#1195119 (C++23(gcc16)) No.5025 Forest Fire

• 問題: No.5025 Forest Fire
• ユーザー: prussian_coder
• 提出日時: 2026-10-24 17:11:39
• 言語: C++23(gcc16) (gcc 16.2.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 1,794 ms / 2,000 ms
• コード長: 9,108 bytes
• コンパイル時間: 2,448 ms
• コンパイル使用メモリ: 265,012 KB
• 実行使用メモリ: 9,932 KB
• スコア: 182,810,030
• 最終ジャッジ日時: 2026-10-24 17:15:58
• 合計ジャッジ時間: 150,644 ms
• ジャッジサーバーID （参考情報）: judge2_0 / <nil>

ファイルパターン	結果
other	AC * 50

ソースコード

#include <algorithm>
#include <chrono>
#include <cmath>
#include <iostream>
#include <limits>
#include <random>
#include <set>
#include <string>
#include <utility>
#include <vector>

using namespace std;
using Connection = pair<int, int>;

constexpr int SAFE_ZONE_CRITERIA = 4;
constexpr int CAND_SIZES_LIM = 10000;
constexpr double TIME_LIMIT = 1.8;
constexpr double START_TEMP = 10000;
constexpr double END_TEMP = 10;
constexpr double TWO_ADD_ONE_REMOVE_PROB = 0.1;
constexpr double TWO_REMOVE_ONE_ADD_PROB = 0.1;

int N, K, N2;
vector<vector<int>> board;
vector<int> danger_zones;

int to_1d(int i, int j) { return i * N2 + j; }
pair<int, int> to_2d(int v) { return {v / N2, v % N2}; }

int connection_dist(int v1, int v2) {
    auto [x1, y1] = to_2d(v1);
    auto [x2, y2] = to_2d(v2);
    return min(abs(x1 - x2), abs(y1 - y2));
}

int connection_dist(Connection edge) {
    return connection_dist(edge.first, edge.second);
}

vector<int> create_route(int v1, int v2) {
    auto [x1, y1] = to_2d(v1);
    auto [x2, y2] = to_2d(v2);
    if (x1 > x2) {
        swap(x1, x2);
        swap(y1, y2);
    }
    vector<int> route;
    int x = x1, y = y1;
    while (x != x2 || y != y2) {
        if (x < x2) ++x;
        if (y < y2) ++y;
        else if (y > y2) --y;
        if (x != x2 || y != y2) route.push_back(to_1d(x, y));
    }
    return route;
}

// 入力と候補辺だけで決まる情報をキャッシュし、反復用メモリを再利用する。
struct SearchWorkspace {
    vector<vector<int>> routes;
    vector<int> distances, danger_idx, trees, parents;
    vector<pair<int, int>> adjacent_dangers;
    vector<unsigned int> used, removed;
    unsigned int tree_stamp = 0, score_stamp = 0;

    explicit SearchWorkspace(const vector<Connection>& candidates)
        : danger_idx(N2 * N2, -1), parents(danger_zones.size()),
          used(N2 * N2, 0), removed(danger_zones.size(), 0) {
        routes.reserve(candidates.size());
        distances.reserve(candidates.size());
        trees.reserve(N2 * N2);
        for (auto [v1, v2] : candidates) {
            vector<int> route;
            for (int v : create_route(v1, v2)) {
                if (board[v / N2][v % N2] != 0) route.push_back(v);
            }
            routes.push_back(std::move(route));
            distances.push_back(connection_dist(v1, v2));
        }
        for (int i = 0; i < static_cast<int>(danger_zones.size()); ++i) {
            danger_idx[danger_zones[i]] = i;
        }
        for (int i = 0; i < static_cast<int>(danger_zones.size()); ++i) {
            int v = danger_zones[i];
            for (int d : {1, N2}) {
                int neighbor = v + d;
                if (neighbor < N2 * N2 && danger_idx[neighbor] >= 0) {
                    adjacent_dangers.emplace_back(i, danger_idx[neighbor]);
                }
            }
        }
    }

    const vector<int>& build(const vector<int>& edges) {
        if (++tree_stamp == 0) {
            fill(used.begin(), used.end(), 0);
            tree_stamp = 1;
        }
        trees.clear();
        for (auto it = edges.rbegin(); it != edges.rend(); ++it) {
            for (int v : routes[*it]) {
                if (used[v] == tree_stamp) continue;
                used[v] = tree_stamp;
                trees.push_back(v);
                if (static_cast<int>(trees.size()) == K) return trees;
            }
        }
        return trees;
    }

    int find_root(int x) {
        if (parents[x] < 0) return x;
        return parents[x] = find_root(parents[x]);
    }

    long long evaluate(const vector<int>& selected_trees) {
        if (++score_stamp == 0) {
            fill(removed.begin(), removed.end(), 0);
            score_stamp = 1;
        }
        for (int v : selected_trees) {
            int idx = danger_idx[v];
            if (idx >= 0) removed[idx] = score_stamp;
        }
        fill(parents.begin(), parents.end(), -1);
        // 無向辺は一度だけ処理する。連結成分と評価値は元の処理と同じ。
        for (auto [a, b] : adjacent_dangers) {
            if (removed[a] == score_stamp || removed[b] == score_stamp) continue;
            a = find_root(a);
            b = find_root(b);
            if (a == b) continue;
            if (parents[a] > parents[b]) swap(a, b);
            parents[a] += parents[b];
            parents[b] = a;
        }
        long long score = 0;
        for (int i = 0; i < static_cast<int>(parents.size()); ++i) {
            if (removed[i] != score_stamp && parents[i] < 0) {
                score += 1LL * parents[i] * parents[i];
            }
        }
        return score;
    }
};

