#865345 (Rust) No.5007 Steiner Space Travel

• 問題: No.5007 Steiner Space Travel
• ユーザー: r3yohei
• 提出日時: 2023-05-02 02:33:00
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 982 ms / 1,000 ms
• コード長: 23,540 bytes
• コンパイル時間: 2,880 ms
• コンパイル使用メモリ: 171,144 KB
• 実行使用メモリ: 4,372 KB
• スコア: 8,872,406
• 最終ジャッジ日時: 2023-05-02 02:33:36
• 合計ジャッジ時間: 35,297 ms
• ジャッジサーバーID （参考情報）: judge13 / judge14

ファイルパターン	結果
other	AC * 30

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 crate::input::{*, marker::*};
use crate::rand::Xoshiro256;
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());
    }
}


mod rand {
    pub(crate) struct Xoshiro256 {
        s0: u64,
        s1: u64,
        s2: u64,
        s3: u64,
    }

    impl Xoshiro256 {
        pub(crate) fn new(mut seed: u64) -> Self {
            let s0 = split_mix_64(&mut seed);
            let s1 = split_mix_64(&mut seed);
            let s2 = split_mix_64(&mut seed);
            let s3 = split_mix_64(&mut seed);
            Self { s0, s1, s2, s3 }
        }

        fn next(&mut self) -> u64 {
            let result = (self.s1.wrapping_mul(5)).rotate_left(7).wrapping_mul(9);
            let t = self.s1 << 17;

            self.s2 ^= self.s0;
            self.s3 ^= self.s1;
            self.s1 ^= self.s2;
            self.s0 ^= self.s3;
            self.s2 ^= t;
            self.s3 = self.s3.rotate_left(45);

            result
        }

        pub(crate) fn gen_usize(&mut self, lower: usize, upper: usize) -> usize {
            assert!(lower < upper);
            let count = upper - lower;
            (self.next() % count as u64) as usize + lower
        }

        pub(crate) fn gen_i64(&mut self, lower: i64, upper: i64) -> i64 {
            assert!(lower < upper);
            let count = upper - lower;
            (self.next() % count as u64) as i64 + lower
        }

        pub(crate) fn gen_f64(&mut self) -> f64 {
            const UPPER_MASK: u64 = 0x3ff0000000000000;
            const LOWER_MASK: u64 = 0xfffffffffffff;
            let result = UPPER_MASK | (self.next() & LOWER_MASK);
            let result: f64 = unsafe { std::mem::transmute(result) };
            result - 1.0
        }

        pub(crate) fn gen_bool(&mut self, prob: f64) -> bool {
            self.gen_f64() < prob
        }
    }

    fn split_mix_64(x: &mut u64) -> u64 {
        *x = x.wrapping_add(0x9e3779b97f4a7c15);
        let mut z = *x;
        z = (z ^ z >> 30).wrapping_mul(0xbf58476d1ce4e5b9);
        z = (z ^ z >> 27).wrapping_mul(0x94d049bb133111eb);
        z ^ z >> 31
    }
}

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 MAP_SIZE: i64 = 1000;
const INF: i64 = 1_000_000_000;
const TL: f64 = 0.98;
// const TL: f64 = 10.0;
// この問題は解の改善幅が10^3オーダーくらい
// 仮に1000悪くなりT=1000のとき，e^(-1) = 1/2.7くらいの確率で採用される
// T=500ならe^(-2) = 1/(2.7)^2
const T0: f64 = 10000.; // 焼きなまし初期温度
const T1: f64 = 20.; // 焼きなまし終温度

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
// あまり宇宙ステーションを贔屓し過ぎないようなパラメータも考慮
pub fn squared_distance(point_i: Position, i: usize, point_j: Position, j: usize) -> i64 {
    if i < N && j < N {
        ((point_i.x - point_j.x) * (point_i.x - point_j.x) + (point_i.y - point_j.y) * (point_i.y - point_j.y)) * ALPHA * ALPHA
    } else if i < N || j < N {
        ((point_i.x - point_j.x) * (point_i.x - point_j.x) + (point_i.y - point_j.y) * (point_i.y - point_j.y)) * ALPHA
    } else {
        ((point_i.x - point_j.x) * (point_i.x - point_j.x) + (point_i.y - point_j.y) * (point_i.y - point_j.y))
    }
}

