#863462 (Rust) No.5007 Steiner Space Travel

• 問題: No.5007 Steiner Space Travel
• ユーザー: r3yohei
• 提出日時: 2023-04-28 14:06:57
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 905 ms / 1,000 ms
• コード長: 20,391 bytes
• コンパイル時間: 2,590 ms
• コンパイル使用メモリ: 175,160 KB
• 実行使用メモリ: 4,376 KB
• スコア: 8,526,594
• 最終ジャッジ日時: 2023-04-28 14:07:44
• 合計ジャッジ時間: 32,149 ms
• ジャッジサーバーID （参考情報）: judge12 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	901 ms; 4,368 KB
testcase_01	AC	903 ms; 4,372 KB
testcase_02	AC	904 ms; 4,372 KB
testcase_03	AC	902 ms; 4,368 KB
testcase_04	AC	902 ms; 4,372 KB
testcase_05	AC	904 ms; 4,368 KB
testcase_06	AC	903 ms; 4,372 KB
testcase_07	AC	904 ms; 4,372 KB
testcase_08	AC	902 ms; 4,368 KB
testcase_09	AC	902 ms; 4,376 KB
testcase_10	AC	904 ms; 4,372 KB
testcase_11	AC	905 ms; 4,368 KB
testcase_12	AC	903 ms; 4,368 KB
testcase_13	AC	905 ms; 4,372 KB
testcase_14	AC	903 ms; 4,368 KB
testcase_15	AC	903 ms; 4,368 KB
testcase_16	AC	904 ms; 4,368 KB
testcase_17	AC	902 ms; 4,368 KB
testcase_18	AC	901 ms; 4,368 KB
testcase_19	AC	903 ms; 4,372 KB
testcase_20	AC	903 ms; 4,368 KB
testcase_21	AC	902 ms; 4,372 KB
testcase_22	AC	902 ms; 4,368 KB
testcase_23	AC	905 ms; 4,372 KB
testcase_24	AC	902 ms; 4,372 KB
testcase_25	AC	902 ms; 4,372 KB
testcase_26	AC	903 ms; 4,368 KB
testcase_27	AC	902 ms; 4,368 KB
testcase_28	AC	903 ms; 4,368 KB
testcase_29	AC	904 ms; 4,368 KB

ソースコード

#![allow(non_snake_case, unused)]

use std::{io::*, hash};
use std::{collections::*, fmt::format};
use std::{cmp::*, vec};
use std::time::SystemTime;
use std::collections::hash_map::DefaultHasher;
use std::hash::{Hash, Hasher};
use std::ops::{Add, Sub, Rem, Mul};
use crate::input::{*, marker::*};
use self::i64::kmeans;

// コピペで使える proconio もどき
// cunitacさんからお借りしています
// https://gist.github.com/cunitac/b00be62bf68c9fb6055d22eb77c17e14
pub mod input {
    use std::{
        cell::RefCell,
        fmt::Debug,
        io::{stdin, BufRead, BufReader, Stdin},
        str::{FromStr, SplitWhitespace},
    };

    thread_local!(
        pub static STDIN_SOURCE: RefCell<Source> = RefCell::new(Source {
            stdin: BufReader::new(stdin()),
            tokens: "".split_whitespace(),
        });
    );

