#719641 (C++17) No.1775 Love Triangle 2

• 問題: No.1775 Love Triangle 2
• ユーザー: 👑 hitonanode
• 提出日時: 2021-11-25 23:58:17
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: CE (最新)
  AC
  (最初)
• 実行時間: -
• コード長: 10,261 bytes
• コンパイル時間: 775 ms
• コンパイル使用メモリ: 95,724 KB
• 最終ジャッジ日時: 2024-04-27 04:00:13
• 合計ジャッジ時間: 1,316 ms
• ジャッジサーバーID （参考情報）: judge4 / judge3

コンパイルメッセージ

twopaths.hpp: In function 'std::pair<std::vector<int>, std::vector<int> > TWOPATHS::twopaths(const std::vector<std::vector<int> >&, const std::vector<int>&, int, int, int, bool)':
twopaths.hpp:36:26: error: variable 'std::array<int, 6> weights' has initializer but incomplete type

ソースコード

// 方針（正当性なし）
// - 現在使われていない頂点のみを使い x -> y に流量 2 を流して，一方の x-y パスを採択する
// - 現在使われていない頂点のみを使い x -> y, x -> z に流量 1 ずつ同時に流して，両方のパスを採択する
// - x -> y パスを消す
// - ランダムに頂点を使用不能にする
// - フローを流す時の重みはランダムに定める

#line 2 "parameter.hpp"

const int MAX_DEL_V = 2;     // 最大ランダム消去頂点数
const int NITER = 3000;      // 反復回数
const int EARLY_STOP = 200;  // この回数反復して既に解が見つかっていたらすぐやめる
#line 9 "uso_drop.cpp"

#include <algorithm>
#include <cassert>
#include <iostream>
#include <utility>
#include <vector>
using namespace std;

#include <tuple>

namespace INPUT {
using namespace std;

tuple<int, int, int, int, vector<vector<int>>> read() {
    int N, M, X, Y, Z;
    cin >> N >> M >> X >> Y >> Z;
    --X, --Y, --Z;
    vector mat(N, vector<int>(N));
    for (int i = 0; i < N; ++i) {
        for (int j = 0; j < N; ++j) { mat[i][j] = (i != j); }
    }
    while (M--) {
        int a, b;
        cin >> a >> b;
        --a, --b;
        mat[a][b] = mat[b][a] = 0;
    }
    assert(mat[X][Y] + mat[Y][X] + mat[X][Z] + mat[Z][X] + mat[Y][Z] + mat[Z][Y] == 0);
    vector<vector<int>> to(N);
    for (int i = 0; i < N; ++i) {
        for (int j = 0; j < N; ++j) {
            if (mat[i][j] > 0) to[i].push_back(j);
        }
    }
    return {N, X, Y, Z, to};
}
}; // namespace INPUT
#line 3 "twopaths.hpp"
#include <atcoder/mincostflow>
#include <cassert>
#line 8 "twopaths.hpp"

namespace TWOPATHS {
using namespace std;
uint32_t rand_int() {
    static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    uint32_t t = x ^ (x << 11);
    x = y;
    y = z;
    z = w;
    return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}

// used_vs に含まれる頂点は使わずに，from -> to1 と from->to2 の点素なパスを構成する．
// 両方のパスが構築できなければ empty vector の組を返す．
pair<vector<int>, vector<int>> twopaths(const vector<vector<int>> &to, const vector<int> &used_vs, int from, int to1, int to2, bool randomize=false) {
    const int N = to.size();
    const int gt = N * 2;
    atcoder::mcf_graph<int, int> graph(gt + 1);

    vector<int> valid_v(N, 1);
    for (auto i : used_vs) valid_v[i] = 0;
    if (!valid_v[to1] or !valid_v[to2] or !valid_v[from]) return {{}, {}};
    valid_v[from] = valid_v[to1] = valid_v[to2] = 0;

    for (int i = 0; i < N; ++i) { graph.add_edge(i, i + N, valid_v[i], 0); }
    graph.add_edge(to1, to1 + N, 1, 0);
    graph.add_edge(to2, to2 + N, 1, 0);

