#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include class JsonDumper { struct KeyValue { std::string key; std::string value; }; std::vector _items; bool dump_at_end = false; public: JsonDumper(bool dump_at_end_ = false) : dump_at_end(dump_at_end_) {} ~JsonDumper() { if (dump_at_end) std::cout << dump() << std::endl; } void set_dump_at_end() { dump_at_end = true; } void operator()(const std::string &key, const std::string &value) { _items.push_back(KeyValue{key, "\"" + value + "\""}); } template void operator()(const std::string &key, T value) { _items.push_back(KeyValue{key, std::to_string(value)}); } std::string dump() const { std::string ret = "{\n"; if (!_items.empty()) { for (const auto &[k, v] : _items) ret += " \"" + k + "\": " + v + ",\n"; ret.erase(ret.end() - 2); } ret += "}"; return ret; } } jdump; #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 bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&...args) { ((is >> args), ...); }, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&...args) { ((os << args << ','), ...); }, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const std::string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) \ std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " \ << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) \ ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ \ << ") " << __FILE__ << COLOR_RESET << std::endl \ : std::cerr) #else #define dbg(x) 0 #define dbgif(cond, x) 0 #endif #ifdef BENCHMARK #define dump_onlinejudge(x) 0 struct setenv { setenv() { jdump.set_dump_at_end(); } } setenv_; #else #define dump_onlinejudge(x) (std::cout << (x) << std::endl) #endif #include #include #include #include using namespace std; using lint = long long; using pint = std::pair; using plint = std::pair; struct fast_ios { fast_ios() { std::cin.tie(nullptr), std::ios::sync_with_stdio(false), std::cout << std::fixed << std::setprecision(20); }; } fast_ios_; constexpr int N = 45; // void gen constexpr lint AMIN = 100000000000000000; constexpr lint AMAX = 1000000000000000000; constexpr lint goalx = 500000000000000000; constexpr lint goaly = 500000000000000000; constexpr int MAXT = 50; #include #include 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)); } double rand_double() { return (double)rand_int() / UINT32_MAX; } template void shuffle_vec(std::vector &vec) { for (int i = 1; i < (int)vec.size(); ++i) { const int j = rand_int() % (i + 1); std::swap(vec.at(i), vec.at(j)); } } #include #include struct rand_int_ { using lint = long long; std::mt19937 mt; rand_int_() : mt(std::chrono::steady_clock::now().time_since_epoch().count()) {} lint operator()(lint x) { return this->operator()(0, x); } // [0, x) lint operator()(lint l, lint r) { std::uniform_int_distribution d(l, r - 1); return d(mt); } } rnd; double eval_diversity(const array &A, const array &B, const bitset &alives, lint cx, lint cy) { const int Z = 60; // const double r = 0.9; const double dec = 2.0; vector hi(Z, -1e18); vector invdsum(Z); REP(i, A.size()) { if (!alives[i]) continue; const lint a = A.at(i); const lint b = B.at(i); const double theta = atan2(b - cy, a - cx); int z = (theta / (2 * M_PI) + 0.5) * Z; // z = (z % Z + Z) % Z; const double dist = max(abs(a - cx), abs(b - cy)) + 1; // chmax(hi.at(z), -log10(dist)); invdsum.at(z) += 1.0 / dist; } REP(z, Z) { if (invdsum.at(z)) hi.at(z) = log10(invdsum.at(z)); } REP(_, 2) { FOR(i, 1, Z) { chmax(hi.at(i), hi.at(i - 1) - dec); } chmax(hi.at(0), hi.at(Z - 1) - dec); IFOR(i, 1, Z) { chmax(hi.at(i - 1), hi.at(i) - dec); } chmax(hi.at(Z - 1), hi.at(0) - dec); } return accumulate(ALL(hi), 0.0); } struct State { State *par = nullptr; std::vector par_op; // par からどのような手でこれに到達するか int num_steps = 0; std::bitset alives; std::array A, B; static State gen_root(const array &A, const array &B) { State s; s.alives.set(); s.A = A; s.B = B; return s; } State gen_next(const vector ops) { State next; next.par = this; next.par_op = ops; next.num_steps = num_steps + (int)ops.size(); next.alives = alives; next.A = A; next.B = B; for (auto [i, j] : ops) { lint tmpa = (next.A.at(i) + next.A.at(j)) / 2; lint tmpb = (next.B.at(i) + next.B.at(j)) / 2; next.A.at(i) = next.A.at(j) = tmpa; next.B.at(i) = next.B.at(j) = tmpb; } return next; } State try_drop(bool force) { lint sumx = 0, sumy = 0; const int nalive = alives.count(); REP(i, N) { if (alives[i]) { sumx += A.at(i) - goalx; sumy += B.at(i) - goaly; } } const double error = 1.0 * max(abs(sumx), abs(sumy)) / nalive; int besti = -1; double besterror = error; // dbg(force); if (force) besterror = 1e30; FOR(i, 1, N) { if (!alives[i]) continue; // if ((sumx > 0) != (A.at(i) > goalx)) continue; // if ((sumy > 0) != (B.at(i) > goaly)) continue; // if (abs(sumx) < abs(A.at(i) - goalx)) continue; // if (abs(sumy) < abs(B.at(i) - goaly)) continue; const double errornew = 1.0 * max(abs(sumx - A.at(i) + goalx), abs(sumy - B.at(i) + goaly)) / (nalive - 1); if (chmin(besterror, errornew)) besti = i; } if (besti < 0) return *this; dbg(make_tuple("Drop", 1.0 * sumx / nalive, 1.0 * sumy / nalive, nalive, besti)); State next = *this; next.alives[besti] = false; return next; } State step() { lint sumx = 0, sumy = 0; const int nalive = alives.count(); REP(i, N) { if (alives[i]) { sumx += A.at(i); sumy += B.at(i); } } vector best_way; double min_error = 1e30; int xmini = -1, xmaxi = -1, ymini = -1, ymaxi = -1; lint xmin = AMAX + 1, xmax = -1e18, ymin = AMAX + 1, ymax = -1e18; REP(i, N) { if (!alives[i]) continue; if (chmin(xmin, A.at(i))) xmini = i; if (chmax(xmax, A.at(i))) xmaxi = i; if (chmin(ymin, B.at(i))) ymini = i; if (chmax(ymax, B.at(i))) ymaxi = i; } if (abs(ymax - ymin) > abs(xmax - xmin)) { best_way.emplace_back(ymini, ymaxi); } else { best_way.emplace_back(xmini, xmaxi); } // if (mode & 1) best_way.emplace_back(xmini, xmaxi); // if (mode & 2) best_way.emplace_back(ymini, ymaxi); return gen_next(best_way); } State primer() { vector best_ops; double best = AMAX; // const lint cx = goalx * 2 - A.at(0); const lint cx = goalx; // const lint cy = goaly * 2 - B.at(0); const lint cy = goaly; const lint d0 = max(abs(A.at(0) - cx), abs(B.at(0) - cy)); auto Anxt = A, Bnxt = B; REP(i, N) REP(j, i) { if (!alives[i] or !alives[j]) continue; lint a = (A.at(i) + A.at(j)) / 2; lint b = (B.at(i) + B.at(j)) / 2; lint d = max(abs(a - cx), abs(b - cy)); if (d > d0) continue; Anxt.at(i) = Anxt.at(j) = a; Bnxt.at(i) = Bnxt.at(j) = b; double after = eval_diversity(Anxt, Bnxt, alives, cx, cy); Anxt.at(i) = A.at(i); Anxt.at(j) = A.at(j); Bnxt.at(i) = B.at(i); Bnxt.at(j) = B.at(j); // double after = log(1.0 * d * d); if (chmin(best, -after)) best_ops = {{i, j}}; } return gen_next(best_ops); } State greedy2() { lint best = AMAX; vector best_ops; // 0-i FOR(i, 1, N) { lint a = (A.at(0) + A.at(i)) / 2; lint b = (B.at(0) + B.at(i)) / 2; if (chmin(best, max(abs(a - goalx), abs(b - goaly)))) { best_ops = {{0, i}}; } } // i-j, 0-i // i-j, 0-i, 0-j if (num_steps + 2 <= MAXT) { FOR(i, 1, N) FOR(j, 1, i) { const lint a1 = (A.at(i) + A.at(j)) / 2; const lint b1 = (B.at(i) + B.at(j)) / 2; { const lint a = (A.at(0) + a1) / 2; const lint b = (B.at(0) + b1) / 2; if (chmin(best, max(abs(a - goalx), abs(b - goaly)))) { best_ops = {{i, j}, {0, i}}; } if (num_steps + 3 <= MAXT) { const lint a2 = (a + a1) / 2; const lint b2 = (b + b1) / 2; if (chmin(best, max(abs(a2 - goalx), abs(b2 - goaly)))) { best_ops = {{i, j}, {0, i}, {0, j}}; } } } } } return gen_next(best_ops); } lint eval_linf() const { return max(abs(A.at(0) - goalx), abs(B.at(0) - goaly)); } }; int calc_score(lint max_v1v2) { if (!max_v1v2) return 2000000 + 50; double sol = 2000000 - 100000 * log10(max_v1v2 + 1); return floor(sol); } void experiment() { constexpr int D = 28; vector A(D), B(D); REP(i, D) { A.at(i) = rnd(AMIN, AMAX); B.at(i) = rnd(AMIN, AMAX); } lint best_s = 0; lint best = 1LL << 60; FOR(S, 1, 1 << D) { lint asum = 0, bsum = 0, num = 0; REP(i, D) { if ((S >> i) & 1) { asum += A.at(i); bsum += B.at(i); ++num; } } asum /= num; bsum /= num; const lint eval = max(abs(asum - goalx), abs(bsum - goaly)); if (chmin(best, eval)) { best_s = S; } if (__builtin_popcount(S + 1) == 1) { dbg(make_tuple(best, best_s, S)); } } } vector generate_seq(const State *s) { vector res; while (s->par) { res.insert(res.end(), s->par_op.rbegin(), s->par_op.rend()); s = s->par; } reverse(ALL(res)); return res; } using SolutionState = vector; double eval_l2(const array &Ainit, const array &Binit, const SolutionState &sol) { array A = Ainit, B = Binit; for (auto [i, j] : sol) { lint tmpa = (A.at(i) + A.at(j)) / 2; lint tmpb = (B.at(i) + B.at(j)) / 2; A.at(i) = A.at(j) = tmpa; B.at(i) = B.at(j) = tmpb; } const double dx = abs(A.at(0) - goalx), dy = abs(B.at(0) - goaly); return sqrt(dx * dx + dy * dy); } lint eval_linf(const array &Ainit, const array &Binit, const SolutionState &sol) { array A = Ainit, B = Binit; for (auto [i, j] : sol) { lint tmpa = (A.at(i) + A.at(j)) / 2; lint tmpb = (B.at(i) + B.at(j)) / 2; A.at(i) = A.at(j) = tmpa; B.at(i) = B.at(j) = tmpb; } const lint dx = abs(A.at(0) - goalx), dy = abs(B.at(0) - goaly); return max(dx, dy); } int main(int argc, char *argv[]) { // experiment(); // int X = 0; // if (argc >= 2) { X = std::stoi(argv[1]); } { int n_; cin >> n_; assert(N == n_); } array A, B; { for (int i = 0; i < N; i++) { cin >> A.at(i) >> B.at(i); } } SolutionState state(N - 1); REP(i, N - 1) state.at(i) = {0, i + 1}; auto best = state; double estate = eval_l2(A, B, state); double ebest = estate; const double Tbegin = 1e16, Tend = 100; REP(_, 2000000) { double T = Tbegin * pow(Tend / Tbegin, 1.0 * _ / 10000000); int a = rnd(N - 1), b = rnd(N - 1); swap(state.at(a), state.at(b)); double ee = eval_l2(A, B, state); if (ee <= estate or exp((estate - ee) / T) > rand_double()) { estate = ee; if (chmin(ebest, estate)) { best = state; dbg(make_tuple(ebest, state)); } } else { swap(state.at(a), state.at(b)); } } dump_onlinejudge(best.size()); for (auto [i, j] : best) { dump_onlinejudge(to_string(i + 1) + " " + to_string(j + 1)); } // vector states(10000); // states.at(0) = State::gen_root(A, B); // int h = 0; // bool mode = false; // while (states.at(h).num_steps < MAXT and states.at(h).alives.count() > 1) { // const int nalive = states.at(h).alives.count(); // const int rem_turn = MAXT - states.at(h).num_steps; // dbg(make_tuple(h, nalive, rem_turn)); // states.at(h + 1) = states.at(h).try_drop(rem_turn * 0.5 + 1 < nalive); // ++h; // // dbg(states.at(h).alives.count()); // // states.at(h + 1) = states.at(h).step(mode); // // mode ^= 1; // // ++h; // if (states.at(h).num_steps < MAXT) { // if (states.at(h).num_steps > MAXT * 0.9) { // states.at(h + 1) = states.at(h).greedy2(); // ++h; // } else { // states.at(h + 1) = states.at(h).step(); // // states.at(h + 1) = states.at(h).primer(); // ++h; // } // mode ^= 1; // } // // if (h % 3 != 2 or states.at(h).num_steps < MAXT * 0.5) { // // states.at(h + 1) = states.at(h).primer(); // // } else { // // states.at(h + 1) = states.at(h).greedy2(); // // } // // ++h; // // dbg(make_tuple(states.at(h).num_steps, states.at(h).eval_linf())); // } // const State *goal_state = &states.at(h); // dbg(goal_state->alives); // auto sol = generate_seq(goal_state); // dump_onlinejudge(sol.size()); // for (auto [i, j] : sol) { // dump_onlinejudge(to_string(i + 1) + " " + to_string(j + 1)); // } const lint cost = eval_linf(A, B, best); const int score = calc_score(cost); jdump("score", score); // dbg(cost); // dbg(score); }