    pub struct Source {
        stdin: BufReader<Stdin>,
        tokens: SplitWhitespace<'static>,
    }
    impl Source {
        pub fn next_token(&mut self) -> Option<&str> {
            self.tokens.next().or_else(|| {
                let mut input = String::new();
                self.stdin.read_line(&mut input).unwrap();
                self.tokens = Box::leak(input.into_boxed_str()).split_whitespace();
                self.tokens.next()
            })
        }
    }
    #[macro_export]
    macro_rules! read_value {
        (from $s:expr, [$t:tt; $n:expr]) => {
            (0..$n).map(|_| $crate::read_value!(from $s, $t)).collect::<Vec<_>>()
        };
        (from $s:expr, [$t:tt]) => {
            let n = $crate::read_value!(from $s, usize);
            $crate::read_value!(from $s, [$t; n])
        };
        (from $s:expr, $t:ty) => {
            <$t as $crate::input::Readable>::read(&mut $s)
        };
        (from $s:expr, $($t:tt),* $(,)?) => {
            ($($crate::read_value!(from $s, $t)),*)
        };
        ($($r:tt)*) => {
            $crate::input::STDIN_SOURCE.with(|s| {
                let mut s = s.borrow_mut();
                $crate::read_value!(from s, $($r)*)
            })
        }
    }
    #[macro_export]
    macro_rules! input {
        () => {
        };
        ($x:tt: $t:tt, $($r:tt)*) => {
            let $x = $crate::read_value!($t);
            $crate::input!($($r)*);
        };
        (mut $x:tt: $t:tt, $($r:tt)*) => {
            let mut $x = $crate::read_value!($t);
            $crate::input!($($r)*);
        };
        (from $s:expr, $x:tt, $t:tt, $($r:tt)*) => {
            let $x = $crate::read_value!(from $s, $t);
            $crate::input!(from $s, $($r)*);
        };
        (from $s:expr, mut $x:tt, $t:tt, $($r:tt)*) => {
            let mut $x = $crate::read_value!(from $s, $t);
            $crate::input!(from $s, $($r)*);
        };
        ($($r:tt)*) => {
            $crate::input!($($r)*,);
        };
    }
    pub trait Readable {
        type Output;
        fn read(source: &mut Source) -> Self::Output;
    }
    impl<T: FromStr<Err = E>, E: Debug> Readable for T {
        type Output = T;
        fn read(source: &mut Source) -> T {
            source.next_token().unwrap().parse().unwrap()
        }
    }
    pub mod marker {
        macro_rules! impl_readable {
            ($e:ident, $t:ty, $u:ty, $f:expr) => {
                pub enum $e {}
                impl $crate::input::Readable for $e {
                    type Output = $t;
                    fn read(mut source: &mut $crate::input::Source) -> $t {
                        $f($crate::read_value!(from source, $u))
                    }
                }
            };
        }
        impl_readable!(Usize1, usize, usize, |x| x - 1);
        impl_readable!(Isize1, isize, isize, |x| x - 1);
        impl_readable!(Chars, Vec<char>, String, |x: String| x.chars().collect());
        impl_readable!(Bytes, Vec<u8>, String, |x: String| x.bytes().collect());
    }
}

// yukicoder用乱数生成器
// 現在時刻のハッシュ値を適当な範囲に変換する
// 半開区間 [min, max) を引数に取る
fn rand<T>(min: T, max: T) -> T
where
    T: UnsignedInteger,
{
    let random_number = generate_random_number();
    T::generate_in_range(random_number, min, max)
}
fn generate_random_number() -> u64 {
    let now = SystemTime::now();
    let mut hasher = DefaultHasher::new();
    now.hash(&mut hasher);
    hasher.finish()
}
trait UnsignedInteger:
    Copy + PartialEq + PartialOrd + Add<Output = Self> + Sub<Output = Self> + Rem<Output = Self> + Mul<Output = Self>
{
    fn generate_in_range(random_number: u64, min: Self, max: Self) -> Self;
}

impl UnsignedInteger for usize {
    fn generate_in_range(random_number: u64, min: Self, max: Self) -> Self {
        (random_number as usize % (max - min)) + min
    }
}

impl UnsignedInteger for u8 {
    fn generate_in_range(random_number: u64, min: Self, max: Self) -> Self {
        (random_number as u8 % (max - min)) + min
    }
}

impl UnsignedInteger for u16 {
    fn generate_in_range(random_number: u64, min: Self, max: Self) -> Self {
        (random_number as u16 % (max - min)) + min
    }
}

impl UnsignedInteger for u32 {
    fn generate_in_range(random_number: u64, min: Self, max: Self) -> Self {
        (random_number as u32 % (max - min)) + min
    }
}

impl UnsignedInteger for u64 {
    fn generate_in_range(random_number: u64, min: Self, max: Self) -> Self {
        (random_number % (max - min)) + min
    }
}

impl UnsignedInteger for u128 {
    fn generate_in_range(random_number: u64, min: Self, max: Self) -> Self {
        (random_number as u128 % (max - min)) + min
    }
}

macro_rules! impl_kmeans {
    ($kind: ty, $modname: ident) => {
        // Since we can't overload methods in rust, we have to use namespacing
        pub mod $modname {
            use std::$modname::MAX;

            /// computes sum of squared deviation between two identically sized vectors
            /// `x`, and `y`.
            fn distance(x: &[$kind], y: &[$kind]) -> $kind {
                x.iter()
                    .zip(y.iter())
                    .fold(0, |dist, (&xi, &yi)| dist + (xi - yi) * (xi - yi))
            }

