#908254 (Rust) No.1326 ふたりのDominator

• 問題: No.1326 ふたりのDominator
• ユーザー: koba-e964
• 提出日時: 2023-08-26 12:42:09
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 225 ms / 2,000 ms
• コード長: 10,956 bytes
• コンパイル時間: 19,847 ms
• コンパイル使用メモリ: 379,696 KB
• 実行使用メモリ: 51,852 KB
• 最終ジャッジ日時: 2024-12-25 08:44:28
• 合計ジャッジ時間: 17,922 ms
• ジャッジサーバーID （参考情報）: judge1 / 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	1 ms; 5,248 KB
testcase_03	AC	1 ms; 5,248 KB
testcase_04	AC	2 ms; 5,248 KB
testcase_05	AC	1 ms; 5,248 KB
testcase_06	AC	1 ms; 5,248 KB
testcase_07	AC	3 ms; 5,248 KB
testcase_08	AC	2 ms; 5,248 KB
testcase_09	AC	2 ms; 5,248 KB
testcase_10	AC	3 ms; 5,248 KB
testcase_11	AC	2 ms; 5,248 KB
testcase_12	AC	223 ms; 31,784 KB
testcase_13	AC	194 ms; 31,612 KB
testcase_14	AC	216 ms; 31,584 KB
testcase_15	AC	185 ms; 31,404 KB
testcase_16	AC	172 ms; 30,244 KB
testcase_17	AC	132 ms; 26,252 KB
testcase_18	AC	109 ms; 26,700 KB
testcase_19	AC	83 ms; 23,800 KB
testcase_20	AC	134 ms; 47,728 KB
testcase_21	AC	174 ms; 47,676 KB
testcase_22	AC	225 ms; 51,852 KB
testcase_23	AC	156 ms; 23,860 KB
testcase_24	AC	200 ms; 31,656 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"));
}

// Lowest Common Ancestor. Call lca(x, y) to get the lca of them.
// Many-rooted version.
// Verified by: https://yukicoder.me/submissions/714482
// These functions use O(n) stack space. 
pub struct LCA {
    n: usize,
    bn: usize,
    parent: Vec<usize>, // r is root <=> parent[r] = r
    dep: Vec<usize>,
    lca_tbl: Vec<Vec<usize>>
}

impl LCA {
    fn dfs(&mut self, edges: &[Vec<usize>], v: usize, par: usize, d: usize) {
        self.parent[v] = par;
        self.dep[v] = d;
        for &u in edges[v].iter() {
            if u != par {
                self.dfs(edges, u, v, d + 1);
            }
        }
    }
    fn lca_init(&mut self) {
        let n = self.n;
        for v in 0 .. n {
            self.lca_tbl[v] = vec![0; self.bn + 1];
            self.lca_tbl[v][0] = self.parent[v];
        }
        for i in 1..self.bn + 1 {
            for v in 0..n {
                self.lca_tbl[v][i] =
                    self.lca_tbl[self.lca_tbl[v][i - 1]][i - 1];
            }
        }
    }
    pub fn lca(&self, mut x: usize, mut y: usize) -> usize {
        let dx = self.dep[x];
        let mut dy = self.dep[y];
        if dx > dy {
            return self.lca(y, x);
        }
        for l in (0..self.bn + 1).rev() {
            if dy - dx >= 1 << l {
                y = self.lca_tbl[y][l];
                dy -= 1 << l;
            }
        }
        assert_eq!(dx, dy);
        