    static array<int, 6> weights{0, 1, 2, 4, 8, 100};
    for (int i = 0; i < N; ++i) {
        for (auto j : to[i]) {
            int cost = 1;
            if (randomize) {
                cost = weights[rand_int() % weights.size()];
            }
            graph.add_edge(i + N, j, 1, cost);
        }
    }

    graph.add_edge(to1 + N, gt, 1, 0);
    graph.add_edge(to2 + N, gt, 1, 0);
    auto f = graph.flow(from + N, gt, 2);
    if (f.first < 2) return {{}, {}};

    vector<vector<int>> conn(N);
    for (auto e : graph.edges()) {
        if (e.flow) {
            if (e.to == gt) continue;
            int s = e.from % N, t = e.to % N;
            if (s != t) conn[s].push_back(t);
        }
    }

    vector<vector<int>> ret;
    while (conn[from].size()) {
        int now = from;
        vector<int> vec{now};
        while (conn[now].size()) {
            int nxt = conn[now].back();
            conn[now].pop_back();
            now = nxt;
            vec.push_back(now);
        }
        ret.push_back(vec);
    }
    assert(ret.size() == 2);
    if (ret[0].back() != to1) swap(ret[0], ret[1]);
    if (ret[1].back() != to2) swap(ret[0], ret[1]);
    assert(ret[0].front() == from and ret[0].back() == to1);
    assert(ret[1].front() == from and ret[1].back() == to2);
    return {ret.at(0), ret.at(1)};
}
}; // namespace TWOPATHS

namespace Heuristic {
uint32_t rand_int() {
    static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    uint32_t t = x ^ (x << 11);
    x = y;
    y = z;
    z = w;
    return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}

struct State {
    int x, y, z;
    vector<vector<int>> to;
    vector<int> xy, yz, zx;
    State(int x_, int y_, int z_, vector<vector<int>> to_) : x(x_), y(y_), z(z_), to(to_) {}
    bool xy_good() const { return xy.size() and xy.front() == x and xy.back() == y; }
    bool yz_good() const { return yz.size() and yz.front() == y and yz.back() == z; }
    bool zx_good() const { return zx.size() and zx.front() == z and zx.back() == x; }
    bool is_feasible() const { return xy_good() and yz_good() and zx_good(); }

    static vector<int> inner(std::vector<int> vs) {
        if (vs.empty()) return {};
        vs.pop_back();
        swap(vs.front(), vs.back());
        vs.pop_back();
        return vs;
    }

    vector<int> enum_inner_vs() const {
        vector<int> ret;
        for (int i = 1; i + 1 < int(xy.size()); ++i) ret.push_back(xy[i]);
        for (int i = 1; i + 1 < int(yz.size()); ++i) ret.push_back(yz[i]);
        for (int i = 1; i + 1 < int(zx.size()); ++i) ret.push_back(zx[i]);
        return ret;
    }

    void opt_xyz() {
        if (!zx_good()) return;
        if (count(zx.begin(), zx.end(), y)) return;
        auto [yxnew, yznew] = TWOPATHS::twopaths(to, inner(zx), y, x, z, !is_feasible());
        xy = yxnew;
        reverse(xy.begin(), xy.end());
        yz = yznew;
        if (!verify()) cerr << "xyz bad" << endl;
    }

    void opt_yzx() {
        if (!xy_good()) return;
        if (count(xy.begin(), xy.end(), z)) return;
        auto [zynew, zxnew] = TWOPATHS::twopaths(to, inner(xy), z, y, x, !is_feasible());
        yz = zynew;
        reverse(yz.begin(), yz.end());
        zx = zxnew;
        if (!verify()) cerr << "yzx bad" << endl;
    }

    void opt_zxy() {
        if (!yz_good()) return;
        if (count(yz.begin(), yz.end(), x)) return;
        auto [xznew, xynew] = TWOPATHS::twopaths(to, inner(yz), x, z, y, !is_feasible());
        zx = xznew;
        reverse(zx.begin(), zx.end());
        xy = xynew;
        if (!verify()) cerr << "zxy bad" << endl;
    }