#[derive(Debug, Clone, Copy, PartialEq, Eq, PartialOrd, Ord)]
pub struct Position {
    x: i64,
    y: i64,
}

impl Position {
    fn new(x: i64, y: i64) -> Self {
        Self { x, y }
    }

    fn dist_sq(&self, other: &Self) -> i64 {
        let dx = self.x - other.x;
        let dy = self.y - other.y;
        (dx * dx + dy * dy) as i64
    }
}

#[derive(Clone)]
pub struct Input {
    pos: Vec<Position>, // 惑星の位置
    dist: Vec<Vec<i64>>, // ステーションを無視した惑星同士の距離
}
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(Position::new(ai, bi));
        }
        let dist = warshall_floyd(&pos);
        Self { pos, dist }
    }
}

// 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<Position>) -> Vec<Vec<i64>> {
    let mut dist = vec![vec![0; pos.len()]; pos.len()];
    // (i,j)間の距離を入れる
    for i in 0..pos.len() {
        for j in i+1..pos.len() {
            dist[i][j] = squared_distance(pos[i], i, pos[j], j);
            dist[j][i] = dist[i][j];
        }
    }
    // ワーシャルフロイド法
    for k in 0..pos.len() {
        for i in 0..pos.len() {
            for j in 0..pos.len() {
                // (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<Position>, s: usize, t: usize) -> Vec<usize> {
    // 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], frm, pos[to], 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 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
        path.push(tt);
        tt = prev[tt];
    }
    path.reverse();
    path
}

// 惑星1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<Position>, dist: &Vec<Vec<i64>>) -> Vec<usize> {
    let mut path = vec![];
    let mut visited = vec![false; N];
    let mut s = 0;
    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 {
            // 目的地以外の最大N-1個の探索
            for j in 0..N {
                if visited[j] || j == 0 {continue;}
                if dist[s][j] < min_dist {
                    min_dist = dist[s][j];
                    t = j;
                }
            }
            // ここまで来てもt = !0のままなら，すべて訪問済みなのでcontinueしてよい
            if t == !0 {continue;}
        } else {
            // 最後は目的地に帰ってきたいので，visitedを無視して設定
            t = 0;
        }
        // eprintln!("s {}, t {}", s, t);
        // s->tパスをダイクストラで見つけ，全体に追加
        let mut small_path = dijkstra(&pos, s, t);
        if t != 0 {
            // 目的地以外では，tが次のsになるので，pathとしては含めなくてよい
            small_path.pop();
        }
        path.extend(small_path);
        // 次のイテレーションのための更新
        s = t;
        visited[t] = true;
    }
    path
}

#[derive(Clone)]
struct State {
    pos: Vec<Position>, // 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>, // 道順 (惑星orステーション，番号)
}
impl State {
    fn new(input: &Input) -> Self {
        // 惑星の位置をinputからもらってくる
        let mut pos = input.pos.clone();
        // kmeansでステーションの初期位置を定めるため，posを変換
        let mut pos_kmeans = vec![];
        for i in 0..pos.len() {
            pos_kmeans.push(vec![pos[i].x, pos[i].y]);
        }
        let (_, station_kmeans) = kmeans(pos_kmeans, 8);
        let mut station = vec![];
        for i in 0..M {
            station.push(Position::new(station_kmeans[i][0], station_kmeans[i][1]));
        }
        pos.extend(station);
        // // ステーションの位置は雑に初期化する
        // for _ in 0..M {
        //     pos.push(pos[0]);
        // }
        // 道順は，とりあえず0~N,0の順に通るよう初期化する
        // let mut path = vec![];
        // for i in 0..N {
        //     path.push(i);
        // }
        // path.push(0);
        let path = init_path(&pos, &input.dist);
        Self {pos, path}
    }
    fn calc_score_all(&self, input: &Input) -> i64 {
        let mut score = 0;

        for w in self.path.windows(2) {
            let (prev, next) = (w[0], w[1]);
            score += self.calc_score(input, prev, next);
        }

        score
    }
    #[inline]
    fn calc_score(&self, input: &Input, prev: usize, next: usize) -> i64 {
        if prev < N && next < N {
            input.dist[prev][next]
        } else {
            let dist_sq = squared_distance(self.pos[prev], prev, self.pos[next], next);
            dist_sq
        }
    }
    // 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].x, self.pos[i + N].y);
        }
        let v = self.path.len();
        println!("{}", v);
        for &i in self.path.iter() {
            if i < N {
                println!("1 {}", i + 1);
            } else {
                println!("2 {}", i + 1 - N);
            }
        }
    }
}

fn restore_solution(input: &Input, solution: &State) -> State {
    let mut new_solution = solution.clone();
    new_solution.path.clear();
    new_solution.path.push(0);

