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

提出ソース

結果

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 12.3.0 + boost 1.83.0)
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
	純コード判定しない問題か言語

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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	884 ms 5,260 KB
testcase_01	AC	895 ms 5,016 KB
testcase_02	AC	873 ms 5,132 KB
testcase_03	AC	867 ms 4,752 KB
testcase_04	AC	885 ms 4,856 KB
testcase_05	AC	870 ms 4,924 KB
testcase_06	AC	861 ms 4,900 KB
testcase_07	AC	869 ms 4,964 KB
testcase_08	AC	858 ms 4,856 KB
testcase_09	AC	892 ms 5,116 KB
testcase_10	AC	868 ms 4,760 KB
testcase_11	AC	876 ms 4,976 KB
testcase_12	AC	856 ms 4,976 KB
testcase_13	AC	875 ms 4,920 KB
testcase_14	AC	872 ms 4,900 KB
testcase_15	AC	874 ms 5,076 KB
testcase_16	AC	862 ms 4,780 KB
testcase_17	AC	864 ms 5,072 KB
testcase_18	AC	864 ms 5,076 KB
testcase_19	AC	867 ms 4,848 KB
testcase_20	AC	859 ms 4,920 KB
testcase_21	AC	865 ms 5,124 KB
testcase_22	AC	880 ms 5,200 KB
testcase_23	AC	887 ms 5,096 KB
testcase_24	AC	864 ms 4,876 KB
testcase_25	AC	883 ms 4,996 KB
testcase_26	AC	880 ms 4,904 KB
testcase_27	AC	871 ms 5,108 KB
testcase_28	AC	874 ms 5,136 KB
testcase_29	AC	878 ms 5,164 KB

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ソースコード

raw source code

#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;
}

yukicoder

結果

テストケース

ソースコード