    void init_xyxy() {
        yz.clear();
        zx.clear();
        auto [xy1, xy2] = TWOPATHS::twopaths(to, {}, x, y, y, true);
        if (rand_int() & 1) {
            xy = xy1;
        } else {
            xy = xy2;
        }
    }

    vector<int> dump() const { // return [x, ..., y, ..., z, ..., x]
        if (!is_feasible()) return {};
        vector<int> ret = xy;
        ret.pop_back();
        ret.insert(ret.end(), yz.begin(), yz.end());
        ret.pop_back();
        ret.insert(ret.end(), zx.begin(), zx.end());
        return ret;
    }

    int optval() const {
        if (!is_feasible()) return to.size() + 1;
        assert(xy.front() == x and xy.back() == y);
        assert(yz.front() == y and yz.back() == z);
        assert(zx.front() == z and zx.back() == x);
        return xy.size() + yz.size() + zx.size() - 3;
    }
    
    bool verify() const {
        if (!is_feasible()) return true;
        auto p = dump();
        int last = -1;
        vector<int> cntr(to.size());
        cntr.at(x)--;
        for (auto k : p) {
            cntr.at(k)++;
            if (cntr[k] > 1) {
                std::cerr << k << ' ' << x << ' ' << y << ' ' << z << std::endl;
            }
            if (last >= 0) {
                int n = count(to[last].begin(), to[last].end(), k);
                if (n == 0) return false;
            }
            last = k;
        }
        if (*max_element(cntr.begin(), cntr.end()) > 1) {
            cerr << "(" << x << ' ' << y << ' ' << z << ")\n";
            for (auto i : xy) cerr << i << ' ';
            cerr << endl;
            for (auto i : yz) cerr << i << ' ';
            cerr << endl;
            for (auto i : zx) cerr << i << ' ';
            cerr << endl;
            return false;
        }
        return true;
    }
};
}; // namespace Heuristic
#line 18 "uso_drop.cpp"

uint32_t rand_int() {
    // XorShift random integer generator
    static uint32_t x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    uint32_t t = x ^ (x << 11);
    x = y;
    y = z;
    z = w;
    return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}

vector<vector<int>> drop_graph(vector<vector<int>> to, int x, int y, int z, int k) {
    // 最大 k 頂点ランダムに消去
    const int n = to.size();

    vector<int> is_erased(n);
    for (int i = 0; i < k; ++i) is_erased[rand_int() % n] = 1;
    is_erased[x] = is_erased[y] = is_erased[z] = 0;

    for (int i = 0; i < n; ++i) {
        if (is_erased[i]) {
            to[i].clear();
        } else {
            for (int j = 0; j < int(to[i].size()); ++j) {
                if (is_erased[to[i][j]]) {
                    swap(to[i][j], to[i].back());
                    to[i].pop_back();
                    --j;
                }
            }
        }
    }
    return to;
}

int main() {
    cin.tie(nullptr), ios::sync_with_stdio(false);

    auto [N, X, Y, Z, to] = INPUT::read();

    vector<int> xyz{X, Y, Z};

    int ret = N + 1;
    for (int ntry = 0; ntry < NITER; ++ntry) {
        int nerase = rand_int() % (MAX_DEL_V + 1);
        // cerr << nerase << ':';
        int d = rand_int() % 3;
        Heuristic::State state(xyz[d], xyz[(d + 1) % 3], xyz[(d + 2) % 3], drop_graph(to, X, Y, Z, nerase));

        state.init_xyxy();
        state.opt_yzx();

        if (!state.is_feasible()) continue;

        for (int iter = 0; iter < 5; ++iter) {
            // auto p = state.dump().size();
            int c = rand_int() % 3;
            if (c == 0) state.opt_xyz();
            if (c == 1) state.opt_yzx();
            if (c == 2) state.opt_zxy();
            // if (state.dump().size() < p) cerr << " (" << iter << ")";
        }
        state.verify();
        ret = min(ret, state.optval());
        if (ntry >= EARLY_STOP and ret <= N) break; // 既に解が見つかっているならば早めにやめる
    }

    cout << (ret <= N ? ret : -1) << '\n';
}