結果

問題 No.1207 グラフX
ユーザー nebocconebocco
提出日時 2021-03-20 12:44:30
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 173 ms / 2,000 ms
コード長 18,125 bytes
コンパイル時間 16,113 ms
コンパイル使用メモリ 378,440 KB
実行使用メモリ 51,544 KB
最終ジャッジ日時 2024-11-20 21:45:49
合計ジャッジ時間 20,689 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 162 ms
51,476 KB
testcase_01 AC 159 ms
51,476 KB
testcase_02 AC 160 ms
51,216 KB
testcase_03 AC 166 ms
51,060 KB
testcase_04 AC 161 ms
51,544 KB
testcase_05 AC 169 ms
45,328 KB
testcase_06 AC 173 ms
45,460 KB
testcase_07 AC 171 ms
45,332 KB
testcase_08 AC 115 ms
33,380 KB
testcase_09 AC 130 ms
41,088 KB
testcase_10 AC 161 ms
45,380 KB
testcase_11 AC 170 ms
45,356 KB
testcase_12 AC 132 ms
35,484 KB
testcase_13 AC 36 ms
14,936 KB
testcase_14 AC 156 ms
48,732 KB
testcase_15 AC 139 ms
39,024 KB
testcase_16 AC 42 ms
16,256 KB
testcase_17 AC 106 ms
29,912 KB
testcase_18 AC 86 ms
29,584 KB
testcase_19 AC 73 ms
23,936 KB
testcase_20 AC 155 ms
50,196 KB
testcase_21 AC 5 ms
5,248 KB
testcase_22 AC 103 ms
30,220 KB
testcase_23 AC 121 ms
34,604 KB
testcase_24 AC 75 ms
26,352 KB
testcase_25 AC 158 ms
49,440 KB
testcase_26 AC 124 ms
37,432 KB
testcase_27 AC 141 ms
44,468 KB
testcase_28 AC 132 ms
41,472 KB
testcase_29 AC 141 ms
43,628 KB
testcase_30 AC 58 ms
19,644 KB
testcase_31 AC 28 ms
12,288 KB
testcase_32 AC 56 ms
19,848 KB
testcase_33 AC 57 ms
19,556 KB
testcase_34 AC 123 ms
38,408 KB
testcase_35 AC 6 ms
5,248 KB
testcase_36 AC 121 ms
40,192 KB
testcase_37 AC 106 ms
32,308 KB
testcase_38 AC 22 ms
9,548 KB
testcase_39 AC 57 ms
21,808 KB
testcase_40 AC 17 ms
8,704 KB
testcase_41 AC 65 ms
23,296 KB
testcase_42 AC 1 ms
5,248 KB
testcase_43 AC 1 ms
5,248 KB
testcase_44 AC 1 ms
5,248 KB
testcase_45 AC 153 ms
50,780 KB
testcase_46 AC 151 ms
50,816 KB
testcase_47 AC 156 ms
50,948 KB
testcase_48 AC 155 ms
50,748 KB
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 # 

fn main() {
	let mut io = IO::new();
    input!{ from io,
		n: usize, m: usize, k: i64,
		mut ed: [(Usize1, Usize1, i64); m]
    }
	let mut g = UndirectedGraph::new(n);
	kruskal(&mut g, &mut ed);
	let (dist, par, size, _) = tree_dfs(&g, 0);
	let mut ans = 0;
	for i in 1..n {
		let z = dist[i] - dist[par[i].unwrap()];
		ans += modpow(k, z, MOD) * size[i] as i64 % MOD * (n - size[i]) as i64 % MOD;
	}
    io.println(ans % MOD);
}

const MOD: i64 = 1_000_000_007;

pub fn modpow(mut x: i64, mut y: i64, modulo: i64) -> i64 {
	x %= modulo;
    if x == 0 { return 0; }
    let mut ret = 1;
    let mut cur = x;
    while y > 0 {
        if y & 1 > 0 {
            ret = ret * cur % modulo;
        }
        cur = cur * cur % modulo;
        y >>= 1;
    }
    ret
}

pub fn tree_dfs<C: Cost, G: Graph<C>>(g: &G, root: usize)
-> (Vec<C>, Vec<Option<usize>>, Vec<usize>, Vec<usize>)
{
    let n = g.size();
    let mut euler = Vec::with_capacity(n);
	let mut dist = vec![C::MAX; n];
	dist[root] = C::zero();
    let mut par = vec![None; n];
    let mut size = vec![1; n];
    let mut q = vec![root];
    while let Some(v) = q.pop() {
        euler.push(v);
        for e in g.edges_from(v) {
            if par[v] == Some(e.to) { continue; }
            par[e.to] = Some(v);
            dist[e.to] = dist[v] + e.cost;
            q.push(e.to);
        }
    }
    for &v in euler.iter().skip(1).rev() {
        size[par[v].unwrap()] += size[v];
    }
    (dist, par, size, euler)
}

