結果

問題 No.1207 グラフX
ユーザー ikdikd
提出日時 2020-09-01 21:41:35
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 446 ms / 2,000 ms
コード長 8,336 bytes
コンパイル時間 14,961 ms
コンパイル使用メモリ 402,568 KB
実行使用メモリ 64,360 KB
最終ジャッジ日時 2024-11-20 17:57:12
合計ジャッジ時間 30,591 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 46
権限があれば一括ダウンロードができます

ソースコード

diff # 

pub struct ProconReader<R: std::io::Read> {
    reader: R,
}

impl<R: std::io::Read> ProconReader<R> {
    pub fn new(reader: R) -> Self {
        Self { reader }
    }
    pub fn get<T: std::str::FromStr>(&mut self) -> T {
        use std::io::Read;
        let buf = self
            .reader
            .by_ref()
            .bytes()
            .map(|b| b.unwrap())
            .skip_while(|&byte| byte == b' ' || byte == b'\n' || byte == b'\r')
            .take_while(|&byte| byte != b' ' && byte != b'\n' && byte != b'\r')
            .collect::<Vec<_>>();
        std::str::from_utf8(&buf)
            .unwrap()
            .parse()
            .ok()
            .expect("Parse Error.")
    }
}

#[allow(dead_code)]
mod mint {
    use std::ops::{Add, BitAnd, Div, Mul, Rem, Shr, Sub};

    #[derive(Copy, Clone)]
    pub struct Mint<T> {
        x: T,
        mo: T,
    }
    impl<T> Mint<T>
    where
        T: Copy,
    {
        pub fn new(x: T, mo: T) -> Mint<T> {
            Mint { x, mo }
        }
    }
    impl<T> Mint<T>
    where
        T: Copy,
    {
        pub fn val(&self) -> T {
            self.x
        }
        pub fn mo(&self) -> T {
            self.mo
        }
    }
    impl<T> Add<T> for Mint<T>
    where
        T: Copy,
        T: Add<Output = T>,
        T: Rem<Output = T>,
    {
        type Output = Mint<T>;
        fn add(self, rhs: T) -> Mint<T> {
            Mint::new((self.val() + rhs % self.mo()) % self.mo(), self.mo())
        }
    }
    impl<T> Add<Mint<T>> for Mint<T>
    where
        T: Copy,
        Mint<T>: Add<T, Output = Mint<T>>,
    {
        type Output = Mint<T>;
        fn add(self, rhs: Mint<T>) -> Mint<T> {
            self + rhs.val()
        }
    }
    impl<T> Sub<T> for Mint<T>
    where
        T: Copy,
        T: Add<Output = T>,
        T: Sub<Output = T>,
        T: Rem<Output = T>,
    {
        type Output = Mint<T>;
        fn sub(self, rhs: T) -> Mint<T> {
            Mint::new(
                (self.val() + self.mo() - rhs % self.mo()) % self.mo(),
                self.mo(),
            )
        }
    }
    impl<T> Sub<Mint<T>> for Mint<T>
    where
        T: Copy,
        Mint<T>: Sub<T, Output = Mint<T>>,
    {
        type Output = Mint<T>;
        fn sub(self, rhs: Mint<T>) -> Mint<T> {
            self - rhs.val()
        }
    }
    impl<T> Mul<T> for Mint<T>
    where
        T: Copy,
        T: Mul<Output = T>,
        T: Rem<Output = T>,
    {
        type Output = Mint<T>;
        fn mul(self, rhs: T) -> Mint<T> {
            Mint::new((self.val() * rhs % self.mo()) % self.mo(), self.mo())
        }
    }
    impl<T> Mul<Mint<T>> for Mint<T>
    where
        T: Copy,
        Mint<T>: Mul<T, Output = Mint<T>>,
    {
        type Output = Mint<T>;
        fn mul(self, rhs: Mint<T>) -> Mint<T> {
            self * rhs.val()
        }
    }

