#783157 (C++17) No.5007 Steiner Space Travel

• 問題: No.5007 Steiner Space Travel
• ユーザー: t33f
• 提出日時: 2022-07-30 16:45:23
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 982 ms / 1,000 ms
• コード長: 7,854 bytes
• コンパイル時間: 1,342 ms
• 実行使用メモリ: 6,952 KB
• スコア: 8,405,705
• 最終ジャッジ日時: 2022-07-30 16:45:57
• 合計ジャッジ時間: 33,540 ms
• ジャッジサーバーID （参考情報）: judge13 / judge15

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	981 ms; 4,900 KB
testcase_01	AC	982 ms; 4,904 KB
testcase_02	AC	982 ms; 4,904 KB
testcase_03	AC	982 ms; 4,900 KB
testcase_04	AC	982 ms; 6,948 KB
testcase_05	AC	982 ms; 6,948 KB
testcase_06	AC	982 ms; 6,948 KB
testcase_07	AC	982 ms; 6,948 KB
testcase_08	AC	982 ms; 6,948 KB
testcase_09	AC	981 ms; 6,952 KB
testcase_10	AC	982 ms; 6,948 KB
testcase_11	AC	982 ms; 4,900 KB
testcase_12	AC	982 ms; 6,952 KB
testcase_13	AC	981 ms; 4,900 KB
testcase_14	AC	982 ms; 4,900 KB
testcase_15	AC	982 ms; 4,900 KB
testcase_16	AC	982 ms; 4,904 KB
testcase_17	AC	982 ms; 4,900 KB
testcase_18	AC	982 ms; 4,904 KB
testcase_19	AC	981 ms; 4,904 KB
testcase_20	AC	981 ms; 4,900 KB
testcase_21	AC	981 ms; 4,900 KB
testcase_22	AC	981 ms; 6,948 KB
testcase_23	AC	982 ms; 6,952 KB
testcase_24	AC	982 ms; 6,948 KB
testcase_25	AC	982 ms; 6,948 KB
testcase_26	AC	981 ms; 4,904 KB
testcase_27	AC	981 ms; 4,900 KB
testcase_28	AC	982 ms; 6,948 KB
testcase_29	AC	981 ms; 4,904 KB

ソースコード

#include <cmath>
#include <map>
#include <array>
#include <algorithm>
#include <chrono>
#include <random>
#include <vector>
#include <numeric>
#include <cassert>
#include <iostream>
using namespace std;

unsigned int xor128() {
    static unsigned int x=123456789, y=362436069, z=521288629, w=88675123;
    unsigned int t;
    t=(x^(x<<11)); x=y; y=z; z=w;
    return (w=(w^(w>>19))^(t^(t>>8)));
}

inline bool rand_bool(double prob) {
    constexpr double x = 1LL<<32; // uint_max+1
    return xor128() < prob * x;
}


class Timer {
    chrono::system_clock::time_point start_time = chrono::system_clock::now();
public:
    Timer() {}
    long long get_elapsed_time() {
        auto diff = chrono::system_clock::now() - start_time;
        return chrono::duration_cast<chrono::milliseconds>(diff).count();
    }
} timer;

using P = pair<int, int>;
constexpr int N = 100, M = 8;

int a[N], b[N];

mt19937 mt;

constexpr int alpha = 5;

int L1(P p, P q) { return abs(p.first - q.first) + abs(p.second - q.second); }

int L22(int x1, int y1, int x2, int y2) {
    const int dx = x1 - x2, dy = y1 - y2;
    return dx * dx + dy * dy;
}

int L22(P p, P q) { return L22(p.first, p.second, q.first, q.second); }

int cost(int i, int j) {
    return L22(a[i], b[i], a[j], b[j]) * alpha * alpha;
}

int cost(int i, int j, P middle) {
    return (L22(a[i], b[i], middle.first, middle.second) +
            L22(a[j], b[j], middle.first, middle.second)) * alpha;
}

int cost(int t1, P p1, int t2, P p2) {
    const int coeff = (t1 == 1 && t2 == 1 ? alpha * alpha :
                       t1 == 1 || t2 == 1 ? alpha :
                       1);
    return coeff * L22(p1, p2);
}

array<array<int, N>, N> mincost;
array<array<int, N>, N> next_idx;
void calc_mincost() {
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++) {
            mincost[i][j] = cost(i, j);
            next_idx[i][j] = j;
        }
    for (int k = 0; k < N; k++)
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                if (mincost[i][k] + mincost[k][j] < mincost[i][j]) {
                    mincost[i][j] = mincost[i][k] + mincost[k][j];
                    assert(i != k);
                    assert(j != k);
                    next_idx[i][j] = next_idx[i][k];
                }
}

void read_input() {
    {
        int n, m;
        cin >> n >> m;
        assert(n == N);
        assert(m == M);
    }
    for (int i = 0; i < N; i++) cin >> a[i] >> b[i];

    calc_mincost();
}

vector<int> solve_tsp(int tl) {
    vector<int> ans(N);
    iota(ans.begin(), ans.end(), 0);
    int total_cost = 0;
    for (int i = 0; i < N; i++) {
        if (i + 1 < N) total_cost += cost(i, i + 1);
        else total_cost += cost(0, N - 1);
    }