        if x == y {
            return x;
        }
        for l in (0..self.bn + 1).rev() {
            if self.lca_tbl[x][l] != self.lca_tbl[y][l] {
                x = self.lca_tbl[x][l];
                y = self.lca_tbl[y][l];
            }
        }
        self.lca_tbl[x][0]
    }
    #[allow(unused)]
    pub fn depth(&self, a: usize) -> usize {
        self.dep[a]
    }
    #[allow(unused)]
    pub fn parent(&self, a: usize) -> usize {
        self.parent[a]
    }
    #[allow(unused)]
    pub fn ancestor(&self, v: usize, dist: usize) -> usize {
        let mut ans = v;
        for i in 0..self.bn + 1 {
            if (dist & 1 << i) != 0 {
                ans = self.lca_tbl[ans][i];
            }
        }
        ans
    }
    #[allow(unused)]
    pub fn child(&self, anc: usize, des: usize) -> usize {
        let x = self.dep[des] - self.dep[anc] - 1;
        let mut ans = des;
        for i in 0..self.bn + 1 {
            if (x & 1 << i) != 0 {
                ans = self.lca_tbl[ans][i];
            }
        }
        ans
    }
    pub fn new(edges: &[Vec<usize>], roots: &[usize]) -> Self {
        let n = edges.len();
        let bn = (n.next_power_of_two() - 1).count_ones() as usize;
        let mut ret = LCA {
            n: n, bn: bn, parent: vec![0; n], dep: vec![0; n],
            lca_tbl: vec![Vec::new(); n] };
        for &r in roots {
            ret.dfs(edges, r, r, 0);
        }
        ret.lca_init();
        ret
    }
}

// Ported from https://kokiymgch.hatenablog.com/entry/2018/03/21/174958
// This library uses O(n) stack space. 

//tree index : [0, 1, ..., bc.size() - 1] -> component
//tree index : [bc.size(), bc.size() + 1, ..., bc.size() + art.size() - 1] -> articulation point
//cmp[index of edge] -> index of the node of the constructed tree
//cmp_node[index of node] -> -1 if it's not an articulation point, otherwise index of the node of the constructed tree
pub struct Bicomp {
    pub cmp: Vec<Option<usize>>,
    pub cmp_node: Vec<Option<usize>>,
    pub g: Vec<Vec<usize>>,
    pub e2i: std::collections::HashMap<(usize, usize), usize>,
    pub tree: Vec<Vec<usize>>,
}

impl Bicomp {
    fn dfs(
        u: usize, prev: usize,
        used: &mut [bool],
        ord: &mut [usize],
        low: &mut [usize],
        k: &mut usize,
        tmp: &mut Vec<(usize, usize)>,
        bc: &mut Vec<Vec<(usize, usize)>>,
        art: &mut Vec<usize>,
        g: &[Vec<usize>],
    ) {
        let n = g.len();
        used[u] = true;
        ord[u] = *k;
        *k += 1;
        low[u] = ord[u];
        let mut is_art = false;
        let mut cnt = 0;
        for &v in &g[u] {
            if v != prev {
                if ord[v] >= n || ord[v] < ord[u] {
                    tmp.push((std::cmp::min(u, v), std::cmp::max(u, v)))
                }
                if !used[v] {
                    cnt += 1;
                    Self::dfs(v, u, used, ord, low, k, tmp, bc, art, g);
                    low[u] = std::cmp::min(low[u], low[v]);
                    if prev < n && low[v] >= ord[u] {
                        is_art = true;
                    }
                    if low[v] >= ord[u] {
                        bc.push(vec![]);
                        loop {
                            let e = tmp.pop().unwrap();
                            let idx = bc.len() - 1;
                            bc[idx].push(e);
                            if (std::cmp::min(u, v), std::cmp::max(u, v)) == e {
                                break;
                            }
                        }
                    }
                } else {
                    low[u] = std::cmp::min(low[u], ord[v]);
                }
            }
        }
        if prev >= n && cnt > 1 {
            is_art = true;
        }
        if is_art {
            art.push(u);
        }
    }
    pub fn new(n: usize, edges: &[(usize, usize)]) -> Self {
        let m = edges.len();
        let mut g = vec![vec![]; n];
        let mut e2i = std::collections::HashMap::new();
        for i in 0..m {
            let (u, v) = edges[i];
            g[u].push(v);
            g[v].push(u);
            e2i.insert((std::cmp::min(u, v), std::cmp::max(u, v)), i);
        }
        let mut cmp_node = vec![None; n];
        let mut cmp = vec![None; m];
        let mut ord = vec![n; n];
        let mut low = vec![n; n];
        let mut used = vec![false; n];
        let mut bc = vec![];
        let mut art = vec![];
        let mut tmp = vec![];
        let mut k = 0;