int main() {
    const auto start_time = chrono::steady_clock::now();
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    if (!(cin >> N >> K)) return 0;
    N2 = N + 2;
    board.assign(N2, vector<int>(N2, 0));
    for (int i = 0; i < N; ++i) {
        string row;
        cin >> row;
        for (int j = 0; j < N; ++j) board[i + 1][j + 1] = row[j] - '0';
    }
    mt19937 rng(random_device{}());
    auto randint = [&](int lo, int hi) {
        return uniform_int_distribution<int>(lo, hi)(rng);
    };
    auto random_real = [&]() {
        return uniform_real_distribution<double>(0.0, 1.0)(rng);
    };
    vector<int> safe_zones;
    for (int i = 0; i < N2; ++i) {
        for (int j = 0; j < N2; ++j) {
            if (board[i][j] <= SAFE_ZONE_CRITERIA) safe_zones.push_back(to_1d(i, j));
            else danger_zones.push_back(to_1d(i, j));
        }
    }
    set<Connection> candidate_set;
    while (candidate_set.size() <= CAND_SIZES_LIM) {
        int v1 = safe_zones[randint(0, static_cast<int>(safe_zones.size()) - 1)];
        int v2 = safe_zones[randint(0, static_cast<int>(safe_zones.size()) - 1)];
        int dist = connection_dist(v1, v2);
        if (2 <= dist && dist <= 50) candidate_set.emplace(v1, v2);
    }
    vector<Connection> edge_candidates(candidate_set.begin(), candidate_set.end());
    SearchWorkspace workspace(edge_candidates);
    vector<int> edges, prev_edges, best_trees;
    edges.reserve(128);
    prev_edges.reserve(128);
    int est_sizes = 0;
    double current_score = numeric_limits<double>::infinity();
    long long best_score = numeric_limits<long long>::max();
    auto contains_edge = [&](int edge) {
        return find(edges.begin(), edges.end(), edge) != edges.end();
    };

    while (true) {
        double elapsed = chrono::duration<double>(chrono::steady_clock::now() - start_time).count();
        if (elapsed > TIME_LIMIT) break;
        double temperature = START_TEMP + (END_TEMP - START_TEMP) * elapsed / TIME_LIMIT;
        int x = randint(0, CAND_SIZES_LIM);
        double r = random_real();
        if (contains_edge(x)) continue;
        prev_edges = edges;
        int prev_est_sizes = est_sizes;
        double move_r = est_sizes > 90 ? random_real() : 0.0;
        if (est_sizes <= 90) {
            est_sizes += workspace.distances[x];
            edges.push_back(x);
        } else if (move_r < TWO_ADD_ONE_REMOVE_PROB && est_sizes < 105) {
            if (edge_candidates.size() - edges.size() < 2) continue;
            int z = randint(0, CAND_SIZES_LIM);
            while (z == x || contains_edge(z)) z = randint(0, CAND_SIZES_LIM);
            int y = randint(0, static_cast<int>(edges.size()) - 1);
            est_sizes -= workspace.distances[edges[y]];
            edges.erase(edges.begin() + y);
            for (int new_edge : {x, z}) {
                edges.push_back(new_edge);
                est_sizes += workspace.distances[new_edge];
            }
        } else if (TWO_ADD_ONE_REMOVE_PROB <= move_r &&
                   move_r < TWO_ADD_ONE_REMOVE_PROB + TWO_REMOVE_ONE_ADD_PROB) {
            if (edges.size() < 2) continue;
            int y1 = randint(0, static_cast<int>(edges.size()) - 1);
            int y2 = randint(0, static_cast<int>(edges.size()) - 2);
            if (y2 >= y1) ++y2;
            if (y1 < y2) swap(y1, y2);
            for (int y : {y1, y2}) {
                est_sizes -= workspace.distances[edges[y]];
                edges.erase(edges.begin() + y);
            }
            edges.push_back(x);
            est_sizes += workspace.distances[x];
        } else {
            int y = randint(0, static_cast<int>(edges.size()) - 1);
            est_sizes -= workspace.distances[edges[y]];
            edges[y] = x;
            est_sizes += workspace.distances[x];
        }
        const auto& trees = workspace.build(edges);
        long long new_score = workspace.evaluate(trees);
        if (new_score <= current_score || r < exp((current_score - new_score) / temperature)) {
            current_score = static_cast<double>(new_score);
        } else {
            edges.swap(prev_edges);
            est_sizes = prev_est_sizes;
        }
        if (new_score < best_score) {
            best_trees = trees;
            best_score = new_score;
        }
    }
    cout << best_trees.size() << '\n';
    for (int v : best_trees) {
        auto [x, y] = to_2d(v);
        cout << x - 1 << ' ' << y - 1 << '\n';
    }
    return 0;
}