#783414 (C++14) No.5007 Steiner Space Travel

• 問題: No.5007 Steiner Space Travel
• ユーザー: yunix
• 提出日時: 2022-07-30 17:57:49
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 895 ms / 1,000 ms
• コード長: 12,647 bytes
• コンパイル時間: 1,912 ms
• 実行使用メモリ: 5,260 KB
• スコア: 8,452,208
• 最終ジャッジ日時: 2022-07-30 17:59:04
• 合計ジャッジ時間: 30,666 ms
• ジャッジサーバーID （参考情報）: judge12 / judge10

ファイルパターン	結果
other	AC * 30

ソースコード

#include <iostream>
#include <string>
#include <vector>
#include <tuple>
#include <chrono>
#include <algorithm>
#include <random>
#include <map>
#include <set>
#include <queue>
#include <random>
#include <chrono>
#include <cmath>
#include <climits>
using namespace std;
using vec_int = vector<int>;
using P = pair<int, int>;
using T = tuple<int, int, int>;
using ll = long long;
// using PQ = priority_queue<pair<float, int>, vector<pair<float,int>>, greater<pair<float, int>>>;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)

float initial_T = 5000;
float final_T = 1000;
float TIME_LIMIT = 1000;
float TIME_LIMIT_STATION = 10;

int RAND_ARR_LEN = 100000;
int RAND_RANGE = 1000000000;

vector<P> DIRS = {make_pair(0, -1), make_pair(-1, 0), make_pair(0, 1), make_pair(1, 0)};

bool is_in(int x, int y, int N)
{
    if (x >= 0 && x < N && y >= 0 && y < N)
        return true;
    return false;
}

// std::mt19937 mt{ std::random_device{}() };
std::mt19937 mt{12345};
std::uniform_int_distribution<int> dist(1, RAND_RANGE);
float get_time(bool init)
{
    static std::chrono::system_clock::time_point start;
    if (init)
    {
        start = std::chrono::system_clock::now();
    }
    std::chrono::system_clock::time_point end = std::chrono::system_clock::now();
    return std::chrono::duration_cast<std::chrono::milliseconds>(end - start).count(); //処理に要した時間をミリ秒に変換
}


class Rand
{
private:
    int count = 0;
    vec_int rand_arr;

public:
    Rand(){
        rep(i, RAND_ARR_LEN){
            rand_arr.push_back(dist(mt));
}
}
;
int get();
int get_rand(int from, int to);
float get_float();
}
;

int Rand::get()
{
    int num = rand_arr.at(count);
    count += 1;
    count %= RAND_ARR_LEN;
    return num;
}

int Rand::get_rand(int from, int to)
{
    int diff = to - from;
    int num = get() % diff;
    return num + from;
}

float Rand::get_float()
{
    // 0~1の間の一様乱数
    return (float)get() / (float)RAND_RANGE;
}

Rand ro;

float current_tmp_station(float current_time)
{
    return final_T + (initial_T - final_T) * (TIME_LIMIT_STATION - current_time) / TIME_LIMIT_STATION;
}

bool is_valid_transition_station(int diff, float current_time)
{
    float t = current_tmp_station(current_time);
    float rand = ro.get_float();
    // cerr<<"tmperature"<<t<<" "<<diff<<endl;
    return rand < exp(((float)diff) / t);
}


int N, M; 
vec_int a, b;
int alpha=5;
int sq_alpha=25;


class SpaceStation{
    public:
    int x;
    int y;
    SpaceStation(){
        x=0;
        y=0;
    };
    SpaceStation(int xpos, int ypos){
        x=xpos;
        y=ypos;
    };
    int square_distance(int x2, int y2){
        return (x2-x)*(x2-x) + (y2-y)*(y2-y);
    };
    void set_pos(int xpos, int ypos){
        x=xpos;
        y=ypos;
    };

    void random_move(){
        int dx = ro.get_rand(-20, 21);
        int dy = ro.get_rand(-20, 21);
        int x2 = x+dx;
        int y2 = y+dy;
        x2 = max(0, x2);
        y2 = max(0, y2);
        x2 = min(1000, x2);
        y2 = min(1000, y2);
        x=x2;
        y=y2;
    }
};

int tot_distance(vector<SpaceStation> &stations, vec_int &excluded){
    int result = 0;
    rep(i, N){
        if(excluded.at(i)==1)continue;
        int tmp_dist = INT_MAX;
        rep(j, M){
            tmp_dist = min(tmp_dist, stations.at(j).square_distance(a.at(i), b.at(i)));
        }
        result += tmp_dist;
    }
    return result;
}

void cout_ans(vector<P> &ans){
    cout<<ans.size()<<endl;
    rep(i, ans.size()){
        cout<<ans.at(i).first<<" "<<ans.at(i).second+1<<endl;
    }
}

int sq_dist_between_cities(int i, int j){
    int result = 0;
    result += (a.at(i)-a.at(j))*(a.at(i)-a.at(j));
    result += (b.at(i)-b.at(j))*(b.at(i)-b.at(j));
    return result;