    impl<T> Mint<T>
    where
        T: Copy,
        T: Sub<Output = T>,
        T: Div<Output = T>,
        T: PartialOrd,
        T: PartialEq,
        T: BitAnd<Output = T>,
        T: Shr<Output = T>,
        Mint<T>: Mul<Output = Mint<T>>,
    {
        pub fn pow(self, y: T) -> Mint<T> {
            let one = self.mo() / self.mo();
            let zero = self.mo() - self.mo();
            let mut res = Mint::one(self.mo());
            let mut base = self;
            let mut exp = y;
            while exp > zero {
                if (exp & one) == one {
                    res = res * base;
                }
                base = base * base;
                exp = exp >> one;
            }
            res
        }
    }
    impl<T> Div<T> for Mint<T>
    where
        T: Copy,
        T: Sub<Output = T>,
        T: Div<Output = T>,
        T: PartialOrd,
        T: PartialEq,
        T: BitAnd<Output = T>,
        T: Shr<Output = T>,
        Mint<T>: Mul<Output = Mint<T>>,
    {
        type Output = Mint<T>;
        fn div(self, rhs: T) -> Mint<T> {
            let one = self.mo() / self.mo();
            self * Mint::new(rhs, self.mo()).pow(self.mo() - one - one)
        }
    }
    impl<T> Div<Mint<T>> for Mint<T>
    where
        T: Copy,
        Mint<T>: Div<T, Output = Mint<T>>,
    {
        type Output = Mint<T>;
        fn div(self, rhs: Mint<T>) -> Mint<T> {
            self / rhs.val()
        }
    }
    impl<T> Mint<T>
    where
        T: Copy,
        T: Div<Output = T>,
        Mint<T>: Div<Output = Mint<T>>,
    {
        pub fn inv(self) -> Mint<T> {
            Mint::one(self.mo()) / self
        }
    }
    impl<T> std::fmt::Display for Mint<T>
    where
        T: Copy + std::fmt::Display,
    {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(f, "{}", self.val())
        }
    }
    impl<T> Mint<T>
    where
        T: Copy,
        T: Sub<Output = T>,
    {
        pub fn zero(mo: T) -> Mint<T> {
            Mint { x: mo - mo, mo }
        }
    }
    impl<T> Mint<T>
    where
        T: Copy,
        T: Div<Output = T>,
    {
        pub fn one(mo: T) -> Mint<T> {
            Mint { x: mo / mo, mo }
        }
    }
}

use mint::Mint;

pub struct UnionFind {
    par: Vec<usize>,
    size: Vec<usize>,
}

impl UnionFind {
    pub fn new(n: usize) -> UnionFind {
        UnionFind {
            par: (0..n).map(|i| i).collect::<Vec<_>>(),
            size: vec![1; n],
        }
    }
    pub fn find(&mut self, i: usize) -> usize {
        if self.par[i] == i {
            self.par[i]
        } else {
            self.par[i] = self.find(self.par[i]);
            self.par[i]
        }
    }
    pub fn unite(&mut self, i: usize, j: usize) {
        let i = self.find(i);
        let j = self.find(j);
        if i == j {
            return;
        }
        let (i, j) = if self.size[i] >= self.size[j] {
            (i, j)
        } else {
            (j, i)
        };
        self.par[j] = i;
        self.size[i] += self.size[j];
    }
    pub fn same(&mut self, i: usize, j: usize) -> bool {
        self.find(i) == self.find(j)
    }
    pub fn get_size(&mut self, i: usize) -> usize {
        let p = self.find(i);
        self.size[p]
    }
}

#[derive(Debug, Clone)]
struct Edge {
    to: usize,
    cost: i64,
}

fn minimum_spanning_tree(g: &Vec<Vec<Edge>>) -> Option<Vec<Vec<Edge>>> {
    let n = g.len();
    let mut edges = vec![];
    for i in 0..n {
        for e in &g[i] {
            edges.push((e.cost, i, e.to));
        }
    }
    edges.sort();
    let mut result = vec![vec![]; n];
    let mut uf = UnionFind::new(n);
    let mut count = 0;
    for e in edges {
        let (c, from, to) = e;
        if !uf.same(from, to) {
            uf.unite(from, to);
            count += 1;
            result[from].push(Edge { to: to, cost: c });
            result[to].push(Edge { to: from, cost: c });
        }
    }
    if count == n - 1 {
        Some(result)
    } else {
        assert!(count < n - 1);
        None
    }
}

fn dfs(g: &Vec<Vec<Edge>>, i: usize, p: usize, size: &mut Vec<usize>) {
    size[i] = 1;
    for e in &g[i] {
        if e.to != p {
            dfs(g, e.to, i, size);
            size[i] += size[e.to];
        }
    }
}

fn main() {
    let stdin = std::io::stdin();
    let mut rd = ProconReader::new(stdin.lock());

    let n: usize = rd.get();
    let m: usize = rd.get();
    let x: usize = rd.get();
    let mut g = vec![vec![]; n];
    for _ in 0..m {
        let u: usize = rd.get();
        let v: usize = rd.get();
        let w: i64 = rd.get();
        g[u - 1].push(Edge { to: v - 1, cost: w });
        g[v - 1].push(Edge { to: u - 1, cost: w });
    }
    let h = minimum_spanning_tree(&g).unwrap();
    let mut size = vec![0; n];
    dfs(&h, 0, !0, &mut size);
    let mut q = std::collections::VecDeque::new();
    q.push_back((0, !0, 0, 0));
    let mo = 1_000_000_000 + 7;
    let mut ans = Mint::zero(mo);
    while let Some((i, p, c, acc)) = q.pop_front() {
        if p != !0 {
            ans = ans + Mint::new(size[i] * acc, mo) * Mint::new(x, mo).pow(c);
        }
        let mut a = acc + 1;
        for e in &h[i] {
            if e.to != p {
                a += size[e.to];
            }
        }
        for e in &h[i] {
            if e.to != p {
                q.push_back((e.to, i, e.cost as usize, a - size[e.to]));
            }
        }
    }
    println!("{}", ans);
}
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