#783191 (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 16:57:39
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	901 ms / 1,000 ms
コード長	11,933 bytes
コンパイル時間	1,742 ms
実行使用メモリ	6,952 KB
スコア	8,455,698
最終ジャッジ日時	2022-07-30 16:58:19
合計ジャッジ時間	30,982 ms
ジャッジサーバーID （参考情報）	judge11 / judge12
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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	882 ms 6,948 KB
testcase_01	AC	898 ms 6,948 KB
testcase_02	AC	880 ms 6,952 KB
testcase_03	AC	884 ms 6,948 KB
testcase_04	AC	876 ms 4,952 KB
testcase_05	AC	867 ms 6,952 KB
testcase_06	AC	879 ms 5,116 KB
testcase_07	AC	876 ms 5,000 KB
testcase_08	AC	885 ms 6,948 KB
testcase_09	AC	879 ms 5,132 KB
testcase_10	AC	878 ms 6,948 KB
testcase_11	AC	886 ms 5,064 KB
testcase_12	AC	889 ms 4,952 KB
testcase_13	AC	895 ms 5,080 KB
testcase_14	AC	886 ms 5,160 KB
testcase_15	AC	887 ms 5,000 KB
testcase_16	AC	892 ms 5,168 KB
testcase_17	AC	878 ms 6,948 KB
testcase_18	AC	892 ms 5,064 KB
testcase_19	AC	887 ms 4,976 KB
testcase_20	AC	886 ms 5,060 KB
testcase_21	AC	874 ms 5,100 KB
testcase_22	AC	881 ms 5,060 KB
testcase_23	AC	898 ms 6,952 KB
testcase_24	AC	901 ms 6,948 KB
testcase_25	AC	879 ms 5,100 KB
testcase_26	AC	892 ms 5,080 KB
testcase_27	AC	877 ms 5,236 KB
testcase_28	AC	885 ms 4,960 KB
testcase_29	AC	901 ms 4,996 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 = 10000;
float final_T = 2000;
float TIME_LIMIT = 1000;
float TIME_LIMIT_STATION = 10;

int RAND_ARR_LEN = 100000;
int RAND_RANGE = 1000000000;
int N_VERTICAL = 10;

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){
    int result = 0;
    rep(i, N){
        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));

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

        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(pos)==1)continue;
            if(pos<N){
                // 都市にたどり着いた時
                visited.at(pos) = 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);

                for(int j=0;j<N;j++){
                    // 都市にいく時
                    if(visited.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(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(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(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(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);
    }

    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<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);

        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);

            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