}

vector<vector<pair<int, vector<P>>>> make_dist_map(vector<SpaceStation> &stations){
    vector<vector<pair<int, vector<P>>>> result(N, vector<pair<int, vector<P>>>(N+M));

    vector<vector<int>> visited(N, vec_int(N+M, 0));
    for(int i=0;i<N;i++){
        // 歳iをstartにする

        priority_queue<T, vector<T>, greater<T>> pq;
        pq.emplace(0, i, -1);

        while(!pq.empty()){
            int dist, pos, prev; tie(dist, pos, prev) = pq.top(); pq.pop();
            if(visited.at(i).at(pos)==1)continue;
            if(pos<N){
                // 都市にたどり着いた時
                visited.at(i).at(pos) = 1;
                visited.at(pos).at(i) = 1;
                vector<P> route;
                if(prev!=-1){
                    route = result.at(i).at(prev).second;
                }
                route.push_back(make_pair(1, pos));
                result.at(i).at(pos) = make_pair(dist, route);
                vector<P> route2 = route;
                reverse(route2.begin(), route2.end());
                result.at(pos).at(i) = make_pair(dist, route2);

                for(int j=0;j<N;j++){
                    // 都市にいく時
                    if(visited.at(i).at(j)==1)continue;
                    int add_dist = sq_dist_between_cities(pos, j) * sq_alpha;
                    pq.emplace(dist+add_dist, j, pos);
                }
                for(int j=0;j<M;j++){
                    // ステーションにいく時
                    if(visited.at(i).at(j+N)==1)continue;
                    int add_dist = stations.at(j).square_distance(a.at(pos), b.at(pos)) * alpha;
                    pq.emplace(dist+add_dist, j+N, pos);
                }
            }else{
                // 宇宙ステーションにたどり着いた時
                visited.at(i).at(pos) = 1;
                vector<P> route;
                if(prev!=-1){
                    route = result.at(i).at(prev).second;
                }
                route.push_back(make_pair(2, pos-N));
                result.at(i).at(pos) = make_pair(dist, route);

                for(int j=0;j<N;j++){
                    // 都市にいく時
                    if(visited.at(i).at(j)==1)continue;
                    int add_dist = stations.at(pos-N).square_distance(a.at(j), b.at(j))*alpha;
                    pq.emplace(dist+add_dist, j, pos);
                }
                for(int j=0;j<M;j++){
                    // ステーションにいく時
                    if(visited.at(i).at(j+N)==1)continue;
                    int add_dist = stations.at(pos-N).square_distance(stations.at(j).x, stations.at(j).y);
                    pq.emplace(dist+add_dist, j+N, pos);
                }
            }
        }
    }
    return result;
}

int calc_dist(vector<SpaceStation> &stations, vector<P> &tmp_ans){
    int result = 0;
    for(int i=1;i<tmp_ans.size();i++){
        int type, pos; tie(type, pos) = tmp_ans.at(i);
        int prev_type, prev_pos;  tie(prev_type, prev_pos) = tmp_ans.at(i-1);

        if(type==1&&prev_type==1){
            result += sq_dist_between_cities(pos, prev_pos)*sq_alpha;
        }else if(type==1&&prev_type==2){
            result += stations.at(prev_pos).square_distance(a.at(pos), b.at(pos))*alpha;
        }else if(type==2 && prev_type==1){
            result += stations.at(pos).square_distance(a.at(prev_pos), b.at(prev_pos))*alpha;
        }else{
            result += stations.at(pos).square_distance(stations.at(prev_pos).x, stations.at(prev_pos).y);
        }
    }
    return result;
}



int greedy_strategy(vector<P> &ans, vector<SpaceStation> &stations, vector<vector<pair<int, vector<P>>>> &dist_mat){
    // 訪れていない場所の中で一番コストが小さくいけそうなところにいく
    int result = 0;

    int pos = 0;
    ans.push_back(make_pair(1, 0));

    vec_int visited(N, 0);
    while(true){
        visited.at(pos) = 1;
        
        int min_dist = INT_MAX;
        int next_pos = -1;
        for(int i=0;i<N;i++){
            if(visited.at(i)==1)continue;
            int tmp_dist = dist_mat.at(pos).at(i).first;
            if(min_dist>tmp_dist){
                min_dist = tmp_dist;
                next_pos = i;
            }
        }


        if(next_pos==-1)break;

        int tmp_dist2 = calc_dist(stations, ans);

