#757365 (Rust) No.1917 LCMST

• 問題: No.1917 LCMST
• ユーザー: hiromi_ayase
• 提出日時: 2022-04-30 06:00:11
• 言語: Rust (1.77.0 + proconio)
• 結果: MLE
• 実行時間: -
• コード長: 4,952 bytes
• コンパイル時間: 13,809 ms
• コンパイル使用メモリ: 378,852 KB
• 実行使用メモリ: 816,396 KB
• 最終ジャッジ日時: 2024-06-29 12:05:44
• 合計ジャッジ時間: 128,292 ms
• ジャッジサーバーID （参考情報）: judge2 / judge1

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; 5,376 KB
testcase_02	AC	1 ms; 5,376 KB
testcase_03	AC	4 ms; 5,376 KB
testcase_04	AC	4 ms; 5,376 KB
testcase_05	AC	5 ms; 5,376 KB
testcase_06	AC	4 ms; 5,376 KB
testcase_07	AC	4 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	MLE	-
testcase_10	MLE	-
testcase_11	MLE	-
testcase_12	MLE	-
testcase_13	MLE	-
testcase_14	MLE	-
testcase_15	MLE	-
testcase_16	MLE	-
testcase_17	MLE	-
testcase_18	MLE	-
testcase_19	MLE	-
testcase_20	MLE	-
testcase_21	MLE	-
testcase_22	MLE	-
testcase_23	MLE	-
testcase_24	AC	2,977 ms; 509,328 KB
testcase_25	MLE	-
testcase_26	MLE	-
testcase_27	MLE	-
testcase_28	MLE	-
testcase_29	AC	3,136 ms; 495,652 KB
testcase_30	MLE	-
testcase_31	AC	3,162 ms; 495,760 KB
testcase_32	AC	3,218 ms; 499,724 KB
testcase_33	MLE	-
testcase_34	MLE	-
testcase_35	AC	1,306 ms; 172,684 KB
testcase_36	MLE	-
testcase_37	MLE	-
testcase_38	MLE	-
testcase_39	MLE	-
testcase_40	AC	3,220 ms; 504,080 KB
testcase_41	MLE	-
testcase_42	AC	3,206 ms; 504,204 KB
testcase_43	MLE	-
testcase_44	--	-

ソースコード

use std::{
    collections::{HashMap},
};

#[allow(clippy::many_single_char_names)]
fn main() {
    let n = getline().parse::<usize>().unwrap();
    let mut a = getline()
        .split(' ')
        .map(|x| x.parse::<i64>().unwrap())
        .collect::<Vec<_>>();

    a.sort();
    let mut div_map: HashMap<i64, _> = HashMap::new();

    let mut edges: Vec<(usize, usize, i64)> = Vec::new();

    for i in 0..n {
        let divs = divisors(a[i]);
        for d in divs {
            div_map.entry(d).or_insert_with(Vec::new).push(i);
        }
    }

    for e in &mut div_map {
        let d = *e.0;
        let u = e.1[0];

        for v in e.1 {
            if u == *v {
                continue;
            }
            edges.push((u, *v, a[u] / d * a[*v]));
        }
    }

    edges.sort_by_key(|e| e.2);
    let mut ds = Dsu::new(n);
    let mut ans = 0;
    for e in edges {
        if ds.same(e.0, e.1) {
            continue;
        }
        ds.merge(e.0, e.1);
        ans += e.2;
    }
    println!("{}", ans);
}

fn divisors(x: i64) -> Vec<i64> {
    let mut ret = vec![];
    let mut i = 1;
    while i * i <= x {
        if x % i == 0 {
            ret.push(i);
            if i * i != x {
                ret.push(x / i);
            }
        }
        i += 1;
    }
    ret
}

fn getline() -> String {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    buf.trim().to_string()
}

pub struct Dsu {
    n: usize,
    // root node: -1 * component size
    // otherwise: parent
    parent_or_size: Vec<i32>,
}

impl Dsu {
    /// Creates a new `Dsu`.
    ///
    /// # Constraints
    ///
    /// - $0 \leq n \leq 10^8$
    ///
    /// # Complexity
    ///
    /// - $O(n)$
    pub fn new(size: usize) -> Self {
        Self {
            n: size,
            parent_or_size: vec![-1; size],
        }
    }

    // `\textsc` does not work in KaTeX
    /// Performs the Uɴɪᴏɴ operation.
    ///
    /// # Constraints
    ///
    /// - $0 \leq a < n$
    /// - $0 \leq b < n$
    ///
    /// # Panics
    ///
    /// Panics if the above constraints are not satisfied.
    ///
    /// # Complexity
    ///
    /// - $O(\alpha(n))$ amortized
    pub fn merge(&mut self, a: usize, b: usize) -> usize {
        assert!(a < self.n);
        assert!(b < self.n);
        let (mut x, mut y) = (self.leader(a), self.leader(b));
        if x == y {
            return x;
        }
        if -self.parent_or_size[x] < -self.parent_or_size[y] {
            std::mem::swap(&mut x, &mut y);
        }
        self.parent_or_size[x] += self.parent_or_size[y];
        self.parent_or_size[y] = x as i32;
        x
    }

    /// Returns whether the vertices $a$ and $b$ are in the same connected component.
    ///
    /// # Constraints
    ///
    /// - $0 \leq a < n$
    /// - $0 \leq b < n$
    ///
    /// # Panics
    ///
    /// Panics if the above constraint is not satisfied.
    ///
    /// # Complexity
    ///
    /// - $O(\alpha(n))$ amortized
    pub fn same(&mut self, a: usize, b: usize) -> bool {
        assert!(a < self.n);
        assert!(b < self.n);
        self.leader(a) == self.leader(b)
    }

    /// Performs the Fɪɴᴅ operation.
    ///
    /// # Constraints
    ///
    /// - $0 \leq a < n$
    ///
    /// # Panics
    ///
    /// Panics if the above constraint is not satisfied.
    ///
    /// # Complexity
    ///
    /// - $O(\alpha(n))$ amortized
    pub fn leader(&mut self, a: usize) -> usize {
        assert!(a < self.n);
        if self.parent_or_size[a] < 0 {
            return a;
        }
        self.parent_or_size[a] = self.leader(self.parent_or_size[a] as usize) as i32;
        self.parent_or_size[a] as usize
    }

    /// Returns the size of the connected component that contains the vertex $a$.
    ///
    /// # Constraints
    ///
    /// - $0 \leq a < n$
    ///
    /// # Panics
    ///
    /// Panics if the above constraint is not satisfied.
    ///
    /// # Complexity
    ///
    /// - $O(\alpha(n))$ amortized
    pub fn size(&mut self, a: usize) -> usize {
        assert!(a < self.n);
        let x = self.leader(a);
        -self.parent_or_size[x] as usize
    }

    /// Divides the graph into connected components.
    ///
    /// The result may not be ordered.
    ///
    /// # Complexity
    ///
    /// - $O(n)$
    pub fn groups(&mut self) -> Vec<Vec<usize>> {
        let mut leader_buf = vec![0; self.n];
        let mut group_size = vec![0; self.n];
        for i in 0..self.n {
            leader_buf[i] = self.leader(i);
            group_size[leader_buf[i]] += 1;
        }
        let mut result = vec![Vec::new(); self.n];
        for i in 0..self.n {
            result[i].reserve(group_size[i]);
        }
        for i in 0..self.n {
            result[leader_buf[i]].push(i);
        }
        result
            .into_iter()
            .filter(|x| !x.is_empty())
            .collect::<Vec<Vec<usize>>>()
    }
}