// ------------ Kruskal's algorithm start ------------

pub fn kruskal<C: Cost>(graph: &mut UndirectedGraph<C>, edges: &mut [(usize, usize, C)]) -> Vec<(usize, usize, C)> {
    edges.sort_by_key(|x| x.2);
    let mut res = Vec::with_capacity(graph.size() - 1);
    let mut uf = UnionFind::new(graph.size());
    for &e in edges.iter() {
        if uf.unite(e.0, e.1).is_ok() {
            graph.add_edge(e.0, e.1, e.2);
            res.push(e);
        }
    }
    res
}

// ------------ Kruskal's algorithm end ------------


// ------------ UnionFind start ------------
#[derive(Clone, Debug)]
pub struct UnionFind(Vec<isize>);

impl UnionFind {
    pub fn new(len: usize) -> Self {
        Self(vec![-1; len])
    }

    pub fn find(&mut self, i: usize) -> usize {
        self._climb(i).0
    }

    pub fn size(&mut self, i: usize) -> usize {
        self._climb(i).1
    }

    pub fn unite(&mut self, u: usize, v: usize) -> Result<(), ()> {
        let (mut u, su) = self._climb(u);
        let (mut v, sv) = self._climb(v);
        if u == v { return Err(()); }
        if su < sv {
            std::mem::swap(&mut u, &mut v);
        }
        self.0[u] += self.0[v];
        self.0[v] = u as isize;
        Ok(())
    }

    pub fn is_same(&mut self, u: usize, v:usize) -> bool {
        self.find(u) == self.find(v)
    }

    fn _climb(&mut self, i: usize) -> (usize, usize) {
        assert!(i < self.0.len());
        let mut v = i;
        while self.0[v] >= 0 {
            let p = self.0[v] as usize;
            if self.0[p] >= 0 {
                self.0[v] = self.0[p];
                v = self.0[p] as usize;
            } else {
                v = p;
            }
        }
        (v, -self.0[v] as usize)
    }
}
// ------------ UnionFind end ------------


// TODO: verify
// ------------ Potentialized UnionFind start ------------

#[derive(Clone, Debug)]
pub struct PotentializedUnionFind<T>{
    data: Vec<isize>,
    ws: Vec<T>
}

impl<T: Group> PotentializedUnionFind<T> {
    pub fn new(len: usize) -> Self {
        Self{
            data: vec![-1; len],
            ws: vec![T::zero(); len]
        }
    }

    pub fn find(&mut self, i: usize) -> usize {
        self._climb(i).0
    }

    pub fn size(&mut self, i: usize) -> usize {
        self._climb(i).1
    }

    pub fn potential(&mut self, i: usize) -> T {
        self._climb(i).2
    }

    /// potential[v] - potential[u] = w
    /// keep potential[u] unchanged
    pub fn unite(&mut self, u: usize, v: usize, mut w: T) -> Result<(), ()> {
        let (u, su, wu) = self._climb(u);
        let (v, sv, wv) = self._climb(v);
		if u == v {
			return if w == -wu + wv { Ok(()) } else { Err(()) };
		}
        w = -self.ws[u].clone() + wu + w + self.ws[v].clone() + -wv;
		if su < sv {
            self.data[v] += self.data[u];
            self.data[u] = v as isize;
            self.ws[v] = self.ws[u].clone() + w.clone();
            self.ws[u] = -w.clone();
        } else {
            self.data[u] += self.data[v];
            self.data[v] = u as isize;
            self.ws[v] = w.clone();
        }
        Ok(())
    }

    pub fn is_same(&mut self, u: usize, v:usize) -> bool {
        self.find(u) == self.find(v)
    }

    /// potential[v] - potential[u]
    pub fn diff(&mut self, u: usize, v: usize) -> Option<T> {
        let (u, _, wu) = self._climb(u);
        let (v, _, wv) = self._climb(v);
        if u == v {
            Some(-wu + wv)
        } else {
            None
        }
    }

    pub fn weigh(&mut self, u: usize, w: T) {
        let p = self.find(u);
        self.ws[p] = self.ws[p].clone() + w;
    }

