#1195281 (C++23) No.5025 Forest Fire

• 問題: No.5025 Forest Fire
• ユーザー: 👑 hitonanode
• 提出日時: 2026-10-24 23:20:51
• 言語: C++23 (gcc 15.3.0 + boost 1.92.0 + ACL)
• 結果: TLE
• 実行時間: -
• コード長: 20,262 bytes
• コンパイル時間: 4,449 ms
• コンパイル使用メモリ: 387,940 KB
• 実行使用メモリ: 9,920 KB
• スコア: 178,355,262
• 最終ジャッジ日時: 2026-10-24 23:24:25
• 合計ジャッジ時間: 144,673 ms
• ジャッジサーバーID （参考情報）: judge6_0 / <nil>

ファイルパターン	結果
other	AC * 47 TLE * 3

ソースコード

#pragma GCC optimize("O3,unroll-loops")
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_CYAN = "\033[1;36m";
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << std::endl : std::cerr)
#define dbg(x) dbgif(true, x)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif

// https://hitonanode.github.io/cplib-cpp/unionfind/unionfind.hpp
#include <algorithm>
#include <numeric>
#include <utility>
#include <vector>

// UnionFind Tree (0-indexed), based on size of each disjoint set
struct UnionFind {
    std::vector<int> par, cou;
    UnionFind(int N = 0) : par(N), cou(N, 1) { iota(par.begin(), par.end(), 0); }
    int find(int x) { return (par[x] == x) ? x : (par[x] = find(par[x])); }
    bool unite(int x, int y) {
        x = find(x), y = find(y);
        if (x == y) return false;
        if (cou[x] < cou[y]) std::swap(x, y);
        par[y] = x, cou[x] += cou[y];
        return true;
    }
    int count(int x) { return cou[find(x)]; }
    bool same(int x, int y) { return find(x) == find(y); }
    std::vector<std::vector<int>> groups() {
        std::vector<std::vector<int>> ret(par.size());
        for (int i = 0; i < int(par.size()); ++i) ret[find(i)].push_back(i);
        ret.erase(std::remove_if(ret.begin(), ret.end(),
                                 [&](const std::vector<int> &v) { return v.empty(); }),
                  ret.end());
        return ret;
    }
};


// https://hitonanode.github.io/cplib-cpp/random/rand_nondeterministic.hpp
#include <cassert>
#include <chrono>
#include <cstdint>
#include <random>

struct RNGMt19937 {
    using lint = long long;
    std::mt19937 mt;
    RNGMt19937(long long seed) : mt(seed) {}
    lint operator()(lint x) { // [0, x)
        assert(x > 0);
        return this->operator()(0, x);
    }
    lint operator()(lint l, lint r) {
        assert(l < r);
        std::uniform_int_distribution<lint> d(l, r - 1);
        return d(mt);
    }
};
// RNGMt19937 rnd(123456789);
// RNGMt19937 rnd(std::chrono::steady_clock::now().time_since_epoch().count());

// Fast random number generator based on xoshiro256++.
struct FastRNG {
    using ull = unsigned long long;
    ull s[4];

    static ull rotl(ull x, int k) { return (x << k) | (x >> (64 - k)); }

    static ull splitmix64(ull &x) {
        ull z = (x += 0x9e3779b97f4a7c15ULL);
        z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9ULL;
        z = (z ^ (z >> 27)) * 0x94d049bb133111ebULL;
        return z ^ (z >> 31);
    }

    FastRNG(ull seed) {
        for (auto &x : s) x = splitmix64(seed);
    }

    ull next_u64() {
        ull res = rotl(s[0] + s[3], 23) + s[0];
        ull t = s[1] << 17;

        s[2] ^= s[0];
        s[3] ^= s[1];
        s[1] ^= s[2];
        s[0] ^= s[3];

        s[2] ^= t;
        s[3] = rotl(s[3], 45);

        return res;
    }

    uint32_t next_u32() { return next_u64() >> 32; }

    // [0, n)
    uint32_t operator()(uint32_t n) {
        assert(n > 0);
        return (uint64_t(next_u32()) * n) >> 32;
    }