            /// Returns a vector containing the indices z<sub>i</sub> in {0, ..., K-1} of
            /// the centroid nearest to each datum.
            fn nearest_centroids(xs: &[Vec<$kind>], centroids: &[Vec<$kind>]) -> Vec<usize> {
                xs.iter()
                    .map(|xi| {
                        // Find the argmin by folding using a tuple containing the argmin
                        // and the minimum distance.
                        let (argmin, _) = centroids.iter().enumerate().fold(
                            (0_usize, MAX),
                            |(min_ix, min_dist), (ix, ci)| {
                                let dist = distance(xi, ci);
                                if dist < min_dist {
                                    (ix, dist)
                                } else {
                                    (min_ix, min_dist)
                                }
                            },
                        );
                        argmin
                    })
                    .collect()
            }

            /// Recompute the centroids given the current clustering
            fn recompute_centroids(
                xs: &[Vec<$kind>],
                clustering: &[usize],
                k: usize,
            ) -> Vec<Vec<$kind>> {
                let ndims = xs[0].len();

                // NOTE: Kind of inefficient because we sweep all the data from each of the
                // k centroids.
                (0..k)
                    .map(|cluster_ix| {
                        let mut centroid: Vec<$kind> = vec![0; ndims];
                        let mut n_cluster: $kind = 0;
                        xs.iter().zip(clustering.iter()).for_each(|(xi, &zi)| {
                            if zi == cluster_ix {
                                n_cluster += 1;
                                xi.iter().enumerate().for_each(|(j, &x_ij)| {
                                    centroid[j] += x_ij;
                                });
                            }
                        });
                        centroid.iter().map(|&c_j| c_j / n_cluster).collect()
                    })
                    .collect()
            }

            /// Assign the N D-dimensional data, `xs`, to `k` clusters using K-Means clustering
            pub fn kmeans(xs: Vec<Vec<$kind>>, k: usize) -> (Vec<usize>, Vec<Vec<$kind>>) {
                assert!(xs.len() >= k);

                // Rather than pulling in a dependency to radomly select the staring
                // points for the centroids, we're going to deterministally choose them by
                // slecting evenly spaced points in `xs`
                let n_per_cluster: usize = xs.len() / k;
                let centroids: Vec<Vec<$kind>> =
                    (0..k).map(|j| xs[j * n_per_cluster].clone()).collect();

                let mut clustering = nearest_centroids(&xs, &centroids);

                loop {
                    let centroids = recompute_centroids(&xs, &clustering, k);
                    let new_clustering = nearest_centroids(&xs, &centroids);

                    // loop until the clustering doesn't change after the new centroids are computed
                    if new_clustering
                        .iter()
                        .zip(clustering.iter())
                        .all(|(&za, &zb)| za == zb)
                    {
                        // We need to use `return` to break out of the `loop`
                        return (clustering, centroids);
                    } else {
                        clustering = new_clustering;
                    }
                }
            }
        }
    };
}
impl_kmeans!(i64, i64);

const N: usize = 100;
const M: usize = 8;
const ALPHA: i64 = 5;
const INF: i64 = 1_000_000_000;
const TL: f64 = 0.9;

pub fn get_time() -> f64 {
    static mut STIME: f64 = -1.0;
    let t = std::time::SystemTime::now().duration_since(std::time::UNIX_EPOCH).unwrap();
    let ms = t.as_secs() as f64 + t.subsec_nanos() as f64 * 1e-9;
    unsafe {
        if STIME < 0.0 {
            STIME = ms;
        }
        // ローカル環境とジャッジ環境の実行速度差はget_timeで吸収しておくと便利
        #[cfg(feature = "local")]
        {
            (ms - STIME) * 1.5
        }
        #[cfg(not(feature = "local"))]
        {
            (ms - STIME)
        }
    }
}

// 頂点の種類によって距離の二乗を返す
pub fn squared_distance(xi: i64, y1: i64, i: usize, xj: i64, y2: i64, j: usize) -> i64 {
    if i < N && j < N {
        ((xi - xj) * (xi - xj) + (y1 - y2) * (y1 - y2)) * ALPHA * ALPHA
    } else if i < N || j < N {
        ((xi - xj) * (xi - xj) + (y1 - y2) * (y1 - y2)) * ALPHA
    } else {
        ((xi - xj) * (xi - xj) + (y1 - y2) * (y1 - y2))
    }
}

#[derive(Clone)]
pub struct Input {
    pos: Vec<Vec<i64>>,
}
impl Input {
    fn new() -> Self {
        input! {
            _n: usize,
            _m: usize,
        }
        let mut pos = vec![];
        for _ in 0..N {
            input! {
                ai: i64,
                bi: i64,
            }
            pos.push(vec![ai, bi]);
        }
        Self { pos }
    }
}