    /// _climb(i) -> (root, group size, potential)
    fn _climb(&mut self, i: usize) -> (usize, usize, T) {
        assert!(i < self.data.len());
        let mut v = i;
        let mut w = T::zero();
        while self.data[v] >= 0 {
			w = self.ws[v].clone() + w;
            let p = self.data[v] as usize;
            if self.data[p] >= 0 {
                self.data[v] = self.data[p];
                self.ws[v] = self.ws[p].clone() + self.ws[v].clone();
            }
            v = p;
        }
        w = self.ws[v].clone() + w;
        (v, -self.data[v] as usize, w)
    }
}
// ------------ Potentialized UnionFind end ------------


// TODO: verify
// ------------ Iterative UnionFind start ------------
#[derive(Clone, Debug)]
pub struct IterativeUnionFind(Vec<isize>, Vec<usize>);

impl IterativeUnionFind {
    pub fn new(len: usize) -> Self {
        Self(vec![-1; len], (0..len).collect())
    }

    pub fn find(&mut self, i: usize) -> usize {
        self._climb(i).0
    }

    pub fn size(&mut self, i: usize) -> usize {
        self._climb(i).1
    }

    pub fn unite(&mut self, u: usize, v: usize) -> Result<(), ()> {
        let (mut u, su) = self._climb(u);
        let (mut v, sv) = self._climb(v);
        if u == v { return Err(()); }
        if su < sv {
            std::mem::swap(&mut u, &mut v);
        }
        self.0[u] += self.0[v];
        self.0[v] = u as isize;
        self.1.swap(u, v);
        Ok(())
    }

    pub fn is_same(&mut self, u: usize, v:usize) -> bool {
        self.find(u) == self.find(v)
    }

    pub fn iter_group(&mut self, u: usize) -> Vec<usize> {
        let mut res = Vec::with_capacity(self.size(u));
        res.push(u);
        let mut v = self.1[u];
        while v != u {
            res.push(v);
            v = self.1[v];
        }
        res
    }

    fn _climb(&mut self, i: usize) -> (usize, usize) {
        assert!(i < self.0.len());
        let mut v = i;
        while self.0[v] >= 0 {
            let p = self.0[v] as usize;
            if self.0[p] >= 0 {
                self.0[v] = self.0[p];
                v = self.0[p] as usize;
            } else {
                v = p;
            }
        }
        (v, -self.0[v] as usize)
    }
}
// ------------ Iterative UnionFind end ------------


// ------------ Graph impl start ------------

pub trait Cost:
    Element
    + Clone + Copy + std::fmt::Display
    + Eq + Ord
    + Zero + One
    + Add<Output = Self> + AddAssign
    + Sub<Output = Self>
    + Neg<Output = Self>
{
    const MAX: Self;
}

#[derive(Copy, Clone)]
pub struct Edge<C = Void> {
    // pub from: usize,
    pub to: usize,
    pub cost: C,
    pub id: usize
}

pub struct UndirectedGraph<C>(pub Vec<Vec<Edge<C>>>, pub usize);
pub struct DirectedGraph<C>{
    pub forward: Vec<Vec<Edge<C>>>,
    pub backward: Vec<Vec<Edge<C>>>,
    pub count: usize,
}

pub trait Graph<C: Element> {
    fn new(size: usize) -> Self;
    fn size(&self) -> usize;
    fn add_edge(&mut self, u: usize, v: usize, cost: C);
    fn edges_from(&self, v: usize) -> std::slice::Iter<Edge<C>>;
}

impl<C: Element> Graph<C> for UndirectedGraph<C> {
    fn new(size: usize) -> Self {
        Self(vec![Vec::<Edge<C>>::new(); size], 0)
    }

    fn size(&self) -> usize {
        self.0.len()
    }

    fn add_edge(&mut self, u: usize, v: usize, cost: C) {
        self.0[u].push(Edge{ to: v, cost: cost.clone(), id: self.1 });
        self.0[v].push(Edge{ to: u, cost: cost.clone(), id: self.1 });
        self.1 += 1;
    }

    fn edges_from(&self, v: usize) -> std::slice::Iter<Edge<C>> {
        self.0[v].iter()
    }
}

impl<C: Element> Graph<C> for DirectedGraph<C> {
    fn new(size: usize) -> Self {
        Self {
            forward: vec![Vec::<Edge<C>>::new(); size],
            backward: vec![Vec::<Edge<C>>::new(); size],
            count: 0
        }
    }

    fn size(&self) -> usize {
        self.forward.len()
    }

    fn add_edge(&mut self, u: usize, v: usize, cost: C) {
        self.forward[u].push(Edge{ to: v, cost: cost.clone(), id: self.count });
        self.backward[v].push(Edge{ to: u, cost: cost.clone(), id: self.count });
        self.count += 1;
    }