        // build() in original
        Self::dfs(0, n, &mut used, &mut ord, &mut low, &mut k, &mut tmp, &mut bc, &mut art, &g);
        for i in 0..bc.len() {
            for &e in &bc[i] {
                let idx = e2i[&(std::cmp::min(e.0, e.1), std::cmp::max(e.1, e.0))];
                cmp[idx] = Some(i);
            }
        }
        let mut tree = vec![vec![]; bc.len() + art.len()];
        let mut tmp = vec![];
        for i in 0..art.len() {
            let j = i + bc.len();
            cmp_node[art[i]] = Some(j);
            let u = art[i];
            for &v in &g[u] {
                let t = cmp[e2i[&(std::cmp::min(u, v), std::cmp::max(v, u))]].unwrap();
                tmp.push(t);
            }
            tmp.sort_unstable(); tmp.dedup();
            for v in tmp.drain(..) {
                tree[j].push(v);
                tree[v].push(j);
            }
        }
        Bicomp {
            cmp: cmp,
            cmp_node: cmp_node,
            g: g,
            e2i: e2i,
            tree: tree,
        }
    }
}

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 dfs(v: usize, par: usize, g: &[Vec<usize>], d: i64, dep: &mut [i64]) {
    dep[v] = d;
    for &w in &g[v] {
        if w == par { continue; }
        dfs(w, v, g, d + 1, dep);
    }
}

// https://yukicoder.me/problems/no/1326 (4)
// グラフが木であれば、(x と y の間にある頂点数) = (x と y の距離) - 1 なので簡単。
// 一般のグラフの場合、二重辺連結成分分解を行ってできた木の各頂点について、
// 元のグラフにおける寄与が 0, 1, 2 のいずれかである。
// これは、頂点数 1 の成分については木の頂点をそのままにし、頂点数が 2 以上である成分については
// 木における頂点を通るだけで距離が 1 増えるように、木の頂点を増幅させれば良い。
// それは元々の頂点を v としたとき v に接続する辺ごとに新しく頂点を作りそれぞれの辺と接続させ、
// それらと v を距離 0.5 で繋げばできる。
// Similar problems: https://yukicoder.me/problems/no/1983
// -> 間違い。二重辺連結成分分解ではなく二重頂点連結成分分解をする必要がある。
// これは関節点と結びつく概念である。他人のライブラリを拝借して AC。
// Tags: articulation-points, biconnected-components
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,
        uv: [(usize1, usize1); m],
        q: usize,
        xy: [(usize1, usize1); q],
    }
    let bct = Bicomp::new(n, &uv);
    let lca = LCA::new(&bct.tree, &[0]);
    let mut dep = vec![0; bct.tree.len()];
    dfs(0, bct.tree.len(), &bct.tree, 0, &mut dep);
    for (x, y) in xy {
        if x == y {
            puts!("0\n");
            continue;
        }
        let bx = if let Some(bx) = bct.cmp_node[x] {
            bx
        } else {
            let w = bct.g[x][0];
            let e = bct.e2i[&(std::cmp::min(x, w), std::cmp::max(x, w))];
            bct.cmp[e].unwrap()
        };
        let by = if let Some(by) = bct.cmp_node[y] {
            by
        } else {
            let w = bct.g[y][0];
            let e = bct.e2i[&(std::cmp::min(y, w), std::cmp::max(y, w))];
            bct.cmp[e].unwrap()
        };
        let l = lca.lca(bx, by);
        let mut dist = dep[bx] + dep[by] - 2 * dep[l];
        if bct.cmp_node[x].is_some() {
            dist -= 1;
        }
        if bct.cmp_node[y].is_some() {
            dist -= 1;
        }
        puts!("{}\n", dist / 2);
    }
}