// ワーシャルフロイドで全点対間最短経路を求める
pub fn warshall_floyd(pos: &Vec<Vec<i64>>) -> Vec<Vec<i64>> {
    let mut dist = vec![vec![INF; N+M]; N+M];
    // 自身への距離は0
    for i in 0..N+M {
        dist[i][i] = 0;    
    }
    // (i,j)間の距離を入れる
    for i in 0..N+M {
        for j in i+1..N+M {
            dist[i][j] = squared_distance(pos[i][0], pos[i][1], i, pos[j][0], pos[j][1], j);
            dist[j][i] = dist[i][j];
        }
    }
    // ワーシャルフロイド法
    for k in 0..N+M {
        for i in 0..N+M {
            for j in 0..N+M {
                // (i,j)間はkを経由したほうが短くなるか調べる
                if dist[i][j] > dist[i][k] + dist[k][j] {
                    dist[i][j] = dist[i][k] + dist[k][j];
                }
            }
        }
    }
    dist
}

// (i, j)間の最短パスをダイクストラで見つける
pub fn dijkstra(pos: &Vec<Vec<i64>>, s: usize, t: usize) -> (Vec<(usize, usize)>, Vec<i64>, i64) {
    // s->tパスをダイクストラで見つける
    let mut dist = vec![INF; N+M];
    dist[s] = 0;
    let mut prev = vec![!0; N+M]; // 経路復元用
    let mut bh = BinaryHeap::new();
    bh.push((Reverse(0), s));
    while let Some((Reverse(d), frm)) = bh.pop() {
        // 目的地についているなら，終了する
        if frm == t {break;}
        // 見ようとしているものより既にいい経路が見つかっていれば飛ばす
        if dist[frm] < d {continue;}
        for to in 0..N+M {
            let energy = squared_distance(pos[frm][0], pos[frm][1], frm, pos[to][0], pos[to][1], to);
            if d + energy < dist[to] {
                // コストを更新したほうがいいなら，更新しつつ優先度付きキューに入れる
                dist[to] = d + energy;
                prev[to] = frm; // 頂点 frm -> toにたどり着いた
                bh.push((Reverse(dist[to]), to));
            }
        }
    }
    // 経路復元
    let mut path = vec![];
    let mut energy = vec![];
    let mut sum_energy = 0;
    let mut tt = t;
    while tt != !0 {
        // toがstartになるまでprev[to]を辿っていく
        // 途中のエネルギーを保存しておく
        if !path.is_empty() {
            let &(last_type, mut last_index) = path.last().unwrap();
            // pathにはちゃんとした回答用のものが入っているので，惑星かステーションかによってindexをずらすかどうか見ないといけない
            last_index = if last_type == 1 {
                // よくわからないが型推論できないと怒られる
                last_index as usize
            } else {
                last_index + N
            };
            // last_index = last_index as usize;
            let tmp_energy = squared_distance(pos[last_index][0], pos[last_index][1], last_index, pos[tt][0], pos[tt][1], tt);
            energy.push(tmp_energy);
            sum_energy += tmp_energy;
        }
        if tt < N {
            // 惑星
            path.push((1, tt));
        } else {
            // ステーション
            path.push((2, tt - N));
        }
        tt = prev[tt];
    }
    path.reverse();
    energy.reverse();
    (path, energy, sum_energy)
}

// 始点sから開始して，未訪問の惑星で一番近いものへのパスを経路復元つきダイクストラで求めていく
pub fn init_path(pos: &Vec<Vec<i64>>, dist_warshall_floyd: &Vec<Vec<i64>>) -> (Vec<(usize, usize)>, Vec<i64>, i64) {
    let mut path = vec![];
    let mut energy = vec![];
    let mut sum_energy = 0;
    let mut s = 0;
    let mut visited = vec![false; N];
    visited[s] = true;
    for i in 0..N {
        // sから未訪問の惑星のうち，一番近いものを見つける
        let mut min_dist = INF;
        let mut t = !0;
        if i < N - 1 {
            // 惑星1以外のN-1個の探索
            for j in 0..N {
                if s == j || visited[j] {continue;}
                if dist_warshall_floyd[s][j] < min_dist {
                    min_dist = dist_warshall_floyd[s][j];
                    t = j;
                }
            }
        } else {
            // 最後は惑星1に帰ってきたいので，visitedを無視してt=0にする
            t = 0;
        }
        // s->tパスをダイクストラで見つけ，全体に追加
        let (mut small_path, small_energy, small_sum_energy) = dijkstra(&pos, s, t);
        if i < N - 1 {
            // 最後に惑星1に帰ってくるまでは，終点は次の始点になり，次のsmall_pathの先頭に含まれるので捨てる
            small_path.pop();
        }
        path.extend(small_path);
        energy.extend(small_energy);
        sum_energy += small_sum_energy;
        // 次のイテレーションのための更新
        s = t;
        visited[t] = true;
    }
    (path, energy, sum_energy)
}