    fn edges_from(&self, v: usize) -> std::slice::Iter<Edge<C>> {
        self.forward[v].iter()
    }
}

impl<C: Element> DirectedGraph<C> {
    pub fn edges_to(&self, u: usize) -> std::slice::Iter<Edge<C>> {
        self.backward[u].iter()
    }

    pub fn reverse(&self) -> Self {
        Self {
            forward: self.backward.clone(),
            backward: self.forward.clone(),
            count: self.count,
        }
    }
}

macro_rules! impl_cost {
    ($($T:ident,)*) => {
        $(
            impl Cost for $T { const MAX: Self = std::$T::MAX; }
        )*
    };
}

impl_cost! {
    i8, i16, i32, i64, i128, isize,
}

#[derive(Clone, Copy, PartialEq, Eq, PartialOrd, Ord)]
pub struct Void();

impl std::fmt::Display for Void {
    fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
        write!(f, "")
    }
}

impl Zero for Void {
    fn zero() -> Self { Void() }
    fn is_zero(&self) -> bool { true }
}

impl One for Void {
    fn one() -> Self { Void() }
    fn is_one(&self) -> bool { true }
}

impl Add for Void {
    type Output = Self;
    fn add(self, _: Self) -> Self { Void() }
}

impl AddAssign for Void {
    fn add_assign(&mut self, _: Self) {}
}

impl Sub for Void {
    type Output = Self;
    fn sub(self, _: Self) -> Self { Void() }
}

impl Neg for Void {
    type Output = Self;
    fn neg(self) -> Self { Void() }
}

impl Cost for Void { const MAX: Self = Void(); }

// ------------ Graph impl end ------------


// ------------ algebraic traits start ------------
use std::marker::Sized;
use std::ops::*;

/// 元
pub trait Element: Sized + Clone + PartialEq {}
impl<T: Sized + Clone + PartialEq> Element for T {}

/// 結合性
pub trait Associative: Magma {}

/// マグマ
pub trait Magma: Element + Add<Output=Self> {}
impl<T: Element + Add<Output=Self>> Magma for T {}

/// 半群
pub trait SemiGroup: Magma + Associative {}
impl<T: Magma + Associative> SemiGroup for T {}

/// モノイド
pub trait Monoid: SemiGroup + Zero {}
impl<T: SemiGroup + Zero> Monoid for T {}

pub trait ComMonoid: Monoid + AddAssign {}
impl<T: Monoid + AddAssign> ComMonoid for T {}

/// 群
pub trait Group: Monoid + Neg<Output=Self> {}
impl<T: Monoid + Neg<Output=Self>> Group for T {}

pub trait ComGroup: Group + ComMonoid {}
impl<T: Group + ComMonoid> ComGroup for T {}

/// 半環
pub trait SemiRing: ComMonoid + Mul<Output=Self> + One {}
impl<T: ComMonoid + Mul<Output=Self> + One> SemiRing for T {}

/// 環
pub trait Ring: ComGroup + SemiRing {}
impl<T: ComGroup + SemiRing> Ring for T {}

pub trait ComRing: Ring + MulAssign {}
impl<T: Ring + MulAssign> ComRing for T {}

/// 体
pub trait Field: ComRing + Div<Output=Self> + DivAssign {}
impl<T: ComRing + Div<Output=Self> + DivAssign> Field for T {}

/// 加法単元
pub trait Zero: Element {
    fn zero() -> Self;
    fn is_zero(&self) -> bool {
        *self == Self::zero()
    }
}

/// 乗法単元
pub trait One: Element {
    fn one() -> Self;
    fn is_one(&self) -> bool {
        *self == Self::one()
    }
}

macro_rules! impl_integer {
    ($($T:ty,)*) => {
        $(
            impl Associative for $T {}

            impl Zero for $T {
                fn zero() -> Self { 0 }
                fn is_zero(&self) -> bool { *self == 0 }
            }

            impl<'a> Zero for &'a $T {
                fn zero() -> Self { &0 }
                fn is_zero(&self) -> bool { *self == &0 }
            }

            impl One for $T {
                fn one() -> Self { 1 }
                fn is_one(&self) -> bool { *self == 1 }
            }

            impl<'a> One for &'a $T {
                fn one() -> Self { &1 }
                fn is_one(&self) -> bool { *self == &1 }
            }
        )*
    };
}

impl_integer! {
    i8, i16, i32, i64, i128, isize,
    u8, u16, u32, u64, u128, usize,
}
// ------------ algebraic traits end ------------