    // [l, r)
    int operator()(int l, int r) {
        assert(l < r);
        uint32_t width = uint64_t(int64_t(r) - int64_t(l));
        return int(int64_t(l) + (*this)(width));
    }

    uint16_t next_u16() { return next_u64() >> 48; }
};
inline FastRNG rnd(123456789);
// FastRNG rnd(std::chrono::steady_clock::now().time_since_epoch().count());

// https://hitonanode.github.io/cplib-cpp/heuristic/exponential_dist_sampler.hpp

#include <cassert>
#include <cmath>
#include <cstdint>
#include <array>

template <int D> struct ExponentialDistSampler {
    std::array<double, (1 << D)> minuslogps;

    constexpr ExponentialDistSampler() {
        for (int i = 0; i < (1 << D); ++i) minuslogps.at(i) = -log((0.5 + i) / (1 << D));
    }

    double sample(uint32_t random_mask) const {
        return minuslogps.at(random_mask & ((1 << D) - 1));
    }

    // p ~ U(0, 1) => -log(p) ~ Ex(1)
    // P[exp(-|dx| / T) >= p] = P[|dx| <= -log(p) * T]
    bool check_sa(double abs_dx, double T, uint32_t random_mask) const {
        return abs_dx <= minuslogps.at(random_mask & ((1 << D) - 1)) * T;
    }
};
const ExponentialDistSampler<16> log_ps;

template <int UPDATE_INTERVAL = 256> struct Annealer {
    static_assert(UPDATE_INTERVAL > 0);

    double temp;
    double ratio;
    int next_update = UPDATE_INTERVAL;

    Annealer(double start_temp, double end_temp, int iterations) : temp(start_temp) {
        assert(iterations > 0);
        const int updates = (iterations - 1) / UPDATE_INTERVAL;
        ratio = updates == 0 ? 1.0 : pow(end_temp / start_temp, 1.0 / updates);
        // ratio = updates == 0 ? 0.0 : (end_temp - start_temp) / updates;
    }

    void update(int iter) {
        if (iter >= next_update) {
            temp *= ratio;
            // temp += ratio;
            next_update += UPDATE_INTERVAL;
        }
    }

    template <class RNG, class Sampler>
    bool accept_score(int delta_score, RNG &rng, const Sampler &sampler) const {
        if (delta_score >= 0) return true;
        return sampler.check_sa(-delta_score, temp, rng.next_u16());
    }

    template <class RNG, class Sampler>
    bool accept_cost(int delta_cost, RNG &rng, const Sampler &sampler) const {
        if (delta_cost <= 0) return true;
        return sampler.check_sa(delta_cost, temp, rng.next_u16());
    }
};


constexpr int N = 50, K = 100;

using InputState = array<char, N * N>;
using RandState = array<char, N * N>;
using BanState = array<bool, N * N>;
RandState Gen() {
    array<char, N * N> ret{};
    for (auto &c : ret) c = '0' + rnd(10);
    return ret;
}

int f(int x, int y) { return x * N + y; }
bool isin(int x, int y) { return 0 <= x and x < N and 0 <= y and y < N; }

int QuadSum(const InputState &input, const RandState &rand_state, const BanState &ban_state) {
    int ret = 0;
    vector<int> visited(N * N);

    auto IsAlive = [&](int x, int y) {
        if (!isin(x, y)) return false;
        const int idx = f(x, y);
        if (ban_state[idx]) return false;
        return input[idx] > rand_state[idx];
    };

    REP(i, N) REP(j, N) {
        if (visited[f(i, j)]) continue;
        int sum = 0;
        auto rec = [&](auto &&self, int x, int y) -> void {
            if (!IsAlive(x, y)) return;
            const int idx = f(x, y);
            if (visited[idx]) return;
            visited[idx] = 1;
            sum++;
            self(self, x + 1, y);
            self(self, x - 1, y);
            self(self, x, y + 1);
            self(self, x, y - 1);
        };
        rec(rec, i, j);

        ret += sum * sum;
    }

    return ret;
}

void BurnProb(const InputState &input, const RandState &rand_state,
              const BanState &ban_state, vector<double> &burn_weight) {
    assert((int)burn_weight.size() == N * N);
    UnionFind uf(N * N);

    auto IsAlive = [&](int x, int y) {
        const int idx = f(x, y);
        if (ban_state[idx]) return false;
        return !ban_state[idx] and (input[idx] > rand_state[idx]);
    };

