#include #include #include #include #include constexpr int max_swap = 50; static int n; static std::mt19937 mt(0); static std::uniform_real_distribution<> uniform(0.,1.); static std::vector a, b; using Entry = std::pair; using Solution = std::vector; long calc_score(const Solution& ans, const std::vector& a, const std::vector& b) { std::vector aa = a; std::vector bb = b; for (auto [u,v] : ans) { long v1 = (aa[u] + aa[v])/2; long v2 = (bb[u] + bb[v])/2; aa[u] = v1; aa[v] = v1; bb[u] = v2; bb[v] = v2; } double v1 = std::abs(aa[0] - 5*1e17); double v2 = std::abs(bb[0] - 5*1e17); long score = 2000000L - 100000L * std::log10(std::max(v1, v2) + 1); return score; } void print_ans(const Solution& ans) { std::cout << ans.size() << std::endl; for (auto [u,v] : ans) { std::cout << u+1 << " " << v+1 << std::endl; } } void debug_print_ans(const Solution& ans) { for (auto [u,v] : ans) { std::cerr << "(" << u << "," << v << ") "; } std::cerr << "score = " << calc_score(ans, a, b) << std::endl; } auto gen_random_ans(int n) { constexpr int m = 50; std::vector ans; for (int i = 0; i < m; i++) { int u, v; while (true) { u = mt() % n; v = mt() % n; if (u != v) { break; } } ans.emplace_back(u,v); } return ans; } auto greedy_ans(int n) { constexpr int m = 50; std::vector ans; long best_score = calc_score(ans, a, b); std::cerr << "initial score: " << best_score << std::endl; for (int i = 0; i < m; i++) { /* std::cerr << i << " th iter" << std::endl; */ int u = 0; int best_v = -1; for (int v = 1; v < n; v++) { ans.emplace_back(u,v); long score = calc_score(ans, a, b); /* std::cerr << "v, score: " << v << ", " << score << std::endl; */ if (score > best_score) { best_score = score; best_v = v; } ans.pop_back(); } /* std::cerr << "best v, score: " << best_v << ", " << best_score << std::endl; */ if (best_v == -1) { break; } else { ans.emplace_back(u,best_v); } } return ans; } auto add_two_swaps(Solution& ans) { constexpr int m = 50; long best_score = calc_score(ans, a, b); for (int u = 1; u < n-1; u++) { for (int v = u+1; v < n; v++) { ans.push_back(Entry{u,v}); ans.push_back(Entry{0,u}); long score = calc_score(ans, a, b); if (score > best_score) { best_score = score; } else { ans.pop_back(); ans.pop_back(); } } } return ans; } auto greedy_iter_two_swap(int n) { Solution ans; while (ans.size() <= max_swap - 2) { auto size = ans.size(); add_two_swaps(ans); if (size == ans.size()) { // no pair inserted break; } } return ans; } void annealing(Solution& ans) { std::cerr << "annealing()" << std::endl; constexpr int m = 50; long best_score = calc_score(ans, a, b); auto start_time = std::chrono::steady_clock::now(); const double duration = 950; // msec const double start_temp = 1000; const double end_temp = 100; /* const long max_iter = 50000000; */ /* for (long iter = 0; iter < max_iter; iter++) { */ /* double temp = start_temp + (end_temp - start_temp) * (static_cast(iter) / max_iter); */ while (true) { auto time = std::chrono::steady_clock::now(); auto elapsed = std::chrono::duration_cast(time - start_time).count(); if (elapsed > duration) { break; } double temp = start_temp + (end_temp - start_temp) * (static_cast(elapsed) / duration); int r = mt() % 2; // add a random entry if (r == 0) { if (ans.size() == m) continue; int u = mt() % n; int v = mt() % n; if (u == v) continue; int pos = mt() % (ans.size() + 1); ans.insert(ans.begin() + pos, Entry{u,v}); long score = calc_score(ans, a, b); double ratio = std::exp((score - best_score) / temp); double dice = uniform(mt); if (dice < ratio) { /* std::cerr << "insert (" << u << ", " << v << ")" << " at " << pos << std::endl; */ /* std::cerr << "score: " << best_score << " -> " << score << std::endl; */ best_score = score; } else { ans.erase(ans.begin() + pos); } } // remove a random entry if (r == 1) { if (ans.size() == 0) continue; int pos = mt() % ans.size(); auto [u,v] = ans[pos]; ans.erase(ans.begin() + pos); long score = calc_score(ans, a, b); double ratio = std::exp((score - best_score) / temp); double dice = uniform(mt); if (dice < ratio) { /* std::cerr << "Delete (" << u << ", " << v << ")" << " at " << pos << std::endl; */ /* std::cerr << "score: " << best_score << " -> " << score << std::endl; */ best_score = score; } else { ans.insert(ans.begin() + pos, Entry{u,v}); } } // replace an entry with random value /* if (r == _) { */ /* if (ans.size() == 0) continue; */ /* int pos = mt() % ans.size(); */ /* int new_u = mt() % n; */ /* int new_v = mt() % n; */ /* auto [u,v] = ans[pos]; */ /* ans[pos] = Entry{new_u, new_v}; */ /* long score = calc_score(ans, a, b); */ /* double ratio = std::exp((score - best_score) / temp); */ /* double dice = uniform(mt); */ /* if (dice < ratio) { */ /* best_score = score; */ /* } */ /* else { */ /* ans[pos] = Entry{u,v}; */ /* } */ /* } */ // swap random two entries /* if (r == _) { */ /* if (ans.size() == 0) continue; */ /* auto i = mt() % ans.size(); */ /* auto j = mt() % ans.size(); */ /* if (i == j) continue; */ /* std::swap(ans[i], ans[j]); */ /* long score = calc_score(ans, a, b); */ /* double ratio = std::exp((score - best_score) / temp); */ /* double dice = uniform(mt); */ /* if (dice < ratio) { */ /* best_score = score; */ /* } */ /* else { */ /* std::swap(ans[i], ans[j]); */ /* } */ /* } */ } } int main() { std::cin >> n; a.resize(n); b.resize(n); for (int i = 0; i < n; i++) { std::cin >> a[i] >> b[i]; } auto ans = greedy_iter_two_swap(n); std::cerr << "-----------------" << std::endl; std::cerr << "greedy: "; debug_print_ans(ans); std::cerr << "-----------------" << std::endl; annealing(ans); std::cerr << "annealing: "; debug_print_ans(ans); std::cerr << "-----------------" << std::endl; std::cerr << "Final score: " << calc_score(ans, a, b) << std::endl; print_ans(ans); }