// ------------ io module start ------------
use std::io::{stdout, BufWriter, Read, StdoutLock, Write};

pub struct IO {
	iter: std::str::SplitAsciiWhitespace<'static>,
	buf: BufWriter<StdoutLock<'static>>,
}

impl IO {
	pub fn new() -> Self {
		let mut input = String::new();
		std::io::stdin().read_to_string(&mut input).unwrap();
		let input = Box::leak(input.into_boxed_str());
		let out = Box::new(stdout());
		IO {
			iter: input.split_ascii_whitespace(),
			buf: BufWriter::new(Box::leak(out).lock()),
		}
	}
	fn scan_str(&mut self) -> &'static str {
		self.iter.next().unwrap()
	}
	pub fn scan<T: Scan>(&mut self) -> <T as Scan>::Output {
		<T as Scan>::scan(self)
	}
	pub fn scan_vec<T: Scan>(&mut self, n: usize) -> Vec<<T as Scan>::Output> {
		(0..n).map(|_| self.scan::<T>()).collect()
	}
	pub fn print<T: Print>(&mut self, x: T) {
		<T as Print>::print(self, x);
	}
	pub fn println<T: Print>(&mut self, x: T) {
		self.print(x);
		self.print("\n");
	}
	pub fn iterln<T: Print, I: Iterator<Item = T>>(&mut self, mut iter: I, delim: &str) {
		if let Some(v) = iter.next() {
			self.print(v);
			for v in iter {
				self.print(delim);
				self.print(v);
			}
		}
		self.print("\n");
	}
	pub fn flush(&mut self) {
		self.buf.flush().unwrap();
	}
}

impl Default for IO {
	fn default() -> Self {
		Self::new()
	}
}

pub trait Scan {
	type Output;
	fn scan(io: &mut IO) -> Self::Output;
}

macro_rules! impl_scan {
	($($t:tt),*) => {
		$(
			impl Scan for $t {
				type Output = Self;
				fn scan(s: &mut IO) -> Self::Output {
					s.scan_str().parse().unwrap()
				}
			}
		)*
	};
}

impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String, f32, f64);

impl Scan for char {
	type Output = char;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().next().unwrap()
	}
}

pub enum Bytes {}
impl Scan for Bytes {
	type Output = &'static [u8];
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().as_bytes()
	}
}

pub enum Chars {}
impl Scan for Chars {
	type Output = Vec<char>;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().collect()
	}
}

pub enum Usize1 {}
impl Scan for Usize1 {
	type Output = usize;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan::<usize>().wrapping_sub(1)
	}
}

impl<T: Scan, U: Scan> Scan for (T, U) {
	type Output = (T::Output, U::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan> Scan for (T, U, V) {
	type Output = (T::Output, U::Output, V::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan, W: Scan> Scan for (T, U, V, W) {
	type Output = (T::Output, U::Output, V::Output, W::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s), W::scan(s))
	}
}

pub trait Print {
	fn print(w: &mut IO, x: Self);
}

macro_rules! impl_print_int {
	($($t:ty),*) => {
		$(
			impl Print for $t {
				fn print(w: &mut IO, x: Self) {
					w.buf.write_all(x.to_string().as_bytes()).unwrap();
				}
			}
		)*
	};
}

impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize, f32, f64);

impl Print for u8 {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(&[x]).unwrap();
	}
}

impl Print for &[u8] {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(x).unwrap();
	}
}

impl Print for &str {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl Print for String {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl<T: Print, U: Print> Print for (T, U) {
	fn print(w: &mut IO, (x, y): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
	}
}

impl<T: Print, U: Print, V: Print> Print for (T, U, V) {
	fn print(w: &mut IO, (x, y, z): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
		w.print(" ");
		w.print(z);
	}
}

mod neboccoio_macro {
	#[macro_export]
	macro_rules! input {
		(@start $io:tt @read @rest) => {};

		(@start $io:tt @read @rest, $($rest: tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @rest mut $($rest:tt)*) => {
			input!(@start $io @read @mut [mut] @rest $($rest)*)
		};

		(@start $io:tt @read @rest $($rest:tt)*) => {
			input!(@start $io @read @mut [] @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [[$kind:tt; $len1:expr]; $len2:expr] $($rest:tt)*) => {
			let $($mut)* $var = (0..$len2).map(|_| $io.scan_vec::<$kind>($len1)).collect::<Vec<Vec<$kind>>>();
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($rest:tt)*) => {
			let $($mut)* $var = $io.scan_vec::<$kind>($len);
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => {
			let $($mut)* $var = $io.scan::<$kind>();
			input!(@start $io @read @rest $($rest)*)
		};

		(from $io:tt $($rest:tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};
	}
}

// ------------ io module end ------------
0