#[derive(Clone)]
struct State {
    turn: i64,
    is_done: bool,
    game_score: i64,
    evaluated_score: i64,
    pos: Vec<Vec<i64>>, // 先頭N個に惑星の場所，続くM個にステーションの場所が格納されている
    path: Vec<(usize, usize)>, // 道順 (惑星orステーション，番号)
    energy: Vec<i64>, // 上記パスを通った場合に消費するエネルギー
    sum_energy: i64, // 上記の合計
}
impl State {
    fn new(input: &Input) -> Self {
        // 各惑星をkmeansでクラスタリングする
        // どのクラスタに所属するかと，各クラスタのセントロイドを保持し，セントロイドは宇宙ステーションとする
        let (cluster, mut station) = kmeans(input.pos.clone(), M);
        let mut pos = input.pos.clone();
        pos.extend(station);
        // 惑星と宇宙ステーションの位置をもとに，(i, j)間の距離をワーシャルフロイドで求めておく
        let dist_warshall_floyd = warshall_floyd(&pos);
        let (path, energy, sum_energy) = init_path(&pos, &dist_warshall_floyd);
        Self {
            turn: 0,
            is_done: false,
            game_score: 0,
            evaluated_score: 0,
            pos,
            path,
            energy,
            sum_energy,
        }
    }
    // 任意のステーションの位置を少しずらす
    pub fn shift_station(&mut self) {
        let target_station = rand(0, M);
        let diff = 25_u64;
        let mut diff_x = rand(1_u64, diff) as i64;
        if rand(1_u8, 3_u8) == 1 {
            diff_x *= -1;
        }
        let mut diff_y = rand(1_u64, diff) as i64;
        if rand(1_u8, 3_u8) == 1 {
            diff_y *= -1;
        }
        // 0~1000の範囲を守ってずらす
        self.pos[N + target_station][0] = min(max(0, self.pos[N + target_station][0] + diff_x), 1000);
        self.pos[N + target_station][1] = min(max(0, self.pos[N + target_station][1] + diff_y), 1000);
        // 惑星と宇宙ステーションの位置をもとに，(i, j)間の距離をワーシャルフロイドで求めておく
        let dist_warshall_floyd = warshall_floyd(&self.pos);
        let (path, energy, sum_energy) = init_path(&self.pos, &dist_warshall_floyd);
        self.path = path;
        self.energy = energy;
        self.sum_energy = sum_energy;
    }
    pub fn two_opt(&mut self) {
        // let v = self.route.len();
    }
    // スコア計算
    pub fn compute_score(&mut self) {
        self.game_score = (1_000_000_000 as f64 / (1_000 as f64 + (self.sum_energy as f64).sqrt())).round() as i64;
    }
    // 1-indexに直しつつ回答を出力
    pub fn print(&self) {
        for i in 0..M {
            println!("{} {}", self.pos[i + N][0], self.pos[i + N][1]);
        }
        let v = self.path.len();
        println!("{}", v);
        for i in 0..v {
            let (ti, ri) = self.path[i];
            println!("{} {}", ti, ri + 1);
        }
    }
}

fn main() {
    // 2-optに見えるが，再訪ありなので単純には適応できない
    // ただ，宇宙ステーションに再訪してもいいが，惑星は再訪しないほうがよい？
    // 近傍: 
    // - 2-opt (ただし，最初と最後が惑星1なのは固定する)
    // - 少なくとも一方が宇宙ステーションであるパスの追加
    // - いずれかの宇宙ステーションの座標をずらす (あるいは，これはあらかじめk-meansで求めておく)
    get_time();
    let input = Input::new();
    let mut state = State::new(&input);
    state.compute_score();

    let mut iter = 0;
    while get_time() < TL {
        iter += 1;
        let mut next_state = state.clone();
        next_state.shift_station();
        next_state.compute_score();
        if next_state.game_score > state.game_score {
            state = next_state;
        }
    }

    state.print();
    eprintln!("iter: {}", iter);
    eprintln!("score: {}", state.game_score);
    eprintln!("time: {}", get_time());
}