        cur_becomp: usize, becomp_count: &mut usize, becomp: &mut [usize], tree: &mut [Vec<(usize, EIdx)>],
        vis: &mut [bool],
    ) {
        becomp[v] = cur_becomp;
        vis[v] = true;
        for &(w, eidx) in g[v].iter() {
            if ord[w] > ord[v] && !vis[w] {
                if ord[v] < low[w] {
                    *becomp_count += 1;
                    tree[cur_becomp].push((*becomp_count, eidx));
                    dfs_comp(w, g, ord, low, *becomp_count, becomp_count, becomp, tree, vis);
                } else {
                    dfs_comp(w, g, ord, low, cur_becomp, becomp_count, becomp, tree, vis);
                }
            }
        }
    }

    type EIdx = usize;

    // Returns (the number of 2-edge connected components, [the id of the component v belongs to | v <- [0 .. g.len()]], the resulting tree, the ids of bridges).
    // Graphs are given and provided in the adjacent list format. (to, edge_id).
    // The provided tree has its own vertex ids, but edge ids are reused.
    // This function uses O(n) stack space.
    pub fn decomp(g: &[Vec<(usize, EIdx)>])
                 -> (usize, Vec<usize>, Vec<Vec<(usize, EIdx)>>, Vec<EIdx>) {
        let n_vert = g.len();
        let mut ord = vec![INF; n_vert];
        let mut low = vec![INF; n_vert];
        let mut k = 0;
        let mut becomp_count = 0;
        let mut becomp = vec![INF; n_vert];
        let mut bridges = Vec::new();
        // rooted forest
        let mut tree = vec![Vec::new(); n_vert];
        let mut vis = vec![false; n_vert];
        for i in 0 .. n_vert {
            if !vis[i] {
                dfs(i, !0, &g, &mut ord, &mut low, &mut k, &mut bridges);
                dfs_comp(i, &g, &ord, &low,
                         becomp_count, &mut becomp_count, &mut becomp,
                         &mut tree, &mut vis);
                becomp_count += 1;
            }
        }
        tree = tree[..becomp_count].to_vec();
        (becomp_count, becomp, tree, bridges)
    }
} // mod tecomp

// Union-Find tree.
// Verified by https://atcoder.jp/contests/pakencamp-2019-day3/submissions/9253305
struct UnionFind { disj: Vec<usize>, rank: Vec<usize> }

impl UnionFind {
    fn new(n: usize) -> Self {
        let disj = (0..n).collect();
        UnionFind { disj: disj, rank: vec![1; n] }
    }
    fn root(&mut self, x: usize) -> usize {
        if x != self.disj[x] {
            let par = self.disj[x];
            let r = self.root(par);
            self.disj[x] = r;
        }
        self.disj[x]
    }
    fn unite(&mut self, x: usize, y: usize) {
        let mut x = self.root(x);
        let mut y = self.root(y);
        if x == y { return }
        if self.rank[x] > self.rank[y] {
            std::mem::swap(&mut x, &mut y);
        }
        self.disj[x] = y;
        self.rank[y] += self.rank[x];
    }
    #[allow(unused)]
    fn is_same_set(&mut self, x: usize, y: usize) -> bool {
        self.root(x) == self.root(y)
    }
    #[allow(unused)]
    fn size(&mut self, x: usize) -> usize {
        let x = self.root(x);
        self.rank[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();
}

// https://yukicoder.me/problems/no/1983 (3.5)
// 関節点と橋を求め、橋だけで関節点・次数 1 の頂点すべてを繋いだときに同じ連結成分に属しているかどうか。
// パスが一意 => 構成する辺は全て橋: 橋以外が含まれているとそれを除去した時連結なので別のパスが取れる。
// パスが一意 => 通過する頂点はすべて関節点 or 次数 1: => そうでないとそれを除去した時、連結なままなので別のパスが取れる。
// 橋の両端は関節点 or 次数 1 であるため、後者の条件はいらないはず。
fn solve() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    input! {
        n: usize, m: usize, q: usize,
        uv: [(usize1, usize1); m],
        xy: [(usize1, usize1); q],
    }
    let mut uf = UnionFind::new(n);
    let mut g = vec![vec![]; n];
    for i in 0..m {
        let (u, v) = uv[i];
        g[u].push((v, i));
        g[v].push((u, i));
    }
    let (_, _, _, bridges) = tecomp::decomp(&g);
    for &idx in &bridges {
        let (u, v) = uv[idx];
        uf.unite(u, v);
    }
    for (x, y) in xy {
        puts!("{}\n", if uf.is_same_set(x, y) { "Yes" } else { "No" });
    }
}