    Timer tsp_timer;
    uniform_int_distribution<int> randindex(0, N - 1);
    int iter = 0, last_upd = 0, stop_threshold = N * N;
    while (tsp_timer.get_elapsed_time() < tl && last_upd + stop_threshold > iter) {
        int i = randindex(mt), j = randindex(mt);
        assert(i < N);
        assert(j < N);
        if (i == j) continue;
        if (i > j) swap(i, j);
        if (i + 1 == j) continue;

        iter++;
        const int k = (j + 1 == N ? 0 : j + 1);
        const int diff = (cost(ans[i], ans[j]) + cost(ans[i + 1], ans[k])
                          - cost(ans[i], ans[i + 1]) - cost(ans[j], ans[k]));
        if (diff <= 0) {
            reverse(ans.begin() + i + 1, ans.begin() + j + 1);
            total_cost += diff;
            last_upd = iter;
            // cerr << iter << ' ' << total_cost << endl;
        }
    }

    cerr << iter << ' ' << total_cost << endl;
    return ans;
}

class DSU {
    vector<int> par, rank;
public:
    explicit DSU(int n) : par(n), rank(n, 0) {
        iota(par.begin(), par.end(), 0);
    }

    int find(int i) {
        return (par[i] == i) ? i : (par[i] = find(par[i]));
    }

    void merge(int i, int j) {
        int x = find(i), y = find(j);
        if (x != y) {
            if (rank[x] < rank[y])
                par[x] = y;
            else {
                par[y] = x;
                if (rank[x] == rank[y]) rank[x]++;
            }
        }
    }

    bool same(int i, int j) { return find(i) == find(j); }
};

struct Target {
    int type, idx;
    Target(int type, int idx) : type(type), idx(idx) {
        assert(type == 1 || type == 2);
    }
};

struct Config {
    vector<int> path;
    array<P, M> stations;
};

pair<vector<Target>, long long> greedy(const Config &conf) {
    vector<Target> ans;
    ans.emplace_back(1, conf.path[0]);
    long long total_cost = 0;
    for (int i = 0; i < N; i++) {
        const int from = conf.path[i], to = conf.path[i + 1];
        int cur_cost = mincost[from][to], s = -1;
        for (int j = 0; j < M; j++) {
            const int tmp = cost(from, to, conf.stations[j]);
            if (tmp < cur_cost) {
                cur_cost = tmp;
                s = j;
            }
        }
        if (s >= 0) {
            const auto [t1, i1] = ans.back();
            assert(t1 == 1);
            total_cost += cost(1, make_pair(a[i1], b[i1]), 2, conf.stations[s]);
            ans.emplace_back(2, s);
            total_cost += cost(2, conf.stations[s], 1, make_pair(a[to], b[to]));
            ans.emplace_back(1, to);
        } else {
            for (int cur = from; cur != to; cur = next_idx[cur][to]) {
                const auto [t1, i1] = ans.back();
                assert(t1 == 1);
                assert(i1 == cur);
                const int nxt = next_idx[cur][to];
                total_cost += cost(1, make_pair(a[cur], b[cur]), 1, make_pair(a[nxt], b[nxt]));
                ans.emplace_back(1, nxt);
            }
        }
    }

    return {ans, total_cost};
}

int timelimit = 1000, margin = 20;

int main() {
    read_input();
    vector<int> path = solve_tsp(200);
    {
        auto start = find(path.begin(), path.end(), 0);
        assert(start != path.end());
        rotate(path.begin(), start, path.end());
        assert(path.front() == 0);
        path.push_back(0);
    }

    array<P, M> stations{
        P{200, 333}, {200, 667},
        {400, 333}, {400, 667},
        {600, 333}, {600, 667},
        {800, 333}, {800, 667},
    };

    auto [cur_ans, cur_cost] = greedy({path, stations});
    vector<Target> best_ans = cur_ans;
    long long best_cost = cur_cost;
    int iter = 0;
    uniform_int_distribution<int> rand_pos(10, 990);
    while (timer.get_elapsed_time() + margin < timelimit) {
        iter++;
        const int i = iter % M;
        const P origp = stations[i],
            newp(rand_pos(mt), rand_pos(mt));
        stations[i] = newp;
        const auto [tmp_ans, tmp_cost] = greedy({path, stations});
        if (tmp_cost < best_cost) {
            cerr << iter << ' ' << tmp_cost << ' ' << round(1e9 / (1000 + sqrt(tmp_cost))) << endl;
            best_cost = tmp_cost;
            best_ans = tmp_ans;
        }

        const long long diff = tmp_cost - cur_cost;
        bool accept = diff <= 0;
        // if (!accept) {
        //     const double start_temp = 2e4, end_temp = 1,
        //         progress = double(timer.get_elapsed_time()) / timelimit,
        //         temp = start_temp + (end_temp - start_temp) * progress,
        //         prob = exp(-diff / temp);
        //     accept = rand_bool(prob);
        //     // cerr << diff << ' ' << prob << endl;
        // }
        if (accept) {
            cur_cost = tmp_cost;
            cur_ans = tmp_ans;
        } else {
            // rollback
            stations[i] = origp;
        }
    }

    cerr << iter << ' ' << round(1e9 / (1000 + sqrt(best_cost))) << endl;

    // output
    for (auto [x, y] : stations) cout << x << ' ' << y << '\n';
    cout << best_ans.size() << '\n';
    for (auto [t, i] : best_ans) cout << t << ' ' << i + 1 << '\n';
}