/* #region Head */ // #include #include #include #include #include // assert.h #include // math.h #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using ll = long long; using ull = unsigned long long; using ld = long double; using pll = pair; template using vc = vector; template using vvc = vc>; using vll = vc; using vvll = vvc; using vld = vc; using vvld = vvc; using vs = vc; using vvs = vvc; template using um = unordered_map; template using pq = priority_queue; template using pqa = priority_queue, greater>; template using us = unordered_set; #define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i)) #define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i)) #define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i)) #define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d)) #define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d)) #define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i)) #define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i)) #define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i)) #define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d)) #define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d)) #define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++) #define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++) #define ALL(x) begin(x), end(x) #define SIZE(x) ((ll)(x).size()) #define ISIZE(x) ((int)(x).size()) #define PERM(c) \ sort(ALL(c)); \ for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c))) #define UNIQ(v) v.erase(unique(ALL(v)), v.end()); #define CEIL(a, b) (((a) + (b)-1) / (b)) #define endl '\n' constexpr ll INF = 1'010'000'000'000'000'017LL; constexpr int IINF = 1'000'000'007LL; constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7 // constexpr ll MOD = 998244353; constexpr ld EPS = 1e-12; constexpr ld PI = 3.14159265358979323846; template istream &operator>>(istream &is, vc &vec) { // vector 入力 for (T &x : vec) is >> x; return is; } template ostream &operator<<(ostream &os, const vc &vec) { // vector 出力 (for dump) os << "{"; REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template ostream &operator>>(ostream &os, const vc &vec) { // vector 出力 (inline) REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " "); return os; } template istream &operator>>(istream &is, array &arr) { // array 入力 REP(i, 0, SIZE(arr)) is >> arr[i]; return is; } template ostream &operator<<(ostream &os, const array &arr) { // array 出力 (for dump) os << "{"; REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", "); os << "}"; return os; } template istream &operator>>(istream &is, pair &pair_var) { // pair 入力 is >> pair_var.first >> pair_var.second; return is; } template ostream &operator<<(ostream &os, const pair &pair_var) { // pair 出力 os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map, um, set, us 出力 template ostream &out_iter(ostream &os, const T &map_var) { os << "{"; REPI(itr, map_var) { os << *itr; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } return os << "}"; } template ostream &operator<<(ostream &os, const map &map_var) { return out_iter(os, map_var); } template ostream &operator<<(ostream &os, const um &map_var) { os << "{"; REPI(itr, map_var) { auto [key, value] = *itr; os << "(" << key << ", " << value << ")"; auto itrcp = itr; if (++itrcp != map_var.end()) os << ", "; } os << "}"; return os; } template ostream &operator<<(ostream &os, const set &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const us &set_var) { return out_iter(os, set_var); } template ostream &operator<<(ostream &os, const pq &pq_var) { pq pq_cp(pq_var); os << "{"; if (!pq_cp.empty()) { os << pq_cp.top(), pq_cp.pop(); while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop(); } return os << "}"; } // tuple 出力 template ostream &operator<<(ostream &os, tuple &a) { if constexpr (N < std::tuple_size_v>) { os << get(a); if constexpr (N + 1 < std::tuple_size_v>) { os << ' '; } else if constexpr (end_line) { os << '\n'; } return operator<< (os, a); } return os; } template void print_tuple(tuple &a) { operator<< <0, true>(std::cout, a); } void pprint() { std::cout << endl; } template void pprint(Head &&head, Tail &&...tail) { std::cout << head; if (sizeof...(Tail) > 0) std::cout << ' '; pprint(move(tail)...); } // dump #define DUMPOUT cerr void dump_func() { DUMPOUT << endl; } template void dump_func(Head &&head, Tail &&...tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(move(tail)...); } // chmax (更新「される」かもしれない値が前) template > bool chmax(T &xmax, const U &x, Comp comp = {}) { if (comp(xmax, x)) { xmax = x; return true; } return false; } // chmin (更新「される」かもしれない値が前) template > bool chmin(T &xmin, const U &x, Comp comp = {}) { if (comp(x, xmin)) { xmin = x; return true; } return false; } // ローカル用 #ifndef ONLINE_JUDGE #define DEBUG_ #endif #ifndef MYLOCAL #undef DEBUG_ #endif #ifdef DEBUG_ #define DEB #define dump(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define dump(...) #endif #define VAR(type, ...) \ type __VA_ARGS__; \ assert((std::cin >> __VA_ARGS__)); template istream &operator,(istream &is, T &rhs) { return is >> rhs; } template ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; } struct AtCoderInitialize { static constexpr int IOS_PREC = 15; static