        for(auto p_pos: dist_mat.at(pos).at(next_pos).second){
            // if(p_pos.second == pos&&p_pos.first==1)continue;
            if(ans.at(ans.size()-1)==p_pos)continue;
            ans.push_back(p_pos);
        }
        int tmp_dist3 = calc_dist(stations, ans);
        pos = next_pos;
        result += min_dist;
    }

    for(auto p_pos: dist_mat.at(pos).at(0).second){
        ans.push_back(p_pos);
    }
    result += dist_mat.at(pos).at(0).first;

    return result;
}

void adjust_station_pos(vector<SpaceStation> &stations, vector<P> &tmp_ans){

    vector<vec_int> station_connections(M);

    rep(i, tmp_ans.size()){
        if(tmp_ans.at(i).first==2){
            int st = tmp_ans.at(i).second;
            if(tmp_ans.at(i-1).first==1){
                station_connections.at(st).push_back(tmp_ans.at(i-1).second);
            }
            if(tmp_ans.at(i+1).first==1){
                station_connections.at(st).push_back(tmp_ans.at(i+1).second);
            }
        }
    }
    
    for(int station = 0;station<M;station++){
        int x = stations.at(station).x;
        int y = stations.at(station).y;

        int min_dist = INT_MAX;
        int best_x = x;
        int best_y = y;

        for(int dx=-100;dx<=100;dx+=2){
        for(int dy=-100;dy<=100;dy+=2){
            int tot_dist = 0;
            int x2 = x+dx;
            int y2 = y+dy;
            if(!(0<=x2 && x2<=1000 && 0<=y2 && y2<=1000))continue;
            stations.at(station).x = x2;
            stations.at(station).y = y2;

            for(auto star: station_connections.at(station)){
                tot_dist += stations.at(station).square_distance(a.at(star), b.at(star));
            }

            if(tot_dist<min_dist){
                min_dist = tot_dist;
                best_x = x2;
                best_y = y2;
            }
        }
        }
        stations.at(station).x=best_x;
        stations.at(station).y=best_y;
    }
}
int main(){
    get_time(true);
    cin>>N>>M;
    rep(i, N){
        int aa, bb; cin>>aa>>bb;
        a.push_back(aa);
        b.push_back(bb);
    }

    vector<T> dist_vec;
    rep(i, N){
        for(int j=i+1;j<N;j++){
            dist_vec.push_back(make_tuple(sq_dist_between_cities(i, j), i, j));
        }
    }
    sort(dist_vec.begin(), dist_vec.end());

    int tot_dist = INT_MAX;
    vector<P> ans;
    vector<SpaceStation> ans_stations;
    while(get_time(false)<TIME_LIMIT*0.85){
        float start_time = get_time(false);

        vector<int> excluded(N, 0);
        for(int i=0;i<ro.get_rand(0,10);i++){
            int d,aa,bb; tie(d, aa, bb) = dist_vec.at(i);
            excluded.at(aa) = 1;
        }
    
        vector<SpaceStation> stations(M);
        rep(i, M){
            stations.at(i) = SpaceStation(ro.get_rand(0, 1001), ro.get_rand(0, 1001));
        }

        int station_score = tot_distance(stations, excluded);

        cerr<<"initial tot square distance:"<<station_score<<endl;
        while(true){
            float ct = get_time(false)-start_time;
            if(ct>TIME_LIMIT_STATION)break;
            int selected_station = ro.get_rand(0, M);
            int old_x = stations.at(selected_station).x;
            int old_y = stations.at(selected_station).y;
            stations.at(selected_station).random_move();

            int new_score = tot_distance(stations, excluded);

            int diff = new_score-station_score;
            if(is_valid_transition_station(-1*diff, ct)){//小さくなる方がいい
                station_score = new_score;
            }else{
                stations.at(selected_station).set_pos(old_x, old_y);
            }
        }
        cerr<<"annealed tot square distance:"<<station_score<<endl;

        cerr<<"time1:"<<get_time(false)<<endl;
        vector<vector<pair<int, vector<P>>>> dist = make_dist_map(stations);
        cerr<<"time2:"<<get_time(false)<<endl;

        vector<P> tmp_ans;
        int tmp_dist = greedy_strategy(tmp_ans, stations, dist);
        
        cerr<<"tmp_dist1"<<tmp_dist<<endl;
        adjust_station_pos(stations, tmp_ans);
        tmp_dist = calc_dist(stations, tmp_ans);
        cerr<<"tmp_dist2"<<tmp_dist<<endl;

        if(tmp_dist<tot_dist){
            tot_dist = tmp_dist;
            ans = tmp_ans;
            ans_stations = stations;
        }
    }

    rep(i, M){
        cout<<ans_stations.at(i).x<<" "<<ans_stations.at(i).y<<endl;
    }
    cerr<<"score:"<<pow(10,9)/(sqrt((float)tot_dist)+1000.)<<endl;
   

    cout_ans(ans);
    return 0;
}