    REP(i, N) REP(j, N) {
        if (!IsAlive(i, j)) continue;
        if (i + 1 < N and IsAlive(i + 1, j)) uf.unite(f(i, j), f(i + 1, j));
        if (j + 1 < N and IsAlive(i, j + 1)) uf.unite(f(i, j), f(i, j + 1));
    }

    REP(i, N) REP(j, N) {
        burn_weight[f(i, j)] += uf.count(f(i, j));
    }
}

double CalcE(const InputState &input, const vector<RandState> &rand_states, const BanState &ban_state) {
    lint quad_sum = 0;
    for (const auto &rand_state : rand_states) {
        quad_sum += QuadSum(input, rand_state, ban_state);
    }

    return double(quad_sum) / ((lint)rand_states.size() * N * N);
}

vector<double> BurnProbMap(const InputState &input, const vector<RandState> &rand_states,
                   const BanState &ban_state) {
    vector<double> ret(N * N);
    for(const auto &rand_state : rand_states) {
        BurnProb(input, rand_state, ban_state, ret);
    }
    for (auto &x : ret) x /= (lint)rand_states.size() * N * N;

    return ret;
}

const vector<int> dxs8{1, -1, 0, 0, 1, 1, -1, -1};
const vector<int> dys8{0, 0, 1, -1, 1, -1, 1, -1};

struct Line {
    int x0, y0;
    int dir;

    template <class OStream>
    friend OStream &operator<<(OStream &os, const Line &line) {
        os << "Line(" << line.x0 << ", " << line.y0 << ", " << line.dir << ")";
        return os;
    }
};

void Apply(BanState &state, const BanState &ban_candidate, const Line &line) {
    const int dx = dxs8[line.dir];
    const int dy = dys8[line.dir];
    int x = line.x0, y = line.y0;
    assert(isin(x, y));

    while (true) {
        if (!ban_candidate[f(x, y)]) break;
        if (state[f(x, y)]) break;
        state[f(x, y)] = true;
        x += dx;
        y += dy;
        if (!isin(x, y)) break;
    }
}

BanState Apply(const vector<Line> &lines, const BanState &ban_candidate) {
    BanState ret{};
    for (const auto &line : lines) Apply(ret, ban_candidate, line);
    return ret;
}

int main() {
    InputState input_state{};
    vector<string> S(N);
    {
        int N_, K_;
        cin >> N_ >> K_;
        assert(N == N_);
        assert(K == K_);
        for (auto &s : S) cin >> s;
        REP(i, N) REP(j, N) input_state[f(i, j)] = S[i][j];
    }

    vector<RandState> rand_states;
    REP(_, 50) rand_states.push_back(Gen());
    dbg(rand_states.size());

    // REP(_, 1000) {
    //     const auto e1 = CalcE(input_state, rand_states, ban0);
    //     // dbg(e1);
    // }
    // const int score = round(1e6 * (1 + log2(e0 / e1)));
    // dbg(score);
    // dbg(BurnProbMap(input_state, rand_states, ban0));

    auto IsTarget = [&](int x, int y) {
        const int idx = f(x, y);
        if (input_state[idx] >= '5') return true;
        if (input_state[idx] < '4') return false;

        for (auto [dx, dy] : grid_dxs) {
            const int nx = x + dx;
            const int ny = y + dy;
            if (isin(nx, ny) && input_state[f(nx, ny)] >= '8') return true;
        }
        return false;
    };

    BanState ban_candidate{};
    REP(x, N) REP(y, N) {
        if (IsTarget(x, y)) ban_candidate[f(x, y)] = true;
    }


    auto FastEval = [&](const BanState &ban_state) {
        UnionFind uf(N * N);