constexpr bool AUTOFLUSH = false; AtCoderInitialize() { ios_base::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr); std::cout << fixed << setprecision(IOS_PREC); if (AUTOFLUSH) std::cout << unitbuf; } } ATCODER_INITIALIZE; void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; } void YN(bool p) { std::cout << (p ? "YES" : "NO") << endl; } template constexpr void operator--(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]--; } template constexpr void operator++(vc &v, int) noexcept { for (int i = 0; i < ISIZE(v); ++i) v[i]++; } /* #endregion */ // #include // using namespace atcoder; constexpr int N = 45; constexpr ll TARGET = 5'00'000'000'000'000'000; /* #region Timer */ #include struct Timer { using clk = chrono::system_clock; clk::time_point start_time; int64_t timespan_microsecs; int64_t elapsed_microsecs; // コンストラクタ Timer(int64_t timespan_microsecs) : start_time(clk::now()), timespan_microsecs(timespan_microsecs), elapsed_microsecs(0) {} // 時間切れかどうかを返す inline bool is_runnable() noexcept { clk::time_point cur_time = clk::now(); elapsed_microsecs = chrono::duration_cast(cur_time - start_time).count(); return elapsed_microsecs < timespan_microsecs; } }; /* #endregion */ /* #region State */ struct State { vc history; array a; // 表 array b; // 裏 ll score; // 差の絶対値のうち大きい方が loss short zero_cnt; State(const array &a, const array &b) : history(0), a(a), b(b), score(-max(abs(a[0] - TARGET), abs(b[0] - TARGET))), zero_cnt(0) { subtract_dist(); } bool operator<(const State &another) const noexcept { return score < another.score; } bool operator>(const State &another) const noexcept { return score > another.score; } bool operator==(const State &another) const noexcept { return history == another.history; } friend ostream &operator<<(ostream &os, const State &x) noexcept { os << "[State score=" << x.score << ", history={"; for (auto const h : x.history) os << h << ", "; os << "}]"; return os; } void subtract_dist() { ll sum = 0; TREP(int, i, 1, N) { sum += abs(a[i] - TARGET); sum += abs(b[i] - TARGET); } score -= sum / (N * 20); } void add_history(const short x) noexcept { history.push_back(x); const short idx0 = x / 100; const short idx1 = x % 100; ll aval = (a[idx0] + a[idx1]) / 2; ll bval = (b[idx0] + b[idx1]) / 2; a[idx0] = aval; a[idx1] = aval; b[idx0] = bval; b[idx1] = bval; if (idx0 == 0 || idx1 == 0) { score = -max(abs(a[0] - TARGET), abs(b[0] - TARGET)); subtract_dist(); zero_cnt++; } } void print_history() const { pprint(SIZE(history)); for (const short &x : history) { const short idx0 = x / 100; const short idx1 = x % 100; pprint(idx0 + 1, idx1 + 1); } } }; /* #endregion */ /* #region hash */ template inline void hash_combine(std::size_t &s, const T &v) { std::hash h; s ^= h(v) + 0x9e3779b9 + (s << 6) + (s >> 2); } namespace std { template <> struct hash { std::size_t operator()(const State &state) const { std::size_t result = 0; for (auto const h : state.history) hash_combine(result, h); hash_combine(result, state.score); return result; } }; } // namespace std /* #endregion */ /* #region ChokudaiSearch */ // chokudaiサーチ // 時間管理もここで行う! State chokudai_search(int T, State first_state, Timer timer) noexcept { vc> vpq_states(T + 1); vc> vus_states(T + 1); // ターンごとに重複管理する場合 vpq_states[0].push(first_state); // 0 手目に first_state を入れる vus_states[0].insert(first_state); int choku = 10; // chokudai幅 int save = 100; // queueに残す状態の数 State best_state = first_state; int cnt = 0; while (timer.is_runnable()) { // 時間いっぱいまで探索する cnt++; REP(turn, 0, T) { // T ターン分まわす { // turn 手目の状態群から save 個まで残して、あとは捨てる pq pq_tmp; REP(i, 0, save) { if (SIZE(vpq_states[turn]) == 0) break; pq_tmp.push(vpq_states[turn].top()); vpq_states[turn].pop(); } vpq_states[turn] = move(pq_tmp); } // turn 手目の状態群から choku 個取り出して遷移をとる REP(i, 0, choku) { if (SIZE(vpq_states[turn]) == 0) break; // queue が空なら次のターンに const State &cur_state = vpq_states[turn].top(); // vpq_states[turn] から1個とる // cur_state の近傍をとって vpq_states[turn+1] に入れていく TREP(short, idx0, 0, N - 1) TREP(short, idx1, idx0 + 1, N) { const short k = idx0 * 100 + idx1; State next_state = cur_state; next_state.add_history(k); vpq_states[turn + 1].push(next_state); if (next_state > best_state) { best_state = next_state; } } vpq_states[turn].pop(); } // end of chokudai width if (not timer.is_runnable()) break; } } // dump(cnt); // vpq_states の一番後ろのキューから一番スコアの高いものを抜き出して返す // State best_state = vpq_states[T].top(); return best_state; } /* #endregion */ // Problem void solve() { Timer timer(950 * 1000); VAR(ll, _n); array a, b; REP(i, 0, N) cin >> a[i], b[i]; // // サンプル: score_sum: 14,119,672, score_avg: 282,393.44 // { // State tmp_state(a, b); // for (int i = 1; i <= N - 1; i++) { // tmp_state.add_history(i); // } // // dump(-(ld)tmp_state.score / TARGET); // // dump(tmp_state.a[0], tmp_state.b[0]); // // tmp_state.print_history(); // // return; // if (tmp_state > best_state) { // best_state = tmp_state; // } // } // score_sum: 25,117,812, score_avg: 502,356.24 // 50回以内 // → 最大深さが決まっているので chokudai サーチする? State first_state(a, b); State best_state = chokudai_search(50, first_state, timer); // dump(-(ld)best_state.score / TARGET); best_state.print_history(); // dump(best_state.a[0], best_state.b[0]); } // entry point int main() { solve(); return 0; }