    for w in solution.path.windows(2) {
        let (prev, next) = (w[0], w[1]);
        let path = dijkstra(&input.pos, prev, next);
        for v in path {
            new_solution.path.push(v);
        }
    }

    new_solution
}


fn main() {
    get_time();
    let mut rng = Xoshiro256::new(42);
    let input = Input::new();
    let mut state = State::new(&input);

    let mut iter = 0;
    let mut accepted_count = 0;
    let mut update_best_count = 0;
    let mut current_score = state.calc_score_all(&input);
    let mut best_score = current_score;
    let mut best_state = state.clone();
    let t = get_time() / TL;
    let mut T = T0.powf(1.0 - t) * T1.powf(t);
    while get_time() < TL {
        iter += 1;
        if (iter & ((1 << 6) - 1)) == 0 {
            let t = get_time() / TL;
            T = T0.powf(1.0 - t) * T1.powf(t);
        }
        // 乱数で生じさせた数値に応じて近傍を選択
        let neighbor_type = rng.gen_usize(0, 10);
        if neighbor_type < 5 {
            // 近傍3: あるstationを一旦削除し、ランダムにずらした上で、各辺でstationを使う/使わないを貪欲に決め直す
            let station_id = N + rng.gen_usize(0, M);
            let mut tmp_path = state.path.clone();
            tmp_path.retain(|&v| v != station_id);

            let old_p = state.pos[station_id];
            let mut p = old_p;
            const MAX_DELTA: f64 = 400.;
            const MIN_DELTA: f64 = 10.;
            let delta = (MAX_DELTA * (1. - get_time()) + MIN_DELTA * get_time()) as i64;
            p.x = rng.gen_i64((p.x - delta).max(0), (p.x + delta).min(MAP_SIZE) + 1);
            p.y = rng.gen_i64((p.y - delta).max(0), (p.y + delta).min(MAP_SIZE) + 1);
            state.pos[station_id] = p;
            let mut new_path = Vec::with_capacity(state.path.len());
            let mut new_score = 0;
            
            // path上の点で，新たにずらしたステーションを使った方がよいかどうかを判断する
            // warshall floydに近い気持ち
            for w in tmp_path.windows(2) {
                let (prev, next) = (w[0], w[1]);
                new_path.push(prev);
                let old_dist = state.calc_score(&input, prev, next);
                let new_dist = state.calc_score(&input, prev, station_id)
                    + state.calc_score(&input, station_id, next);
                if new_dist < old_dist {
                    new_score += new_dist;
                    new_path.push(station_id);
                } else {
                    new_score += old_dist;
                }
            }
            // 惑星1に帰ってくる
            new_path.push(0);

            let score_diff = new_score - current_score;
            if score_diff <= 0 || rng.gen_bool(f64::exp(-score_diff as f64 / T)) {
                // 解の更新
                current_score = new_score;
                accepted_count += 1;
                state.path = new_path;
            } else {
                // ロールバック
                state.pos[station_id] = old_p;
            }
        } else {
            // 近傍4: 2-opt
            let from = rng.gen_usize(1, state.path.len() - 1);
            let to = rng.gen_usize(from + 1, state.path.len());

            let i0 = state.path[from - 1];
            let i1 = state.path[from];
            let i2 = state.path[to - 1];
            let i3 = state.path[to];

            let d01 = state.calc_score(&input, i0, i1);
            let d23 = state.calc_score(&input, i2, i3);
            let d02 = state.calc_score(&input, i0, i2);
            let d13 = state.calc_score(&input, i1, i3);

            // スコア計算
            let score_diff = d02 + d13 - d01 - d23;
            let new_score = current_score + score_diff;

            if score_diff <= 0 || rng.gen_bool(f64::exp(-score_diff as f64 / T)) {
                // 解の更新
                current_score = new_score;
                accepted_count += 1;
                state.path[from..to].reverse();
            }
        }
        // どの近傍でもベスト更新は常に採用する
        if current_score < best_score {
            best_score = current_score;
            best_state = state.clone();
            update_best_count += 1;
            // eprintln!("update best: {}", best_score);
            // eprintln!("update iter: {}", iter);
        }
    }

    best_state.print();
    eprintln!("iter: {}", iter);
    eprintln!("accepted: {}", accepted_count);
    eprintln!("update best: {}", update_best_count);
    eprintln!("energy: {}", best_score);
    eprintln!(
        "score: {}",
        (1e9 / (1e3 + (best_score as f64).sqrt())).round() as i64
    );
    eprintln!("time: {}", get_time());
}