        REP(x, N) REP(y, N) {
            if (ban_state[f(x, y)]) continue;
            if (!IsTarget(x, y)) continue;
            if (x + 1 < N && !ban_state[f(x + 1, y)] && IsTarget(x + 1, y)) uf.unite(f(x, y), f(x + 1, y));
            if (y + 1 < N && !ban_state[f(x, y + 1)] && IsTarget(x, y + 1)) uf.unite(f(x, y), f(x, y + 1));
        }

        lint ret = 0;
        REP(idx, N * N) {
            if (ban_state[idx]) continue;
            if (!IsTarget(idx / N, idx % N)) continue;
            if (uf.find(idx) == idx) {
                const lint c = uf.count(idx);
                ret += c * c * c;
            }
        }

        return ret;
    };

    BanState state{};
    vector<Line> best_lines;
    while (true) {
        const int k = count(ALL(state), true);
        const int rem = K - k;
        if (rem <= 0) break;

        double max_eval = -1e200;
        Line best_line{-1, -1, -1};

        const auto orig_e = FastEval(state);
        REP(x0, N) REP(y0, N) {
            if (!IsTarget(x0, y0)) continue;
            if (state[f(x0, y0)]) continue;
            if ((x0 + y0) % 2) continue;
            FOR(dir, 4, 8) {
                const int dx = dxs8[dir];
                const int dy = dys8[dir];

                int nban = 0;
                BanState next_state = state;

                FOR(len, 1, N + 1) {
                    const int nx = x0 + dx * (len - 1);
                    const int ny = y0 + dy * (len - 1);
                    if (!isin(nx, ny)) break;
                    if (!IsTarget(nx, ny)) break;

                    if (chmax(next_state[f(nx, ny)], true)) {
                        ++nban;

                        if (nban > 30 or nban > rem) break;

                        const int nnx = nx + dx;
                        const int nny = ny + dy;

                        if (!isin(nnx, nny) or !IsTarget(nnx, nny) or state[f(nnx, nny)]) {

                            const double imp = orig_e - FastEval(next_state);
                            if (chmax(max_eval, imp * imp * imp / nban / nban)) {
                                best_line = Line{x0, y0, dir};
                            }

                            break;
                        }
                    } else {
                        break;
                    }
                }
            }
        }

        dbg(make_tuple(best_line, max_eval));

        if (best_line.x0 != -1) {
            Apply(state, ban_candidate, best_line);
            best_lines.push_back(best_line);
        } else {
            break;
        }
    }

    dbg(best_lines);

    auto best_eval = CalcE(input_state, rand_states, Apply(best_lines, ban_candidate));
    dbg(best_eval);

    {
        // auto state = best_state;
        auto current_lines = best_lines;
        auto state_eval = best_eval;

        Annealer sa(0.1, 0.01, 800);
        REP(_, 800) {
            sa.update(_);
            auto lines = current_lines;
            const int idx = rnd(lines.size());
            const int d = rnd(8);
            lines[idx].x0 += dxs8[d];
            lines[idx].y0 += dys8[d];
            if (!isin(lines[idx].x0, lines[idx].y0) or !IsTarget(lines[idx].x0, lines[idx].y0))
                continue;

            auto new_state = Apply(lines, ban_candidate);
            if (count(ALL(new_state), true) > K) continue;

            const auto new_eval = CalcE(input_state, rand_states, new_state);

            if (chmin(best_eval, new_eval)) {
                best_eval = new_eval;
                best_lines = lines;
                dbg(make_tuple(_, new_eval));
            }

            if (sa.accept_cost(new_eval - state_eval, rnd, log_ps)) {
                dbg(make_tuple(_, new_eval, state_eval));
                state_eval = new_eval;
                current_lines = lines;
            }
        }
    }

    {
        auto best_state = Apply(best_lines, ban_candidate);
        cout << count(ALL(best_state), true) << "\n";
        REP(i, N) REP(j, N) {
            if (best_state[f(i, j)]) cout << i << " " << j << "\n";
        }
    }
}