結果

問題 No.168 ものさし
ユーザー nebocco
提出日時 2021-03-20 12:33:16
言語 Rust
(1.83.0 + proconio)
結果
AC  
実行時間 72 ms / 2,000 ms
コード長 18,075 bytes
コンパイル時間 14,834 ms
コンパイル使用メモリ 401,948 KB
実行使用メモリ 19,848 KB
最終ジャッジ日時 2024-11-20 21:35:15
合計ジャッジ時間 16,563 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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ファイルパターン 結果
sample AC * 4
other AC * 19
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ソースコード

diff #
プレゼンテーションモードにする

fn main() {
    let mut io = IO::new();
    input!{ from io,
        n: usize,
        p: [(i64, i64); n]
    }
    let mut g = UndirectedGraph::new(n);
    let mut edges = Vec::with_capacity(n*n);
    for i in 0..n {
        for j in i+1..n {
            edges.push((i, j, (p[i].0 - p[j].0).pow(2) + (p[i].1 - p[j].1).pow(2)));
        }
    }
    kruskal(&mut g, &mut edges);
    let dist = tree_dfs(&g, 0).0;
    let tar = dist[n-1];
    let mut x = sqrt_floor(tar);
    if x * x < tar {
        x += 1;
    }
    io.println((x + 9) / 10 * 10);
}
pub fn sqrt_floor(x: i64) -> i64 {
    let c = (64 - x.leading_zeros() + 1) / 2;
    let mut v = if c < 32 {
        1 << c
    } else {
        3_037_000_499
    };
    while v * v > x {
        v = (v + x / v) / 2;
    }
    v
}
// ------------ 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 ------------
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].max(e.cost);
            q.push(e.to);
        }
    }
    for &v in euler.iter().skip(1).rev() {
        size[par[v].unwrap()] += size[v];
    }
    (dist, par, size, euler)
}
// ------------ 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 ------------
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